Complete User's Guide & Function Reference — everything you need to operate the SC-991BF scientific calculator emulator, with every example result computed by the calculator engine.
eBidyaloy · Model SC-991BF · Scientific Calculator Emulator
The eBidyaloy SC-991BF is an on-screen scientific calculator emulator for classrooms and study — available on Windows, macOS, Web, Android and iOS. It reproduces a modern ClassWiz-style scientific calculator: a natural “textbook” display, 13 calculator apps, physical constants, unit conversions, and a live step-by-step explainer for teaching.
Throughout this guide, every worked Example shows the expression, the calculator display, and the exact key operation. All results are produced by the actual SC-991BF calculation engine, so what you read here is what the emulator computes.
How to read the key operations
Key presses are shown as chips, e.g. 7×8EXE. A key’s SHIFT function (orange label above the key) is written SHIFT then the key; a VARIABLE letter (gold) is entered from the VARIABLE menu.
Keys & Key Markings
The FaceplateZones
The SC-991BF keypad is arranged in the same zones as a modern scientific calculator: a title strip, the LCD, a control cluster, five soft keys, two scientific rows, and the number pad.
eBidyaloy
SC-991BF
−100%+⧉✕
Math DEG
▏
0
ON
⌂
⚙
↺
▲▼◀▶OK
⇳MODE
⤒
⤓
SHIFT
VARIABLE
FUNCTION
CATALOG
TOOLS
x
▢¾▢∕▢
∛▢√▢
▢³▢²
▢√▢▢^
10ˣlog
eˣln
QRAns
sin⁻¹sin
cos⁻¹cos
tan⁻¹tan
%(
,)
π7
e8
i9
INSDEL
OFFAC
4A
5B
6C
nPr×
nCr÷
1D
2E
3F
°’”+
(−)−
0x
.y
×10ˣz
FORMAT⇄
≈EXE
Key Markings — three functions per key
Most keys have up to three functions:
7 Primary — printed on the key; press it directly.
π SHIFT — the orange label above the key; press SHIFT first, then the key.
A VARIABLE — the gold letter; entered from the VARIABLE menu.
For example, SHIFT7 inputs π, and SHIFTsin inputs sin⁻¹.
Control Cluster
Key
Function
ON
Turns the calculator on and clears the current entry (AC also clears).
⌂ HOME
Opens the HOME screen — the menu of all calculator apps.
⚙ SETTINGS
Opens the SETTINGS menu (Calc Settings and Reset).
↺ Back
Deletes the character before the cursor, or steps back one menu level.
▲ ▼ ◀ ▶
Cursor keys — move the entry cursor, or move the highlight in menus and tables.
OK
Executes the calculation or selects the highlighted menu item (same as EXE).
⤒ ⤓
Page keys — jump to the top / bottom of a long result, menu, table or list.
Soft Keys
Soft key
Opens
SHIFT
Selects the alternate (orange) function printed above the next key you press.
VARIABLE
The variable menu — recall or store the memories A, B, C, D, E, F, x, y, z and M (M also has M+ / M−).
FUNCTION
A function menu for the current app (e.g. Abs, arg, Conjg, ReP, ImP for complex work).
CATALOG
The CATALOG of commands and functions, plus CONST ▸ (physical constants) and CONV ▸ (unit conversions).
TOOLS
App tools for the current screen. In Calculate it holds Undo / Redo for the last editing change; in the data apps (Statistics, Table, Distribution) it holds the row tools Insert Row / Delete Row / Delete All (Statistics adds Sort Ascending / Descending); in Spreadsheet it holds Fill / Copy / Grab and the display options. Result conversions (S⇔D, recurring decimal, ° ’ ”, improper fraction) live on the ⇄ (FORMAT) key and in the CATALOG.
Scientific Keys
Key
SHIFT
Function
x
—
Inserts the variable x.
▢∕▢
▢¾
Fraction template a⁄b. SHIFT inserts a mixed-number template.
√▢
∛▢
Square root. SHIFT inserts a cube root.
▢²
▢³
Square (x²). SHIFT cube (x³).
▢^
▢√▢
Power xʸ. SHIFT the x-th root of a value.
log
10ˣ
Common logarithm (base 10). SHIFT raises 10 to a power.
ln
eˣ
Natural logarithm (base e). SHIFT raises e to a power.
Ans
QR
Inserts the previous answer. SHIFT shares the current calculation as a QR code and link.
sin
sin⁻¹
Sine. SHIFT arcsine (inverse).
cos
cos⁻¹
Cosine. SHIFT arccosine (inverse).
tan
tan⁻¹
Tangent. SHIFT arctangent (inverse).
(
%
Open parenthesis. SHIFT the percent operator.
)
,
Close parenthesis. SHIFT a comma (argument separator).
Number Pad
Key
SHIFT
VARIABLE
Function
7 8 9
π e i
—
Digits. SHIFT: 7→π, 8→e, 9→i (imaginary unit).
4 5 6
—
A B C
Digits, or recall variables A / B / C via VARIABLE.
1 2 3
—
D E F
Digits, or recall variables D / E / F via VARIABLE.
0 .
—
x y
Digit / decimal point, or variables x / y.
DEL
INS
—
Deletes the item left of the cursor. SHIFT (INS) arms the next function key (√, ∛, sin, cos, tan, ln, log) to wrap the value to the right of the cursor as its argument — e.g. cursor left of 30, INS, then √ gives √(30).
Subtract. SHIFT the negative sign for a signed value.
×10ˣ
—
z
Enters a power-of-ten exponent (scientific entry). Inserts a compact ᴇ mark or a ×10^ power expression depending on the ×10 Key setting. VARIABLE: z.
⇄ (FORMAT)
—
—
S⇔D: toggles the result between decimal and exact (fraction / √ / π) form. Opens the FORMAT menu when set to do so.
EXE
≈
—
Executes the calculation. SHIFT forces a decimal (≈) result.
Menu-Operation Shorthand
To keep instructions short, this guide writes menu paths in a compact form. For example:
⚙ − [Calc Settings] > [Angle Unit] > [Degree]
…is the same as the full operation:
1. Press ⚙. 2. Use ▲▼ to select [Calc Settings], then press OK. 3. Select [Angle Unit], then press OK. 4. Select [Degree], then press OK.
Note
Where a menu item shows an option number to its left, you can also press that number key to jump straight to the item — see Using Menus.
Entering & Editing Calculations
Entering a CalculationNatural textbook input
The SC-991BF uses natural textbook input (MathI): fractions, roots, powers and other expressions appear on screen just as they are written on paper. You type an expression from left to right and press EXE to evaluate it. (By default results are shown in their exact “Standard” form — a fraction, surd or π; press ⇄ to switch to the decimal, or see Input/Output in SETTINGS to show decimals first.)
Keys such as ▢∕▢ (fraction), √▢ (root) and ▢^ (power) insert an empty template with boxes to fill. Type into the highlighted box, and press ▶ to move out of it and continue the calculation.
Example 1To enter 1½ + √4
SHIFT▢∕▢1, 1, 2▶+√▢4▶EXE
Math DEG
1½ + √4
3.5
The mixed-number template SHIFT▢∕▢ creates three boxes (whole, numerator, denominator); ▶ steps out of the root before EXE. The result 1.5 + 2 = 3.5 is shown.
Editing a CalculationCursor, insert & delete
Moving the cursor
Use the arrow keys to move the flashing cursor through an expression without erasing anything:
Key
Movement
◀▶
Move left / right one item along the current line.
▲▼
Move between levels of a template — for example up into the numerator of a fraction or down into the denominator.
Deleting and inserting
To correct a mistake, move the cursor to the spot and use:
Key
Action
DEL
Delete the item immediately to the left of the cursor.
SHIFTDEL (INS)
Use the value to the right as an argument. Arms the next function key so it wraps the value immediately right of the cursor — see below.
AC
Clear the whole expression and start again.
Example 2To fix 7 × 9 typed as 7 × 8
◀DEL9EXE
Math DEG
7 × 9
63
With the cursor after the 8, press DEL to remove it, type 9, then EXE. Only the wrong digit is changed — the rest of the expression is untouched.
Using INS — wrap a value into a function
Sometimes you have already typed a value and then realise it should sit inside a function — for example you typed 30 but wanted √30. Instead of deleting and retyping, place the cursor to the left of the value, press SHIFTDEL (INS) to arm it, then press the function key. The function is inserted and the value to its right is pulled into the function's argument automatically.
INS arms these function keys: √▢ (and ∛), sin, cos, tan (and their inverses), ln and log. The value it grabs is the next number, the next parenthesised group, or the next single template (fraction, root, variable…).
Example 3To turn 30 into √30 without retyping
cursor left of 30SHIFTDEL (INS)√▢
Math DEG
√30
5.477225575
With the cursor before the 3, SHIFTDEL arms INS; pressing √▢ inserts the radical and wraps 30 inside it, giving √30. Without arming, √▢ would insert an empty √▢ before the 30 instead.
Note
INS is a one-shot arm: it applies only to the very next function key you press, then clears. It has no effect on SHIFT that does not insert a wrapping function.
Correcting after a result
After you press EXE and see a result, you have two choices:
Begin a new calculation — just start typing, and the previous entry is cleared.
Edit the previous entry — press ◀ or ▶ to bring the expression back with the cursor in it, change what you need, and press EXE again.
When a calculation has an error
If you press EXE on an expression the calculator cannot evaluate, it shows an error message — most often Syntax ERROR or Math ERROR, sometimes a more specific name (see Error Messages in the appendix) — and returns you to the expression with the cursor placed at the point that caused the error — not at the end of the line. You can start fixing straight away without hunting for the fault. For example, an unmatched bracket or a stray operator leaves the cursor exactly where the parser stopped; a Math ERROR such as division by zero leaves it on the offending term.
Example 4The cursor lands on the error
enter 5 + × 2EXE→cursor sits on the ×
Math DEG
5 + × 2
Syntax ERROR
The doubled operator + × is invalid; EXE reports Syntax ERROR and drops the cursor on the ×. Press DEL to remove it and continue — you never have to retype the line.
Calculation HistoryRecall & replay
The calculator keeps your last 30 calculations. From a result, press ▲ to step back through previous entries and ▼ to step forward. A recalled entry can be re-used in two ways:
Press EXE to re-run the recalled calculation as it is.
Move the cursor into it, edit the expression, then press EXE to evaluate the changed version.
Example 5To recall and re-run a previous calculation
at a result→▲browse →EXEre-run
Math DEG
7 × 8 − 4 × 5
36
Pressing ▲ brings back an earlier entry such as 7 × 8 − 4 × 5; EXE evaluates it again. Editing it first lets you try a variation without retyping the whole line.
Important!
Calculation history is cleared when you switch to a different app or reset the calculator. Use a variable (Store into A–F, x, y, z, M) to keep a value you will need after leaving the app.
Reusing the last answer with Ans
The result of the most recent calculation is held in Ans. Start a new calculation with an operator (for example + or ×) and the calculator inserts Ans automatically, or press Ans to use it anywhere in an expression.
Example 6To chain calculations with Ans
1000− 200EXE→×2EXE
Math DEG
Ans × 2
1600
After 1000 − 200 = 800, pressing × 2 continues from that answer: Ans × 2 = 1600. This lets you build up a long calculation one step at a time.
Using Menus & Settings
Using MenusNavigation
Many operations use menu screens. Press ⚙ while using a calculator app to open the SETTINGS menu shown below. Each item with a ▸ opens a further menu.
❶Calc Settings▸
❷Reset▸
Two ways to select an item:
Method 1 — use ▲▼ to move the highlight, then press OK.
Method 2 — press the number key shown to the left of the item (its option number). For example, press 2 to open Reset directly.
Press ↺ to step back one level, or AC to leave the menu.
Note
Option numbers (❶ ❷ ❸ …) let you jump to an item even before its menu is showing. Pressing ⚙ on the HOME screen opens Get Started instead of SETTINGS.
Using the SETTINGS MenuCalc Settings & Reset
The SETTINGS menu has two groups: Calc Settings (how calculations behave and display) and Reset. Drill in with OK; each setting shows a numbered list of options to choose from.
Calc Settings
❶Input/Output▸
❷Angle Unit▸
❸Number Format▸
❹Fraction Result▸
Angle Unit
❶Degree
❷Radian
❸Gradian
Calc Settings
Setting
Options
What it does
Input/Output
MathI/MathO · MathI/DecimalO
Natural textbook entry either way (fractions, roots and powers appear in two-dimensional form). MathO (the default) shows a result in its exact “Standard” form first — a fraction, a surd or π — and the ⇄ (S⇔D) key switches to the decimal value. DecimalO shows the decimal first instead, with ⇄ switching to the exact form. (Fix/Sci number formats always show a decimal.)
Angle Unit
Degree · Radian · Gradian
The angle unit used by trigonometric functions and their results.
Number Format
Norm 1 · Norm 2 · Fix 0–9 · Sci 1–10
How results are shown. Norm (the default is Norm 2) shows a decimal result to at most 6 decimal places, trimming trailing zeros, and switches to exponential form outside a range (Norm 1 switches sooner). Fix fixes the number of decimal places (0–9 — choose Fix 7–9 to show more than six); Sci fixes the number of significant figures.
Fraction Result
Improp Fraction · Mixed Number
Whether a fractional answer shows as an improper fraction (7⁄3) or a mixed number (2 1⁄3).
Complex Result
a+bi · r∠θ
Whether a complex answer shows in rectangular (a + bi) or polar (r∠θ) form.
FORMAT Key
Decimal · Format Menu
What the ⇄ FORMAT key does — toggle straight to decimal, or open the FORMAT menu of display options.
×10 Key
Sci-Notation · Power
What the ×10ˣ key inserts — a compact ᴇ exponent mark (3ᴇ5) or a written-out ×10^ power expression (3×10⁵). Both evaluate the same.
Digit Separator
On · Off
Thousands grouping in results, e.g. 1,234,567.
Decimal Mark
Dot · Comma
The decimal character and matching grouping: 1,234.5 (Dot) or 1.234,5 (Comma).
Example — set the angle unit to Degree:⚙ − [Calc Settings] > [Angle Unit] > [Degree]. Trigonometric calculations now use degrees.
Reset
Reset item
What it does
Settings & Data
Returns all settings to their defaults and clears app data.
Variable Memory
Clears the variables A, B, C, D, E, F, x, y, z and M.
Initialize All
Resets everything — settings, memory and data.
Note
A reset cannot be undone. Settings & Data and Initialize All clear your work, so use them deliberately.
Using CATALOG, FUNCTION & TOOLS
Advanced-Command Soft KeysCATALOG · FUNCTION · TOOLS
Three soft keys along the top of the keypad — CATALOG, FUNCTION and TOOLS — open on-screen menus that reach the calculator's advanced commands without dedicated keys. What each menu offers depends on the app you are in, so the same key does the right thing in Calculate, Complex, Spreadsheet and the rest. This chapter explains all three, with worked examples.
Note
Every result below is produced by the actual SC-991BF engine. Menu tags in the key path (grey pills such as [SOLVE]) are the item you highlight and insert with OK.
The CATALOG MenuCommands, functions & symbols
Press CATALOG to open a scrollable list of the commands, functions and symbols available in the current app. Move the highlight with ▲▼, press OK to insert (or run) the selected item, and press ↺ to close without inserting.
CATALOG
d/dx( derivative
∫( integral
Σ( summation
GCD( LCM(
CONST ▸▸
CONV ▸▸
Most items are inserted into your calculation with the caret placed ready for the first argument. A few — the special commands such as SOLVE, CALC, FACT, ENG and VERIFY — act on what is already there instead of being inserted. Two items open sub-menus: CONST ▸ (physical constants) and CONV ▸ (unit conversions).
Note
On the SC-991BF the CATALOG is one combined list. The groups in the table below are a reading aid — on-screen you simply scroll a single list.
CATALOG list
Group
Commands available from CATALOG
Function Analysis
d/dx( derivative · ∫( integral · Σ( summation · Π( product · log▢(▢) log to any base · x⁻¹ reciprocal · x! factorial
Defined functions
f(▢) evaluate f(x) · g(▢) evaluate g(x) — the functions you register in the Table app (see the Table chapter)
Numeric
GCD( · LCM( · RanInt#( random integer · Ran# random number · Pol( rectangular→polar · Rec( polar→rectangular · Int / Frac / Intg / Rnd
Hyperbolic
sinh · cosh · tanh · sinh⁻¹ · cosh⁻¹ · tanh⁻¹
Special commands
SOLVE f(x)=0 · CALC evaluate with variables · FACT prime factorise · ENG / ENG→ engineering form · RECUR recurring decimal (output) · ▨̄ input recurring (type 0.3̄) · VERIFY test a relation
Symbols
: multi-statement · → store to variable · =, ≠, <, >, ≤, ≥ relations · ° ʳ ᵍ angle units
These build a calculus or algebra template with empty boxes; type into each box and move between them with ▶ or the D-pad, then press EXE.
Example 1log to any base — log₂ 32
CATALOGlog▢(▢)2▶32EXE
Math DEG
log₂ 32
5
Enter the base in the small box, the number in the large box: log₂ 32 = 5, because 2⁵ = 32.
Example 2Reciprocal — 4⁻¹
4CATALOGx⁻¹EXE
Math DEG
4⁻¹
0.25
x⁻¹ appends the reciprocal power to the value on the line: 4⁻¹ = 1 ÷ 4 = 0.25.
Example 3Factorial — 5!
5CATALOGx!EXE
Math DEG
5!
120
x! multiplies every whole number down to 1: 5! = 5·4·3·2·1 = 120.
Example 4Derivative — d/dx(x²) at x = 3
CATALOGd/dx(x²▶3EXE
Math DEG
d/dx (x²)|₃
6
The numerical derivative evaluates the slope of x² at x = 3, which is 2x = 6.
Example 5Integral — ∫ x² dx from 0 to 1
CATALOG∫(x²▶0▶1EXE
Math DEG
∫₀¹ x² dx
0.3333333333
The definite integral is the area under x² between 0 and 1: 1⁄3 ≈ 0.3333.
Example 6Summation — Σ x for x = 1 to 10
CATALOGΣ(x▶1▶10EXE
Math DEG
Σ x (1→10)
55
Σ adds the expression as x runs over the range: 1 + 2 + … + 10 = 55.
Example 7Product — Π x for x = 1 to 5
CATALOGΠ(x▶1▶5EXE
Math DEG
Π x (1→5)
120
Π multiplies instead of adds: 1·2·3·4·5 = 5! = 120.
Numeric commands
Example 8Greatest common divisor — GCD(1071, 462)
CATALOGGCD(1071,462)EXE
Math DEG
GCD(1071, 462)
21
The greatest common divisor of 1071 and 462 is 21.
Example 9Least common multiple — LCM(4, 18)
CATALOGLCM(4,18)EXE
Math DEG
LCM(4, 18)
36
The least common multiple of 4 and 18 is 36.
Example 10Random integer — RanInt#(1, 6) (a dice roll)
CATALOGRanInt#(1,6)EXE
Math DEG
RanInt#(1, 6)
4
Each press returns a fresh whole number between 1 and 6 — your value will differ. Ran# (no arguments) instead gives a random decimal in [0, 1).
Example 11Rectangular → polar — Pol(3, 4)
CATALOGPol(3,4)EXE
Math DEG
Pol(3, 4)
r = 5, θ = 53.13°
The point (3, 4) has magnitude r = 5 and angle θ = 53.13° (Degree mode). The pair is stored to x (= r) and y (= θ).
Example 12Polar → rectangular — Rec(2, 60°)
CATALOGRec(2,60)EXE
Math DEG
Rec(2, 60)
x = 1, y = 1.732
The polar point r = 2, θ = 60° becomes (1, 1.732); the pair is stored to x and y.
Example 13Int, Frac & Intg — the parts of −3.5
CATALOGInt−3.5)EXE
Math DEG
Int(−3.5) Frac(−3.5) Intg(−3.5)
−3 −0.5 −4
Int truncates toward zero (−3), Frac keeps the fractional part (−0.5), Intg takes the floor — the largest integer not above the value (−4).
Hyperbolic functions
Example 14sinh 1
CATALOGsinh1)EXE
Math DEG
sinh 1
1.1752011936
sinh 1 = (e − e⁻¹) / 2 ≈ 1.1752. cosh, tanh and their inverses are on the same menu.
Special commands (they act, not insert)
These CATALOG entries operate on the expression or result already on screen rather than inserting a template.
Example 15SOLVE — a root of x² − 4 = 0
x▢²−4CATALOGSOLVEEXE
Math DEG
x² − 4 = 0
x = 2
SOLVE applies Newton's method from the stored value of x and finds the nearby root x = 2, storing it back into x.
Example 16CALC — evaluate 2A + B with A = 3, B = 4
2VARIABLEA+VARIABLEBCATALOGCALC
Math DEG
2A + B
10
CALC keeps the expression and prompts for each variable it contains — enter A = 3 then B = 4 — then evaluates 2·3 + 4 = 10. Press EXE on the result to re-enter values.
Example 17FACT — prime-factorise 1080
1080EXECATALOGFACT
Math DEG
1080
2³ × 3³ × 5
FACT rewrites a whole-number result as its prime factors: 1080 = 2³ × 3³ × 5.
Example 18ENG — engineering notation for 12345
12345EXECATALOGENG
Math DEG
12345
12.345 × 10³
ENG shifts the exponent to a multiple of three; ◀▶ step it further. ENG→ shows the same value with an SI prefix instead (12.345 k).
Example 19RECUR — the repeating form of 1 ÷ 7
1÷7EXECATALOGRECUR
Math DEG
1 ÷ 7
0.[142857]
RECUR shows the repeating block in brackets: 1 ÷ 7 = 0.[142857] = 0.142857142857…
Example 20VERIFY — is 3 × 4 = 12 ?
3×4CATALOGVERIFY=12EXE
Math DEG
3 × 4 = 12
True
VERIFY tests a relation built with =, ≠, <, >, ≤ or ≥ and reports True or False.
Defining your own functions — f(x) and g(x)
The Table app lets you register two functions f(x) and g(x), but you can also define them right here in Calculate. Type an expression in x, then choose Define f(x) (or Define g(x)) from the CATALOG. The line is stored, and f(▢) / g(▢) become callable from any app — no need to open the Table app. Definitions persist until you overwrite them or reset.
Example 21Define f(x) = 2x + 1, then evaluate f(3)
2x+1CATALOGDefine f(x)→CATALOGf(▢)3)EXE
Math DEG
f(3)
7
Typing 2x + 1 and choosing Define f(x) stores it (the display confirms “f(x) defined”). Then f(▢) with 3 inside gives f(3) = 2·3 + 1 = 7.
Example 22Compose defined functions — g(f(2)), with g(x) = x²
define g(x)=x²CATALOGg(▢)CATALOGf(▢)2))EXE
Math DEG
g(f(2))
25
With f(x) = 2x + 1 and g(x) = x², nesting the calls gives g(f(2)) = g(5) = 5² = 25. A definition may call the other function; a self-referential loop is caught and stopped with a Stack ERROR.
CONST — physical constants (CATALOG → CONST ▸)
CONST ▸ opens a menu of scientific constants (CODATA-2022) in six categories. Choose a category, then a constant, to insert its value into your calculation.
CONST
❶Universal▸
❷Electromagnetic▸
❸Atomic & Nuclear▸
❹Physico-Chem▸
For example, inserting c (speed of light) inserts 299 792 458. The complete list is in the Constants & Conversions reference chapter.
CONV — unit conversions (CATALOG → CONV ▸)
CONV ▸ applies a unit conversion to the value on the display. First compute a value, then choose a category and a conversion; the result is replaced by the converted value.
UNIT CONVERT
❶Length▸
❷Area▸
❸Volume▸
❹Mass▸
Conversions cover Length, Area, Volume, Mass, Velocity, Pressure, Energy, Power and Temperature. The full list is in the reference chapter.
The FUNCTION MenuModulus, argument & complex parts
Press FUNCTION to insert the functions that describe a number's size, angle and parts. Abs works on any real or complex value; arg, Conjg, ReP, ImP and the polar operator ∠ are used with complex numbers. Highlight an item, press OK to insert it, and the caret lands inside its parentheses.
FUNCTION
Abs |z|
arg angle
Conjg z̄
ReP real part
ImP imaginary part
∠ polar r∠θ
Abs |z| — magnitude · arg — angle · Conjg z̄ — sign-flip the imaginary part · ReP / ImP — real / imaginary part · ∠ — enter a number in polar form r∠θ.
Example 23Abs — the absolute value |2 − 7|
FUNCTIONAbs2−7)EXE
Math DEG
|2 − 7|
5
Absolute value strips the sign: |−5| = 5. On a real number Abs is just its distance from zero.
Example 24Abs — the modulus of a complex number |3 + 4i|
FUNCTIONAbs3+4i)EXE
Math DEG
|3 + 4i|
5
For a complex number Abs is the modulus √(3² + 4²) = 5.
Note
Abs adapts to its argument: a real number → its distance from zero; a complex number → its modulus; a vector → its magnitude |v|; a matrix → a new matrix with the absolute value of every element (see the Matrix chapter).
Example 25arg — the argument of 3 + 4i
FUNCTIONarg3+4i)EXE
Math DEG
arg(3 + 4i)
53.13°
arg returns the angle of the number in the complex plane, in the current Angle Unit: 53.13° in Degree mode.
Example 26Conjg — the conjugate of 3 + 4i
FUNCTIONConjg3+4i)EXE
Math DEG
Conjg(3 + 4i)
3 − 4i
Conjg flips the sign of the imaginary part: 3 + 4i becomes 3 − 4i.
Example 27ReP & ImP — the parts of 3 + 4i
FUNCTIONReP3+4i)EXE
Math DEG
ReP(3+4i) ImP(3+4i)
3 4
ReP returns the real part (3) and ImP the imaginary part (4).
Note
The FUNCTION items are also reachable in the Complex app, where the whole calculation is complex by default. The polar operator ∠ lets you type a number as r∠θ (for example 5∠53.13°).
The TOOLS MenuApp tools for the current screen
Press TOOLS to reach tools for the app you are in. TOOLS is context-sensitive — it holds editing and app operations, not result-format conversions. (Those live on the ⇄ FORMAT key and the CATALOG; see the table below.)
TOOLS in Calculate — Undo / Redo
TOOLS
Undo reverse last edit
Redo re-apply
On the Calculate screen the TOOLS menu holds Undo and Redo. Undo reverses your last editing change to the current expression — a mistaken DEL, a template you did not mean to insert, or a cleared line — and Redo re-applies it. This works on the expression you are editing, before you press EXE.
TOOLS in the data apps — row editing
In the list-based apps, TOOLS edits the data list. In Statistics you can also sort:
App
TOOLS menu offers
Calculate
Undo · Redo — reverse / re-apply the last editing change.
Statistics
Insert Row · Delete Row · Delete All · Sort Ascending · Sort Descending (sorts the highlighted column; a paired x/Freq or x/y list is kept aligned).
Table / Distribution
Insert Row · Delete Row · Delete All (no sort — row order is meaningful).
Spreadsheet
Edit Cell · Fill Formula · Fill Value · Copy & Paste · Cut & Paste · Grab (insert a cell reference) · Show Cell · Auto Calc (on/off) · Recalculate · Delete All.
Equation
Complex Roots — toggle whether roots with a negative discriminant are shown as complex numbers or reported as “No Real Roots”.
Where the result-format conversions live
Conversions such as S⇔D, recurring decimal, engineering form and prime factorisation are not on the TOOLS menu. Reach them here:
To…
Press
Toggle a result between exact ⇄ decimal (S⇔D)
⇄ (FORMAT) after a result
Open the full FORMAT menu — Standard (π √ frac) · Decimal · Prime Factor · Recurring Decimal · Rectangular / Polar Coord · Improper / Mixed Fraction · Standard Form a×10ⁿ · Sexagesimal
SHIFT⇄, or ⇄ when the FORMAT Key setting is “Format Menu”
Engineering form — ENG / ENG→ (with SI symbol)
CATALOG ▸ ENG / ENG→
Verify a relation is true
CATALOG ▸ VERIFY
Note
The Calculate chapter works through each of these conversions with numbered examples.
Calculator Apps
Selecting a Calculator AppHOME screen
Press ⌂ to display the HOME screen — the menu of all installed calculator apps. Use ▲▼◀▶ to move the highlight to an app, then press OK. Alternatively, press the number key shown on an app’s icon (its option number) to open it directly.
eBidyaloy
SC-991BF
−100%+⧉✕
HOME (Scroll to see all apps)▼
=Calculate
ΣStatistics
▦Table
ƒEquation
≶Inequality
∩Distribution
iComplex
⊞Matrix
→Vector
Calculate
ON
⌂
⚙
↺
▲▼◀▶OK
⇳MODE
⤒
⤓
SHIFT
VARIABLE
FUNCTION
CATALOG
TOOLS
x
▢¾▢∕▢
∛▢√▢
▢³▢²
▢√▢▢^
10ˣlog
eˣln
QRAns
sin⁻¹sin
cos⁻¹cos
tan⁻¹tan
%(
,)
π7
e8
i9
INSDEL
OFFAC
4A
5B
6C
nPr×
nCr÷
1D
2E
3F
°’”+
(−)−
0x
.y
×10ˣz
FORMAT⇄
≈EXE
The HOME screen on the SC-991BF — every installed app in a scrollable 3-across grid, the highlighted app (Calculate here) named along the bottom. Move the highlight with ▲▼◀▶ and press OK to open it.
1
×÷
Calculate
2
▁▄█
Statistics
3
▦
Table
4
x=
Equation
5
x>
Inequality
6
◠
Distribution
7
i
Complex
8
[▦]
Matrix
9
→
Vector
10
田
Spreadsheet
11
a:b
Ratio
12
⚄
Math Box
13
0x
Base-N
Note
Each app remembers its own screen, data and CATALOG. Switching apps does not clear another app’s data.
Installed Calculator App List13 apps
App
Description
1
×÷
Calculate
General and scientific calculations — arithmetic, functions, powers, roots, logs, complex numbers and every CATALOG command.
2
▁▄█
Statistics
1- and 2-variable statistics and seven regression models, with a data-entry table and a full set of summary results.
3
▦
Table
Generates a table of values from one or two functions, f(x) and g(x), over a start/end/step range.
4
x=
Equation
Solves simultaneous linear equations (2 to 4 unknowns) and polynomial equations (quadratic, cubic, quartic).
5
x>
Inequality
Solves quadratic, cubic and quartic inequalities and reports the solution intervals.
6
◠
Distribution
Normal, Binomial and Poisson probability — both probability density (PD) and cumulative distribution (CD).
7
i
Complex
Dedicated complex-number arithmetic with rectangular (a + bi) and polar (r∠θ) results.
8
[▦]
Matrix
Matrix arithmetic up to 4×4 — addition, subtraction, multiplication, determinant, inverse and transpose.
9
→
Vector
2D and 3D vector operations — dot product, cross product, magnitude, angle and unit vectors.
10
田
Spreadsheet
A 5-column (A–E) × 45-row spreadsheet with cell formulas, fill/copy tools and range functions (Sum, Min, Max, Mean).
11
a:b
Ratio
Solves proportions of the form a : b = c : x for the unknown term.
12
⚄
Math Box
Probability and learning tools — dice roll, coin toss, number line and circle simulations.
13
0x
Base-N
Binary, octal, decimal and hexadecimal calculations with logic operators (and, or, xor, not).
App Screens at a GlanceEntry screens
When you open an app you see either a calculation screen or a short menu to choose the calculation type. Each app is documented in full — every function with worked examples — in the chapters that follow.
1
×÷
Calculate
App 1
Calculate
General and scientific calculations — arithmetic, functions, powers, roots, logs, complex numbers and every CATALOG command.
Math DEG
0
2
▁▄█
Statistics
App 2
Statistics
1- and 2-variable statistics and seven regression models, with a data-entry table and a full set of summary results.
Statistics
❶1-Variable
❷y=a+bx
❸y=a+bx+cx²
3
▦
Table
App 3
Table
Generates a table of values from one or two functions, f(x) and g(x), over a start/end/step range.
Table
f(x)=
4
x=
Equation
App 4
Equation
Solves simultaneous linear equations (2 to 4 unknowns) and polynomial equations (quadratic, cubic, quartic).
Equation
❶Simult. Equation
❷Polynomial
5
x>
Inequality
App 5
Inequality
Solves quadratic, cubic and quartic inequalities and reports the solution intervals.
Inequality
❶Order 2 (ax²…)
❷Order 3
❸Order 4
6
◠
Distribution
App 6
Distribution
Normal, Binomial and Poisson probability — both probability density (PD) and cumulative distribution (CD).
Distribution
❶Normal PD
❷Normal CD
❸Binomial PD
7
i
Complex
App 7
Complex
Dedicated complex-number arithmetic with rectangular (a + bi) and polar (r∠θ) results.
Math Complex
0
8
[▦]
Matrix
App 8
Matrix
Matrix arithmetic up to 4×4 — addition, subtraction, multiplication, determinant, inverse and transpose.
Matrix
❶Define MatA
❷Define MatB
❸MatA + MatB
9
→
Vector
App 9
Vector
2D and 3D vector operations — dot product, cross product, magnitude, angle and unit vectors.
Vector
❶Define VctA
❷Define VctB
❸VctA · VctB
10
田
Spreadsheet
App 10
Spreadsheet
A 5-column (A–E) × 45-row spreadsheet with cell formulas, fill/copy tools and range functions (Sum, Min, Max, Mean).
Spreadsheet
A1
11
a:b
Ratio
App 11
Ratio
Solves proportions of the form a : b = c : x for the unknown term.
Ratio
❶a:b = c:x
❷a:b = x:d
12
⚄
Math Box
App 12
Math Box
Probability and learning tools — dice roll, coin toss, number line and circle simulations.
Math Box
❶Dice Roll
❷Coin Toss
❸Number Line
13
0x
Base-N
App 13
Base-N
Binary, octal, decimal and hexadecimal calculations with logic operators (and, or, xor, not).
Base-N DEC
0
Extended Display & Explainer
The Extended DisplayPresentation mode
When teaching with the SC-991BF on a large screen, open the extended display with the ⧉ (cast) button in the title bar. A greatly enlarged copy of the calculator’s LCD appears beside the keypad so the whole class can read the current expression and result. The panel is marked LIVE DISPLAY and refreshes automatically as you type.
Use the size controls (−%+) to fit the calculator to any display, and press HIDE to collapse the panel. The extended display always mirrors exactly what is on the calculator’s own screen.
The ExplainerEXPLANATION & STEPS
Below the extended display, the explainer turns any Calculate result into a lesson. It has two tabs:
EXPLANATION — a plain-language walkthrough of what each function and operation does, in order.
STEPS — the working shown as a reduction: the expression is rewritten one step at a time, each line a little more simplified, down to the final answer (shown in green).
Note
The explainer is available in the Calculate app for any expression you evaluate. Both the wording and the step chain are produced by the calculator itself — they always match the actual computation.
Example 1 — roots and arithmetic
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
Math DEG
2×√(2)+3
5.8284271248
EXPLANATIONSTEPS
EXPLANATION
A square root asks: which number, multiplied by itself, gives 2? Since 1.4142135624 × 1.4142135624 = 2, we get √2 = 1.4142135624.
Multiply 2 by 1.4142135624: 2 × 1.4142135624 = 2.8284271248.
Add 2.8284271248 and 3 together: 2.8284271248 + 3 = 5.8284271248.
STEPS
2×√(2)+3
√2 = 1.4142135624
= 2 × 1.4142135624 = 2.8284271248
= 2.8284271248 + 3 = 5.8284271248
Example 2 — trigonometry (Degree)
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
Math DEG
sin(30)+cos(60)
1
EXPLANATIONSTEPS
EXPLANATION
sin gives sine of the angle. Here sin(30°) = 0.5.
cos gives cosine of the angle. Here cos(60°) = 0.5.
Add 0.5 and 0.5 together: 0.5 + 0.5 = 1.
STEPS
sin(30)+cos(60)
sin(30°) = 0.5
= cos(60°) = 0.5
= 0.5 + 0.5 = 1
Example 3 — powers
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
Math DEG
3^2+4^2
25
EXPLANATIONSTEPS
EXPLANATION
Squaring means multiplying a number by itself. So 3² = 3 × 3 = 9.
Squaring means multiplying a number by itself. So 4² = 4 × 4 = 16.
Add 9 and 16 together: 9 + 16 = 25.
STEPS
3^2+4^2
3² = 9
= 4² = 16
= 9 + 16 = 25
Example 4 — logarithms
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
Math DEG
log(1000)+ln(1)
3
EXPLANATIONSTEPS
EXPLANATION
log gives logarithm (base 10). Here log(1,000) = 3.
ln gives natural logarithm (base e). Here ln(1) = 0.
Add 3 and 0 together: 3 + 0 = 3.
STEPS
log(1000)+ln(1)
log(1,000) = 3
= ln(1) = 0
= 3 + 0 = 3
Example 5 — implicit multiplication priority
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
Math DEG
6÷2(1+2)
1
EXPLANATIONSTEPS
EXPLANATION
Divide 6 by 2 — splitting 6 into 2 equal parts: 6 ÷ 2 = 3.
Add 1 and 2 together: 1 + 2 = 3.
Multiply 3 by 3 (writing them side by side means multiply): 3 × 3 = 1.
STEPS
6÷2(1+2)
6 ÷ 2 = 3
= 1 + 2 = 3
= 3 × 3 = 1
Example 6 — order of operations
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
Math DEG
7+3×4−2
17
EXPLANATIONSTEPS
EXPLANATION
Multiply 3 by 4: 3 × 4 = 12.
Add 7 and 12 together: 7 + 12 = 19.
Subtract 2 from 19: 19 − 2 = 17.
STEPS
7+3×4−2
3 × 4 = 12
= 7 + 12 = 19
= 19 − 2 = 17
Sharing Calculations (QR & Link)
Sharing a CalculationQR code & link
Any result on the SC-991BF can be turned into a QR code and a shareable web link. A student scans the code (or opens the link) to see the calculation on a phone or computer — typeset neatly, with the step-by-step working and, where it applies, a graph. It is the fastest way to put a worked example on the board, into a worksheet, or into a chat with a student.
Press SHIFTAns(the orange QR label above the Ans key) to share the calculation currently on screen. A panel shows the QR code and a copyable link.
Sharing works in every app
Sharing is not limited to the Calculate app. Press SHIFTAns on the result screen of any app — Statistics, Equation, Matrix, Vector, Complex, Base-N, Distribution, Inequality, Ratio or Table — and that result is shared with its heading, its answer (matrices and tables included) and its working.
Note
Sharing is anonymous: no login is needed to open a shared link. The shared page is read-only — it shows the calculation but cannot change your calculator.
The Shared PageWhat the link opens
Opening a shared link shows a clean, read-only page with the calculation rendered in proper mathematical notation. Depending on the app, the page can include:
Typeset math — the expression and answer in textbook form (fractions, roots, powers, matrices).
A graph — for Table (the function curve), Statistics (the scatter of points with the fitted regression line) and Distribution (the normal curve or probability bars).
Step by step — the same teaching breakdown the calculator's explainer shows.
Institute name — when shared from a signed-in institute account, the page shows which institute it came from.
Sample shared page (with a graph)
eB
eBidyaloy SC-991BF
Shared calculation
Table · Degree
Function Table f(x) = x²
x
f(x)
−3
9
−2
4
−1
1
0
0
1
1
2
4
3
9
Graph
Step by step
Each row evaluates f(x) = x² at one x value. The points trace a symmetric U-shaped parabola with its vertex at (0, 0).
⏳ Kept for 2 weeks — expires on 30 Jul 2026.
Shared by Dream Model Academy
A shared Table result for f(x) = x². The page shows the value table, the plotted parabola, the step-by-step note, the institute that shared it, and the expiry date. This is exactly what a student sees after scanning the QR code — no app to install.
Important!
Shared calculations are kept on the server for 2 weeks, then they are deleted automatically. The shared page always shows the exact date the link expires. Share a calculation again to get a fresh 2-week link.
Open in calculator
A shared Calculate link also offers “Open in calculator”, which reloads the exact expression back into the SC-991BF so it can be edited and re-run. This needs an eBidyaloy account with the calculator enabled; anyone else can still read the shared page.
Note
Available on Windows, macOS, Web and Android. The shared page opens in any modern browser on any device.
Calculate App Reference
CalculateGeneral & scientific calculation
The Calculate app is the calculator's main workspace. Enter an expression in natural textbook format and press EXE to evaluate it. This chapter covers every function available in Calculate, grouped by type, each with a worked example.
Note
Unless a note says otherwise, examples assume the default settings — Angle Unit: Degree, and MathI/MathO input/output. Under MathO (the default) a result appears in its exact “Standard” form first — a fraction, surd or π; press ⇄ (S⇔D) to switch to its decimal value. Where an example quotes a decimal, that is the ⇄ (decimal) form. Switch Input/Output to DecimalO to show the decimal first instead.
Basic Arithmetic & Priority
Use +−×÷ for the four operations and () to group terms. Calculations follow standard priority: functions and powers first, then × ÷, then + −. An omitted × (implicit multiplication) before a bracket or constant binds tighter than ÷.
Example 1To calculate 7 × 8 − 4 × 5
7×8−4×5EXE
Math DEG
7 × 8 − 4 × 5
36
Multiplication is done before subtraction: 56 − 20 = 36.
Example 2To calculate 6 ÷ 2(1 + 2)
6÷2(1+2)EXE
Math DEG
6 ÷ 2(1 + 2)
1
Implicit multiplication binds tighter than ÷, so this reads 6 ÷ (2 × (1 + 2)) = 6 ÷ 6 = 1.
Fractions
Press ▢∕▢ for a fraction template and SHIFT▢∕▢ for a mixed number. With the default MathO output a result appears as the exact fraction; press ⇄ (FORMAT / S⇔D) to switch to its decimal value (or select DecimalO to show the decimal first).
Example 3To calculate 3⁄4 + 1⁄6
3▢∕▢4▶+1▢∕▢6EXE
Math DEG
3⁄4 + 1⁄6
0.9166666667
The result is shown as the decimal 0.9166666667. Press ⇄ to see it in exact form as the fraction 11⁄12.
Powers & Roots
▢² squares, SHIFT▢² cubes, ▢^ raises to any power, √▢ is a square root, SHIFT√▢ a cube root, and SHIFT▢^ gives the x-th root.
Example 4To calculate 5² + 12²
5▢²+12▢²EXE
Math DEG
5² + 12²
169
25 + 144 = 169. (Its square root, 13, is the hypotenuse of a 5-12-13 triangle.)
Example 5To calculate the 5th root of 32
SHIFT▢^5▶32EXE
Math DEG
⁵√32
2
The x-th root key gives ⁵√32 = 2, because 2⁵ = 32.
Example 6To calculate 4⁻¹ (reciprocal)
4CATALOGx⁻¹EXE
Math DEG
4⁻¹
0.25
The reciprocal x⁻¹ is 1 ÷ x, so 4⁻¹ = 0.25.
Exponential & Logarithmic
log is base-10 log, ln is natural log, SHIFTlog is 10ˣ, SHIFTln is eˣ. Use the CATALOG log▢(▢) for a logarithm to any base.
Example 7To calculate log 1000
log1000)EXE
Math DEG
log 1000
3
log 1000 = 3, because 10³ = 1000.
Example 8To calculate log₂ 32 (log to base 2)
CATALOGlog▢(▢)→ 2, 32 →EXE
Math DEG
log₂ 32
5
Enter the base in the small box: log₂ 32 = 5, because 2⁵ = 32.
Example 9To calculate ln e³ (natural logarithm)
lne▢^3▶)EXE
Math DEG
ln e³
3
ln is the natural logarithm (base e). It undoes eˣ, so ln e³ = 3.
Example 10To calculate e² (eˣ)
SHIFTln2)EXE
Math DEG
e²
7.3890560989
SHIFTln inputs eˣ (e raised to a power): e² ≈ 7.3891.
Trigonometric Functions
sincostan and their inverses (SHIFT + the key) use the current Angle Unit. Append ° ʳ ᵍ (from CATALOG) to give a value in a specific unit regardless of the mode.
Example 11To calculate sin 30° (Degree mode)
sin30)EXE
Math DEG
sin 30°
0.5
In Degree mode sin 30° = 0.5.
Example 12To calculate tan⁻¹ 1 (Degree mode)
SHIFTtan1)EXE
Math DEG
tan⁻¹ 1
45
The inverse tangent of 1 is the angle whose tangent is 1: 45°.
Hyperbolic Functions
The hyperbolic functions sinh, cosh, tanh and their inverses are on the CATALOG menu.
Example 13To calculate sinh 1
CATALOGsinh1)EXE
Math DEG
sinh 1
1.1752011936
sinh 1 = (e − e⁻¹) / 2 ≈ 1.1752.
Percentage
Enter a value followed by SHIFT( (the % operator). A percentage is interpreted as “per hundred”.
Example 14To calculate 150 × 20%
150×20SHIFT(EXE
Math DEG
150 × 20%
30
20% of 150 is 30.
Permutation, Combination & Factorial
SHIFT× is nPr, SHIFT÷ is nCr, and x! (factorial) is on the CATALOG menu.
Example 15To calculate 5 P 2 (permutations)
5SHIFT×2EXE
Math DEG
5 P 2
20
The number of ordered arrangements of 2 from 5 is 20.
Example 16To calculate 8 C 3 (combinations)
8SHIFT÷3EXE
Math DEG
8 C 3
56
The number of unordered selections of 3 from 8 is 56.
Example 17To calculate 5! (factorial)
5CATALOGx!EXE
Math DEG
5!
120
The factorial x! multiplies every whole number down to 1: 5! = 5 × 4 × 3 × 2 × 1 = 120.
Numeric Functions
The CATALOG provides Abs (absolute value), Int (truncate), Frac (fractional part), Intg (floor), Rnd (round to the display) and x⁻¹ (reciprocal).
Example 18To calculate |2 − 7| (absolute value)
FUNCTIONAbs2−7)EXE
Math DEG
|2 − 7|
5
The absolute value strips the sign: |−5| = 5.
Example 19Int, Frac & Intg — the parts of −3.5
CATALOGInt−3.5)EXE
Math DEG
Int(−3.5) Frac(−3.5) Intg(−3.5)
−3 −0.5 −4
Int truncates toward zero (−3), Frac keeps the fractional part (−0.5), and Intg takes the floor — the largest integer not above the value (−4).
Example 20Rnd — round off 2 ÷ 3
CATALOGRnd2÷3)EXE
Math DEG
Rnd(2 ÷ 3)
0.6666666667
Rnd rounds the value to the calculator's 10-digit display precision, discarding the internal guard digits it normally keeps.
GCD, LCM & Random
From the CATALOG: GCD(, LCM(, RanInt#( (a random integer in a range) and Ran# (a random number in [0, 1)).
Example 21To calculate GCD(48, 36)
CATALOGGCD(48, 36 →EXE
Math DEG
GCD(48, 36)
12
The greatest common divisor of 48 and 36 is 12.
Example 22To calculate LCM(6, 8)
CATALOGLCM(6, 8 →EXE
Math DEG
LCM(6, 8)
24
The least common multiple of 6 and 8 is 24.
Example 23RanInt#( — a random integer from 1 to 6 (a dice roll)
CATALOGRanInt#(1, 6)EXE
Math DEG
RanInt#(1, 6)
4
Each press returns a fresh whole number between 1 and 6 — your value will differ. Ran# (no arguments) instead gives a random decimal in [0, 1).
Calculus — Derivative & Integral
The CATALOG offers d/dx (numerical derivative at a point) and ∫dx (definite integral between limits).
Example 24To calculate d/dx(x²) at x = 3
CATALOGd/dx→ x², at 3 →EXE
Math DEG
d/dx (x²)|₃
6
The slope of x² at x = 3 is 2x = 6.
Example 25To calculate ∫ x² dx from 0 to 1
CATALOG∫dx→ x², 0, 1 →EXE
Math DEG
∫₀¹ x² dx
0.3333333333
The area under x² from 0 to 1 is 1⁄3 ≈ 0.3333.
Summation & Product
Σ sums and Π multiplies an expression as a counter runs from a lower to an upper limit.
Example 26To calculate Σ x for x = 1 to 10
CATALOGΣ→ x, 1, 10 →EXE
Math DEG
Σ x (1 → 10)
55
1 + 2 + … + 10 = 55.
Example 27To calculate Π x for x = 1 to 5
CATALOGΠ→ x, 1, 5 →EXE
Math DEG
Π x (1 → 5)
120
1 × 2 × 3 × 4 × 5 = 5! = 120.
SOLVE, CALC & VERIFY
SOLVE finds a root of f(x) = 0 by Newton's method. CALC evaluates an expression after prompting for each variable. VERIFY tests whether a relation (=, ≠, <, >, ≤, ≥) is true.
Example 28SOLVE — a root of x² − 4 = 0
x▢²−4CATALOGSOLVEEXE
Math DEG
x² − 4 = 0
x = 2
SOLVE searches from the stored x and finds the nearby root x = 2.
Note
If SOLVE cannot converge within its iteration limit it shows the best value so far with the prompt Could not converge · OK Continue · AC Exit: press OK to iterate further from that value, or AC to keep the near-solution. (Same behaviour as the Equation app's Solver.)
Example 29CALC — evaluate 2A + B with A = 3, B = 4
2VARIABLEA+VARIABLEBCATALOGCALC
Math DEG
2A + B
10
CALC prompts for A then B, then evaluates 2·3 + 4 = 10.
Example 30VERIFY — is 3 × 4 = 12 ?
3×4CATALOGVERIFY= 12EXE
Math DEG
3 × 4 = 12
True
VERIFY confirms the relation is True.
Coordinate Conversion
Pol( converts rectangular (x, y) to polar (r, θ); Rec( converts polar (r, θ) back to rectangular (x, y). Both are on the CATALOG.
Example 31Pol( — convert (3, 4) to polar
CATALOGPol(3, 4 →EXE
Math DEG
Pol(3, 4)
r = 5, θ = 53.13°
The point (3, 4) has magnitude r = 5 and angle θ = 53.13° (Degree mode).
Example 32Rec( — convert (2, 60°) to rectangular
CATALOGRec(2, 60 →EXE
Math DEG
Rec(2, 60°)
x = 1, y = 1.732
The polar point r = 2, θ = 60° becomes (1, 1.732).
Variables & Independent Memory (M)
The calculator has ten memories — A B C D E F x y z and the independent memory M — that each hold one number. Press VARIABLE to open the menu, highlight a memory with ▲▼ and press OK; a small action menu then appears offering Recall or Store (M additionally offers M+ and M−).
VARIABLE
A
B
C
D
E
F
x
y
z
M
A
Recall
Store
Store evaluates whatever is on the current line — or reuses Ans if the line is empty — and saves the value into the chosen memory, replacing what was there.
Recall inserts the memory's stored value into the calculation you are editing. Recalling straight after a result begins a fresh line.
M+ / M− add or subtract the current value to/from M without overwriting it — ideal for accumulating a running total.
Clear all ten memories at once with ⚙ − [Reset] > [Variable Memory].
To store a value into a memory (for example, save 5 into A):
Type the value — 5 — on the line. (Leave the line empty to store the last answer, Ans, instead.)
Press VARIABLE to open the memory list.
Highlight the memory (A) with ▲▼ and press OK.
Choose Store. The value is now held in A until you overwrite it or reset the memory.
To recall a stored value: press VARIABLE, highlight the memory, press OK, then choose Recall — the stored value drops straight into whatever you are calculating.
Example 33Store 5 into the variable A
5VARIABLEAStore
Math DEG
5
5
The value 5 is now held in A; the display confirms 5. It stays stored until you overwrite it or reset the memory.
Example 34Recall A and calculate A × 3
VARIABLEARecall×3EXE
Math DEG
A × 3
15
Recalling A (= 5) gives 5 × 3 = 15.
Example 35Running total with M+ : 3 × 4 then 5 × 6
3×4VARIABLEMM+5×6VARIABLEMM+
Math DEG
5 × 6
M = 42
Each M+ adds the line's value to M — first 12, then +30. Recall M (VARIABLE ▸ M ▸ Recall) to read the total 42.
Note
M+ / M− act on the current line's value. To add a value into M without displaying it first, type the value then choose VARIABLE ▸ M ▸ M+.
Storing a result from another app
You are not limited to storing from Calculate. On the result screen of the Equation solver, Distribution, Vector, Complex or Matrix app, press VARIABLE and the displayed value is captured; pick a memory (A–F, x, y, z) to store it. This lets you carry a solved root, a probability, a dot product or a determinant straight into a follow-up calculation without copying it down.
Example 36Store an equation root into A, then reuse it
Equation result x = 3VARIABLEAStore
Math DEG
x² − 5x + 6 = 0 → A
3
Solving x² − 5x + 6 = 0 gives x = 3; on the result screen VARIABLE ▸ A stores 3 into A. Back in Calculate, A is now 3 and can be used anywhere. (A matrix result stores into MatA–MatD instead — see the Matrix chapter.)
Note
The value stored is the one on screen. On a list result (Distribution, or simultaneous equations) it stores the highlighted row / first variable; scroll to the value you want before pressing VARIABLE.
Ans, π, e & Constants
Ans reuses the previous answer; SHIFT7/8 insert π and e. Physical constants come from CATALOG → CONST ▸.
Example 37To calculate π × 2
SHIFT7×2EXE
Math DEG
π × 2
6.2831853072
π × 2 ≈ 6.2832. Press ⇄ to keep the exact form 2π.
Standard Form (a × 10ⁿ)
Press ×10ˣ to type a power-of-ten exponent directly — the natural way to enter very large or very small numbers. To have results shown in standard form, set ⚙ − [Calc Settings] > [Number Format] > [Sci].
Example 38To enter 1.5 × 10⁴
1.5×10ˣ4EXE
Math DEG
1.5 × 10⁴
15,000
The ×10ˣ key enters the “× 10 to the power” part in a single keystroke: 1.5 × 10⁴ = 15000.
The ×10 Key setting (⚙ ▸ Calc Settings) chooses what that key inserts. With Sci-Notation it inserts a compact ᴇ exponent mark; with Power it inserts a written-out ×10^ expression. Both evaluate identically.
Example 39Sci-Notation mode — the compact ᴇ mark
×10 Key ▸ Sci-Notation3×10ˣ5EXE
Math DEG
3ᴇ5
300000
Here ×10ˣ inserts ᴇ: 3ᴇ5 means 3 × 10⁵ = 300000. This matches how scientific results are displayed.
Example 40Power mode — a written-out ×10^ expression
×10 Key ▸ Power3×10ˣ5EXE
Math DEG
3×10^5
300000
In Power mode the same key inserts ×10^, so the entry reads 3×10⁵ on screen — clearer for teaching standard form. The value is the same 300000.
Result Formats & Tools
After a result, ⇄ (FORMAT / S⇔D) toggles exact ⇄ decimal, and the full FORMAT menu (SHIFT⇄) offers Prime Factor, Recurring Decimal, Sexagesimal, Standard Form and the fraction forms. The CATALOG adds ENG (engineering form), FACT and RECUR. (The TOOLS key here is Undo / Redo — see the CATALOG chapter.)
Example 41S⇔D — toggle √8 between exact and decimal
√8)EXE⇄
Math DEG
√8
2√2 ⇄ 2.8284271248
The exact form 2√2 and the decimal 2.8284… are the same value shown two ways.
Example 42FACT — prime-factorise 360
360EXECATALOGFACT
Math DEG
360
2³ × 3² × 5
FACT breaks a whole number into its prime factors.
Example 43ENG — engineering notation for 12345
12345EXECATALOGENG
Math DEG
12345
12.345 × 10³
ENG shifts the exponent to a multiple of 3, ready for SI prefixes.
Example 44ENG→ — the same value with an SI prefix
12345EXECATALOGENG→
Math DEG
12345
12.345 k
ENG→ replaces the ×10ⁿ part with its SI prefix, so 10³ becomes k: 12345 = 12.345 k. Prefixes run from a (10⁻¹⁸) through m, k, M … up to E (10¹⁸); ◀▶ step the exponent.
Example 45Recurring Decimal — the repeating form of 1 ÷ 7
1÷7EXESHIFT⇄Recurring Decimal
Math DEG
1÷7
0.[142857]
FORMAT ▸ Recurring Decimal shows the repeating block in brackets: 1 ÷ 7 = 0.[142857] = 0.142857142857… (The CATALOG command RECUR does the same.)
Typing a recurring decimal
You can also enter a recurring decimal directly, using the CATALOG command ▨̄ input recurring. It inserts an overline block; type the repeating digits inside it, then press ▶ to leave the block. The calculator uses the exact value in the calculation.
Example 46To enter 0.3̄ (= 1⁄3)
0.CATALOG▨̄ input recurring3EXE
Math DEG
0.3
0.3333333333
With no digits before the block, the whole fractional part repeats: 0.3̄ = 1⁄3 = 0.3333333333.
Example 47A block after ordinary digits — 0.16̄ (= 1⁄6)
0.1CATALOG▨̄ input recurring6EXE
Math DEG
0.16
0.1666666667
Digits typed before the block are not repeated — only the 6 recurs: 0.16̄ = 1⁄6 = 0.1666666667. A block can hold several digits, so 0.142857 = 1⁄7.
Example 48Sexagesimal — enter and read degrees-minutes-seconds
1°′″30°′″0°′″EXE
Math DEG
1°30′0″
1.5
The °′″ key (SHIFT + +) enters a sexagesimal value: 1°30′0″ equals 1.5. On a decimal result, FORMAT ▸ Sexagesimal converts the other way (1.5 → 1°30′0″).
The FORMAT menu — every result conversion
All result conversions live on the FORMAT menu, opened with SHIFT⇄ (or a bare ⇄ when the FORMAT Key setting is “Format Menu”). Each item reshapes the current result without retyping it; only the ones that make sense for the result are active.
FORMAT
Standard (π √ frac)
Decimal
Prime Factor
Recurring Decimal
Rectangular Coord
Polar Coord
Improper Fraction
Mixed Number
Standard Form a×10ⁿ
Sexagesimal
Standard ⇄ Decimal is the ⇄ toggle; Prime Factor, Recurring Decimal and Sexagesimal match the CATALOG commands above. Rectangular ⇄ Polar Coord apply to a complex result (see the Complex chapter). The two below convert between fraction shapes and to standard form.
Example 49Improper ⇄ Mixed number — 13⁄4
13▢∕▢4EXESHIFT⇄Mixed Number
Math DEG
13⁄4 ⇄ 3 1⁄4
3 1⁄4
A result shown as the improper fraction 13⁄4 becomes the mixed number 3 1⁄4 under FORMAT ▸ Mixed Number; FORMAT ▸ Improper Fraction turns it back. (The ⇄ key still toggles fraction ⇄ decimal.)
Example 50Standard Form — convert a result to a × 10ⁿ
123456EXESHIFT⇄Standard Form
Math DEG
123456
1.23456 × 10⁵
FORMAT ▸ Standard Form rewrites the displayed value 123456 as 1.23456 × 10⁵ — the scientific-notation form — without changing the number. This converts an existing result, whereas the ×10ˣ key is for entering such a value.
Statistics App Reference
Statistics1-variable & 2-variable analysis
The Statistics app summarises a set of data and fits regression models. You type values into a list, then read off statistics such as the mean, standard deviation and quartiles; for paired data it also finds the line or curve of best fit. Open it from HOME by pointing to Statistics and pressing OK.
Choosing an analysis type
Select Calculation
11-Variable
2y = a + bx
3y = a + bx + cx²
4y = a + b·ln(x)
5y = a·e^(bx)
Choose 1-Variable for a single list of numbers, or one of the 2-Variable regression models for paired (x, y) data. The list continues with y = a·bx, y = a·xb and y = a + b/x. Changing the type later clears the data.
Entering data
Type a value and press EXE to drop to the next row. Move with the arrow keys, overwrite a cell by typing over it, and delete a value with DEL. Press TOOLS on the data editor for the row tools — Insert Row, Delete Row, Delete All and Sort Ascending / Descending (see “Editing and extending the data list” below). To weight values by how often they occur, turn on the Frequency column from ⚙ → Statistics ▸ Frequency ▸ On.
1-Variable statistics
Example 1To summarise the data 2, 5, 6, 8, 9
Statistics▸1-Variable→ enter data →FUNCTION
1-Variable Result (1/2)
x̄6
Σx30
Σx²210
Σx³1,590
Σx⁴12,594
σₓ2.4494897428
sₓ2.7386127875
The mean is x̄ = Σx / n = 30 / 5 = 6. The result also lists the running sums of powers Σx, Σx², Σx³, Σx⁴ used by the formulas. Two standard deviations are reported: σₓ (population, ÷ n) and sₓ (sample, ÷ n − 1); their squares are the variances σ²ₓ = 6 and s²ₓ = 7.5, also shown on the list.
Enter the data with:
2›EXE›5›EXE›6›EXE›8›EXE›9›EXE›FUNCTION
Example 2To read the order statistics (same data)
scroll the result with▼
1-Variable Result (2/2)
minX2
Q₁3.5
Median6
Q₃8.5
maxX9
Scrolling down shows the five-number summary: minimum 2, first quartile 3.5, median 6, third quartile 8.5 and maximum 9.
Note
σ (divide by n) treats the data as the whole population; s (divide by n − 1) treats it as a sample estimating a larger population. Both are always shown.
Example 3To weight values with a frequency column
⚙ Frequency ▸ On→ enter x and Freq
1-Variable
x
Freq
10
2
20
5
30
3
Here the value 10 occurs twice, 20 five times and 30 three times (n = 10 in total), giving x̄ = 21, σₓ = 7 and sₓ = 7.3786….
Normal distribution from 1-variable data
On the 1-variable result screen, press EXE to open the Norm-Dist tools. They convert a data value x to a probability using the fitted mean and σ: P(t) is the lower-tail area Φ(t), Q(t) = Φ(t) − 0.5, R(t) = 1 − Φ(t), and ▸t standardises x into t = (x − x̄) / σₓ.
Example 4To standardise x = 8 and read its probability
1-Variable Result→EXE→▸t / P(
Norm-Dist
▸t (x=8)0.8164965809
P(t)0.792891967
Q(t)0.292891967
R(t)0.207108033
The value 8 standardises to t = (8 − 6) / 2.449 = 0.8165, and about 79.3% of a normal population lies below it (P(t)).
Two-variable regression
Choose a 2-variable model to get an x and a y column. Enter each pair, then press FUNCTION for the fitted coefficients and the correlation r.
Example 5To fit a line to (1,3) (2,5) (3,7) (4,8) (5,11)
Statistics▸y = a + bx→ enter pairs →FUNCTION
Regression Result
a1.1
b1.9
r0.9904434668
x̄3
ȳ6.8
The line of best fit is y = 1.1 + 1.9x and the correlation r = 0.990 shows a strong positive relationship.
Example 6To estimate ŷ and x̂ from the fitted line
VARIABLE▸ŷ / x̂
Estimated Values
ŷ (x = 6)12.5
x̂ (y = 9)4.1578947368
Type a value then the estimate function: ŷ predicts y on the line at x = 6 (12.5); x̂ solves the line for x when y = 9.
The data doubles each step, so the fit is y = 1·e^(0.6931x) — and e^0.6931 = 2 exactly. Non-linear models drop any point that transforms to an undefined value.
Example 8To fit a quadratic y = a + bx + cx² to (1,1) (2,4) (3,9) (4,16) (5,25)
Statistics▸y = a + bx + cx²→ enter pairs →FUNCTION
Quadratic Regression
a0
b0
c1
The points lie exactly on y = x², so the fit returns a = 0, b = 0, c = 1. The quadratic model reports the three coefficients a, b, c (it does not report a correlation r).
Example 9To fit a power model y = a·xᵇ to (1,2) (2,8) (3,18) (4,32)
Statistics▸y = a·xᵇ→ enter pairs →FUNCTION
Power Regression
a2
b2
r1
These points are exactly y = 2x², so the power fit recovers a = 2, b = 2 with a perfect correlation r = 1. The power, ab-exponential and inverse models are fitted the same way — pick the shape that matches your data.
Menu item
Model
Reports r?
y = a + bx
Linear
Yes
y = a + bx + cx²
Quadratic
No (a, b, c)
y = a + b·ln(x)
Logarithmic
Yes
y = a·ebx
e Exponential
Yes
y = a·bx
ab Exponential
Yes
y = a·xb
Power
Yes
y = a + b/x
Inverse
Yes
The other regression models
The logarithmic, ab-exponential and inverse models are fitted exactly like the ones above — choose the shape that matches your data, enter the pairs, and press FUNCTION. Each reports its own a, b (and correlation r).
Example 10Logarithmic fit y = a + b·ln(x) to (1,2) (2,4) (3,5) (4,6)
Statistics▸y = a + b·ln(x)→ enter pairs →FUNCTION
Logarithmic Regression
a1.9953857485
b2.8377294683
r0.9989026513
The best-fit curve is y = 1.9954 + 2.8377·ln(x) with a very strong correlation r = 0.999. Use this model when y rises quickly then flattens.
Example 11ab-exponential fit y = a·bˣ to (1,6) (2,18) (3,54) (4,162)
Statistics▸y = a·bˣ→ enter pairs →FUNCTION
ab-Exp Regression
a2
b3
r1
The data triples each step, so the fit is exactly y = 2·3ˣ (a = 2, b = 3) with r = 1. The ab-exponential form multiplies by a constant factor b each step; the e-exponential form (Example 7) uses base e instead.
Example 12Inverse fit y = a + b/x to (1,7) (2,4) (4,2.5)
Statistics▸y = a + b/x→ enter pairs →FUNCTION
Inverse Regression
a1
b6
r1
These points sit exactly on y = 1 + 6/x (a = 1, b = 6, r = 1). The inverse model suits data that falls off like 1/x and levels toward a constant a.
Switching the model without re-entering data
All seven 2-variable models use the same (x, y) columns, so you can try a different fit on the same data without retyping it. On the regression result screen press FUNCTION to open Select Reg Type, choose a model (▲▼ and OK, or the number keys 1–7), and the calculator re-fits the entered pairs and shows the new coefficients. This makes it easy to compare, say, a linear against a quadratic fit and read off which has the better correlation.
Example 13To re-fit the same data as a quadratic — Select Reg Type
2-var resultFUNCTIONSelect Reg Type▸y = a + bx + cx²OK
Re-fit · Quadratic
a1.6
b1.4714285714
c0.0714285714
r—
Starting from the linear fit of Example 5, FUNCTION ▸ Select Reg Type ▸ quadratic re-fits the very same five pairs as y = a + bx + cx², now reporting a third coefficient c. Switching between 1-Variable and 2-Variable, however, still clears the list (the columns differ).
The full 2-variable statistics list
Beyond the fit coefficients, a 2-variable result lists every summary statistic — the running sums, both standard deviations for x and y, and the data ranges. Scroll the result with ▼ to reach them.
Example 14The complete read-out for the line data (1,3) (2,5) (3,7) (4,8) (5,11)
Regression Result→ scroll▼
2-Variable Result (sums)
n5
Σx15
Σy34
Σx²55
Σy²268
Σxy121
Σx³225
Σx²y489
Σx⁴979
These are the running sums the regression uses. Scrolling further lists the means x̄ = 3, ȳ = 6.8; the population deviations σx = 1.4142135624, σy = 2.7129319932; the sample deviations sx = 1.5811388301, sy = 3.0331501776 (with variances σ²x, σ²y, s²x, s²y as their squares); and the ranges minX = 1, maxX = 5, minY = 3, maxY = 11. (Same data as Example 5.)
Editing and extending the data list
You can revise the data at any time without leaving the app. Move the cursor with the arrow keys and:
Correct a value — point to the cell, type the new value and press EXE; it replaces the old one.
Clear a cell — empty it with DEL. A blank row is simply skipped when the statistics are calculated, so you don't have to shuffle the rows below.
Add more data — scroll to the first empty row at the bottom of the list and keep typing.
To reshape the list itself, press TOOLS on the data editor for the row tools:
Insert Row — push a blank row in above the highlighted row (so you can add a value you missed between two others).
Delete Row — remove the highlighted row and close the gap.
Delete All — clear the whole list to start over.
Sort Ascending / Descending — reorder on whichever column the cursor is in (x, y or Freq). A paired list is kept aligned, so each x keeps its own frequency or y partner. Note that a sort cannot be undone — the original order is not recoverable.
Press FUNCTION again after any change and every statistic is recomputed from the current list.
Note
You can also copy a single cell's value into a memory: on the Statistics Editor, put the cursor on the cell and press VARIABLE, then pick a variable (A–F, x, y, z) and choose Store. Handy for pulling one data point into another calculation.
Example 15To correct a mistyped value (the 6 was entered as 60)
point to the wrong cell →6EXE→FUNCTION
1-Variable
x
2
5
6
8
9
Overwriting cell x₃ with 6 and pressing FUNCTION refreshes the whole result — no need to re-enter the other four values.
Example 16To insert a missing value and then sort the list
point to a row →TOOLSInsert Rowtype 4 →TOOLSSort Ascending
1-Variable
x
2
4
5
6
8
9
Highlighting the row that held 5 and choosing Insert Row opens a blank line above it; typing 4 fills it. Sort Ascending then reorders the whole column to 2, 4, 5, 6, 8, 9. With a Freq or y column present, each partner value moves with its x.
Statistics calculation screen
The Statistics Calc screen (TOOLS ▸ Stat-Calc from a result) is a free-form editor in which you can recall any statistical value by name and combine it with ordinary arithmetic. Press VARIABLE to pick the value to insert. The available values are:
Group
Values you can recall
Summation
n · Σx · Σx² · Σx³ · Σx⁴ (paired data adds Σy · Σy² · Σxy · Σx²y)
Example 17To combine statistics in an expression (x̄ × 2 + Σx)
TOOLS▸Stat-Calc→VARIABLEinserts x̄, Σx …
Stat DEG
x̄ × 2 + Σx
42
Press TOOLS on a result screen for this editor. Using the 1-variable data (x̄ = 6, Σx = 30): x̄ × 2 + Σx = 12 + 30 = 42. Any statistic can be reused this way.
Example 18To recall a regression coefficient in the Stat-Calc screen
2-variable dataTOOLS▸Stat-Calc→VARIABLEa / b / r
Recalled coefficients
a1.1
b1.9
r0.9904434668
With the line data from Example 5, VARIABLE recalls the fitted coefficients individually — here a = 1.1, b = 1.9, r = 0.990 — so you can feed them straight into a further calculation (for example b × 10 or a prediction a + b·7).
Estimating x from a quadratic fit
For a linear model, estimating x from a y value gives a single x̂ (Example 6). A quadratic model is not one-to-one, so a given y can correspond to two x values — the calculator returns both, x̂₁ and x̂₂.
Example 19To estimate x when y = 9 on the quadratic fit y = x²
VARIABLE▸x̂→ 9 →EXE
Estimated x
x̂₁ (y = 9)3
x̂₂ (y = 9)−3
Using the quadratic fit from Example 8 (y = x²), the value y = 9 is reached at both x = 3 and x = −3, so the estimate returns the pair x̂₁ = 3, x̂₂ = −3. When the two roots coincide, or the quadratic term c is zero, a single value is returned instead.
Statistical calculation formulas
For reference, these are the formulas the app uses. Sums run over all n data values (weighted by the Frequency column when it is on).
Mean x̄ =Σxn ȳ =Σyn Population SD σₓ = √( Σ(x − x̄)²n ) Sample SD sₓ = √( Σ(x − x̄)²n − 1 ) Variance σ²ₓ and s²ₓ are the squares of the deviations above.
Linear regression y = a + bx:
b =n·Σxy − Σx·Σyn·Σx² − (Σx)² a =Σy − b·Σxn = ȳ − b·x̄ r =n·Σxy − Σx·Σy√[ (n·Σx² − (Σx)²)(n·Σy² − (Σy)²) ] Estimates ŷ = a + bx x̂ =y − ab
Quadratic regression y = a + bx + cx² — the coefficients a, b, c come from the least-squares normal equations, and x is estimated from a y value by solving the quadratic:
The non-linear models (logarithmic, exponential, ab-exponential, power, inverse) are fitted by applying the same linear formulas to the transformed data — for example the log model fits a + b·X with X = ln x, then maps back.
Distribution App Reference
DistributionNormal, Binomial & Poisson
The Distribution app evaluates the common probability distributions. Choose a distribution from the menu, enter its parameters, and read the probability — or, for the list distributions, a whole table of probabilities.
Choosing a distribution
Distribution
1Normal PD
2Normal CD
3Inverse Normal
4Binomial PD
5Binomial CD
PD gives the density / mass at a point; CD gives the cumulative probability up to a bound. The list also has Poisson PD and Poisson CD.
Normal distribution
Example 1Normal PD — density f(x) at x = 0.5, μ = 0, σ = 1
Distribution▸Normal PD→ x, μ, σ →EXE
Normal PD
x0.5
μ0
σ1
f(x)0.3520653268
f(x) is the height of the bell curve, not a probability. For the standard normal the height at x = 0.5 is 0.3521.
Example 2Normal CD — P(−1 ≤ X ≤ 1) for μ = 0, σ = 1
Distribution▸Normal CD→ Lower, Upper, μ, σ →EXE
Normal CD
Lower−1
Upper1
P0.6826894723
The area between the bounds is the probability. This is the classic “68% within one σ”.
Example 3Normal CD — heights ~N(170, 6), P(160 ≤ X ≤ 180)
Normal CD→ 160, 180, 170, 6 →EXE
Normal CD
Lower160
Upper180
μ170
σ6
P0.9044193359
About 90.4% of this population lies between 160 and 180 cm. For a one-sided probability use a very large or very small bound (e.g. Lower = −1×10⁹⁹).
Example 4Inverse Normal — the value with 97.5% below it
Distribution▸Inverse Normal→ Area, μ, σ →EXE
Inverse Normal
Area0.975
μ0
σ1
xInv1.9599639861
Inverse Normal reverses the question. The value with 97.5% of the standard-normal area below it is 1.96 — the familiar 95%-confidence cut-off.
Binomial distribution (list input)
Enter N (trials) and p (success probability) once, then a growable list of x values; a probability is returned for each. PD gives P(X = x); CD gives P(X ≤ x).
Example 5Binomial PD — N = 10, p = 0.5, for x = 0…4
Ten fair coin tosses: the probability of exactly 3 heads is 0.1172. Add as many x values as you like to build the whole table.
Example 6Binomial CD — P(X ≤ 3), N = 10, p = 0.5
Binomial CD→ N=10, p=0.5, x=3 →EXE
Binomial CD
x
P
3
0.171875
The cumulative form adds P(X = 0…3) = 0.171875 — the chance of at most 3 heads.
Poisson distribution (list input)
Example 7Poisson PD — λ = 3, for x = 0…4
Distribution▸Poisson PD→ λ=3, x-list →EXE
Poisson PD
x
P
0
0.0497870684
1
0.1493612051
2
0.2240418077
3
0.2240418077
4
0.1680313557
Events at an average rate λ = 3. The most likely counts are 2 and 3, each with probability 0.2240.
Example 8Poisson CD — P(X ≤ 2), λ = 3
Poisson CD→ λ=3, x=2 →EXE
Poisson CD
x
P
2
0.4231900811
Adding P(X = 0, 1, 2) gives 0.4232 — the chance of two or fewer events.
Valid parameter ranges
Each distribution accepts parameters only within its natural range; a value outside the range produces a Math ERROR. Re-enter a value inside the range to continue.
Distribution
Parameter constraints
Binomial PD / CD
0 ≤ p ≤ 1, N ≥ 0 (integer), 0 ≤ x ≤ N
Poisson PD / CD
λ ≥ 0, x ≥ 0 (integer)
Normal PD / CD
σ > 0
Inverse Normal
0 < Area < 1, σ > 0
Example 9An out-of-range parameter is rejected (Inverse Normal, Area = 1.5)
Inverse Normal→ Area = 1.5 →EXE
Inverse Normal
Area1.5
μ0
σ1
Math ERROR
An area must be a probability between 0 and 1, so 1.5 gives Math ERROR. The same happens for a Normal σ ≤ 0 or a Binomial p outside [0, 1] — correct the value and press EXE again.
Important!
List distributions accept several x values at once — add rows to the x list and every row is evaluated, giving a probability table you can scroll.
Note
Press TOOLS on the x list for the row tools — Insert Row (add an x value between two others), Delete Row and Delete All. The list keeps its order, so there is no Sort here.
Table App Reference
TableFunction value tables
The Table app tabulates one or two functions over a range of x — ideal for plotting points, spotting where a function crosses zero, and comparing two functions side by side.
Defining the function(s) and range
Type the formula for f(x) using the x key for the variable. To tabulate a second function, turn on g(x) from ⚙ → Table ▸ f(x)/g(x). The calculator then asks for Start, End and Step and builds a row for each x (up to 45 rows for a single function, or 30 rows when both f(x) and g(x) are tabulated).
Between x = 1 and x = 2 the value changes sign (−2 → 1), so the graph crosses zero there — a quick way to locate a root. Scroll with ▲▼.
Enter the function with:
x›x²›−›3›EXE›1›EXE›5›EXE›1›EXE
Example 2To tabulate f(x) = x² − 3 and g(x) = 2x + 1 together
⚙ f(x)/g(x) ▸ On→ g(x) = 2x + 1 → x = 1 … 4
Table
x
f(x)
g(x)
1
−2
3
2
1
5
3
6
7
4
13
9
The two columns are closest near x = 3 (6 vs 7), showing roughly where the curves x² − 3 and 2x + 1 intersect.
Note
The row limit is 45 for a single function but only 30 when g(x) is also on (as in Example 2). If Start, End and Step would produce more rows than the limit, the list is truncated to fit. Edit the function or range from the ⚙ menu and the table regenerates.
Note
On the generated table, press TOOLS for the row tools — Insert Row, Delete Row and Delete All — to prune or add individual x rows without changing the Start/End/Step range.
Registering & using f(x) and g(x)
Defining a function in the Table app also registers it. Once f(x) (and optionally g(x)) is entered, you can call it by name in the Calculate app: insert f(▢) or g(▢) from the CATALOG and type a value for x in the box. This lets you reuse a formula without retyping it.
Note
You don't have to open the Table app to register a function — in Calculate, type an expression in x and choose CATALOG ▸ Define f(x) (or Define g(x)). See “Defining your own functions” in the CATALOG chapter.
Example 3Evaluate a registered function — f(3), where f(x) = 2x + 1
CalculateCATALOGf(▢)3)EXE
Math DEG
f(3)
7
With f(x) = 2x + 1 registered in the Table app, f(3) = 2·3 + 1 = 7.
Example 4Composite function — g(f(2)), where f(x) = 2x + 1 and g(x) = x²
CalculateCATALOGg(▢)→f(▢)2 →))EXE
Math DEG
g(f(2))
25
The inner call gives f(2) = 5, then g(5) = 5² = 25. You can also make a function itself composite — define g(x) = f(x)² — and the calculator resolves the nested call (a built-in guard stops any accidental circular reference with a Stack ERROR).
Note
Data retention: f(x) and g(x) stay registered when you switch between apps, so define them once in Table and use them in Calculate. Registering new functions replaces them; ⚙ − [Reset] > [Variable Memory] clears them.
Equation App Reference
EquationSimultaneous systems & polynomials
The Equation app solves two kinds of problem: simultaneous linear systems with 2, 3 or 4 unknowns, and polynomial equations of degree 2, 3 or 4. You enter only the coefficients and the calculator returns the complete solution set.
Choosing an equation type
Equation Type
1Simultaneous · 2 unknowns
2Simultaneous · 3 unknowns
3Simultaneous · 4 unknowns
4Polynomial · ax²+bx+c
5Polynomial · ax³+…
The list continues with Polynomial · ax⁴+bx³+cx²+dx+e and a free-form Solver · f(x)=0. Point to a type and press OK; the calculator lays out exactly the coefficient boxes that type needs (or, for the Solver, a single expression editor).
Simultaneous equations
Each row of the grid is one equation. For 2 unknowns the columns are x, y and the constant =. Enter the coefficients left to right, pressing EXE after each.
Enter the two rows (2, 3, 8) and (1, −1, −1). The unique solution is x = 1, y = 2.
Key operation:
2›EXE›3›EXE›8›EXE›1›EXE›(−)›1›EXE›(−)›1›EXE
Example 2To solve a 3-unknown system
Equation▸Simultaneous · 3 unknowns→EXE
Solution
x1
y2
z3
For x + y + z = 6, x − y + 2z = 5 and 2x + y − z = 1 the solution is x = 1, y = 2, z = 3. A 4-unknown system adds a w column.
Note
If a system has no unique solution the calculator reports Infinite Solutions or No Solution instead of values.
Polynomial equations
Enter the coefficients from the highest power down. The quadratic x² − 5x + 6 = 0 uses a = 1, b = −5, c = 6.
Example 3To solve the quadratic x² − 5x + 6 = 0
Equation▸Polynomial · ax²+bx+c→ 1, −5, 6 →EXE
Roots
x₁3
x₂2
The two roots are x = 3 and x = 2. Scrolling down also shows the vertex of the curve — see “Minimum / maximum of the curve” below.
Example 4To solve the cubic x³ − 6x² + 11x − 6 = 0
Polynomial · ax³+…→ 1, −6, 11, −6 →EXE
Cubic Roots
x₁3
x₂1
x₃2
Three real roots: 1, 2 and 3.
Example 5To solve the quartic x⁴ − 5x² + 4 = 0
Polynomial · ax⁴+…→ 1, 0, −5, 0, 4 →EXE
Quartic Roots
x₁2
x₂1
x₃−1
x₄−2
Four real roots: ±1 and ±2. Enter 0 for any missing power (here b and d are 0).
Minimum / maximum of the curve
After you solve a quadratic or cubic, the result screen also reports the turning point(s) of the curve y = f(x): a quadratic has a single vertex (its minimum if a > 0, maximum if a < 0); a cubic has a local maximum and a local minimum when its shape has them.
Example 6The vertex of the quadratic x² − 5x + 6
Polynomial · ax²+bx+c→ 1, −5, 6 → solve →scroll▼
Roots + Vertex
x₁3
x₂2
Min x2.5
Min y−0.25
Below the two roots the screen shows the vertex. For x² − 5x + 6 (a = 1 > 0) it is a minimum at (x, y) = (2.5, −0.25) — the lowest point of the parabola, halfway between the roots.
Example 7The local max & min of the cubic x³ − 3x
Polynomial · ax³+…→ 1, 0, −3, 0 → solve →scroll▼
Local Extrema
Max x−1
Max y2
Min x1
Min y−2
The cubic x³ − 3x turns twice: a local maximum at (−1, 2) and a local minimum at (1, −2). A cubic with no turning points (a monotonic curve) instead reports No Local Max/Min.
Complex roots
When a polynomial has non-real roots, the Complex Roots toggle decides whether they are shown. It is Off by default (only real roots appear). Turn it on from the Equation TOOLS menu → Complex Roots ▸ On.
Example 8To show the complex roots of x² + 2x + 5 = 0
TOOLS▸Complex Roots ▸ On→ solve
Complex Roots
x₁−1 + 2i
x₂−1 − 2i
This equation has no real roots. With the setting on it returns the conjugate pair −1 ± 2i; with it off it reports No Real Roots.
Solver — one equation in x
The Solver is the last item on the type menu. Instead of coefficients you type a whole expression f(x) (or an equation L = R), and the calculator finds a value of x that makes it zero using Newton's method, starting from the current value of x.
Example 9To solve x³ − 2x − 5 = 0 with the Solver
Equation▸Solver · f(x)=0→ x³ − 2x − 5 →EXE
Solver
x2.0945514815
L − R0
The Solver converges to x = 2.0945514815. The L − R line is the residual f(x) at that root — here 0 to display precision — showing how exactly the equation is satisfied. Type f(x) with the x key; to solve an equation such as 2x = x + 5, insert “=” from the CATALOG and enter both sides.
Note
The Solver returns the one root nearest the starting guess. To reach a different root, store a new starting value into x (VARIABLE ▸ x ▸ Store) before solving; to get every root of a polynomial at once, use the Polynomial types instead.
Example 10When the Solver cannot converge — Continue or Exit
solve a hard f(x)→OK Continue / AC Exit
Solver
x1.732050807
L − R−3.2 × 10⁻⁶
Could not convergeOK Continue · AC Exit
If Newton's method has not settled within its iteration limit, the Solver does not just give up — it shows the best value so far, its residual L − R, and the prompt Could not converge · OK Continue · AC Exit. Press OK to run more iterations starting from that best value (repeat until L − R is acceptably small), or AC to Exit and keep the near-solution. A residual close to zero means the value is already a good approximate root.
Note
On the Solver result screen you can also store the root: press VARIABLE and pick a memory (A–F, x, y, z). See “Storing a result from another app” in the Calculate chapter.
Inequality App Reference
InequalityPolynomial inequalities
The Inequality app solves a polynomial inequality and reports the solution as a set of intervals on the number line. It handles quadratic, cubic and quartic inequalities against 0.
Choosing degree and direction
Inequality Degree
1Quadratic ax²+bx+c
2Cubic ax³+bx²+cx+d
3Quartic ax⁴+…+e
After the degree, choose the direction against zero — > 0, < 0, ≥ 0 or ≤ 0 — then enter the coefficients exactly as in the Equation app.
Example 1To solve x² − 5x + 6 > 0
Inequality▸Quadratic▸> 0→ 1, −5, 6 →EXE
Ineq DEG
x² − 5x + 6 > 0
x < 2 or x > 3
The factors are (x − 2)(x − 3), so the expression is positive outside the roots: x < 2 or x > 3.
Example 2To solve x² − 5x + 6 ≤ 0
Quadratic▸≤ 0→ 1, −5, 6 →EXE
Ineq DEG
x² − 5x + 6 ≤ 0
2 ≤ x ≤ 3
With ≤, the boundary roots are included, so the answer is the closed interval 2 ≤ x ≤ 3. The app writes ≤ / ≥ for inclusive directions and < / > for strict ones.
Example 3To solve x³ − x > 0
Cubic▸> 0→ 1, 0, −1, 0 →EXE
Ineq DEG
x³ − x > 0
−1 < x < 0 or x > 1
The roots are −1, 0 and 1; testing each region gives two solution intervals, joined with “or”.
Note
If the inequality is true everywhere the app shows All Real Numbers; if it is never true it shows No Solution.
Complex App Reference
ComplexArithmetic with complex numbers
The Complex app performs the four operations on two complex numbers z₁ = a + bi and z₂ = c + di, and can show the result in rectangular (a + bi) or polar (r∠θ) form. The imaginary unit i satisfies i² = −1.
Selecting the operation
Operation
1z₁ + z₂
2z₁ − z₂
3z₁ × z₂
4z₁ ÷ z₂
Pick the operation first, then enter the real and imaginary parts of each number into the coefficient grid. The examples below all use z₁ = 3 + 2i and z₂ = 1 + 4i.
Example 1To add (3 + 2i) + (1 + 4i)
Complex▸z₁ + z₂→ 3, 2, 1, 4 →EXE
Result
z₁ + z₂4 + 6i
Add the real parts and the imaginary parts separately: (3 + 1) + (2 + 4)i = 4 + 6i.
Use the distributive law with i² = −1: (3·1 − 2·4) + (3·4 + 2·1)i = −5 + 14i. Enter it with
3›EXE›2›EXE›1›EXE›4›EXE›FUNCTION
Example 4To divide (3 + 2i) ÷ (1 + 4i)
z₁ ÷ z₂→EXE
Result
z₁ ÷ z₂0.6470588235 − 0.5882352941i
Multiply top and bottom by the conjugate of the denominator (1 − 4i). The denominator becomes 1² + 4² = 17, a real number.
Polar form and complex functions
Set Complex Result ▸ r∠θ in SETTINGS to read a result in polar form. The FUNCTION menu inside the app also offers Abs (modulus |z|), arg (argument), Conjg (conjugate z̄), ReP (real part) and ImP (imaginary part).
Example 5To read 1 + i in polar form
SETTINGS▸Complex Result ▸ r∠θ
Polar (Deg)
1 + i√2 ∠ 45°
|1 + i|1.4142135624
arg(1 + i)45
1 + i has modulus r = √2 ≈ 1.4142 and argument θ = 45° (in Degree mode). Changing the Angle Unit changes how θ is reported.
Example 6To enter a number in polar form — 2∠60°
FUNCTION▸∠→ 2 ∠ 60 →EXE
Polar Input (Deg)
2∠60°1 + 1.7320508076i
The ∠ operator on the FUNCTION menu lets you type a complex number by magnitude and angle as r∠θ. In Degree mode 2∠60° converts to rectangular 1 + 1.7320508076i (= 1 + √3·i). You can mix polar and rectangular values in the same expression.
Note
Conjg flips the sign of the imaginary part (a + bi → a − bi); ReP and ImP extract the real and imaginary components as ordinary numbers.
Powers and functions in the Calculate app
The Complex app is a guided z₁ ∘ z₂ workspace. For anything richer — powers of a complex number, longer expressions, or the FUNCTION functions applied on their own — use the Calculate app, where you type i with the i key and enter a free expression. Complex results there obey the same FUNCTION menu (Abs, arg, Conjg, ReP, ImP) and the SETTINGS r∠θ output.
Example 7Conjg, ReP and ImP of 2 + 3i (Calculate app)
CalculateFUNCTION▸Conjg / ReP / ImP→ 2 + 3i →EXE
Complex functions
Conjg(2 + 3i)2 − 3i
ReP(2 + 3i)2
ImP(2 + 3i)3
Conjg gives the conjugate 2 − 3i; ReP returns the real part 2 and ImP the imaginary part 3 as ordinary numbers.
Example 8A power of a complex number — (1 + i)⁴ + (1 − i)²
Calculate→ (1 + i)▢^4 + (1 − i)▢^2 →EXE
Complex power
(1+i)⁴ + (1−i)²−4 − 2i
Raise a complex number to a whole-number power with the ▢^ key: (1 + i)⁴ = −4 and (1 − i)² = −2i, so the sum is −4 − 2i. The exponent may be any integer.
Base-N App Reference
Base-NBinary, octal, decimal & hexadecimal
The Base-N app works with whole numbers in four bases — DEC (10), HEX (16), OCT (8) and BIN (2) — and includes the bitwise logic operators. All arithmetic is integer arithmetic on a 32-bit two's-complement value.
Switching base
The active base is shown at the top of the screen. Press the base soft keys DEC, HEX, OCT, BIN to re-display the current value in another base — the value never changes, only its notation.
Example 1To view the number 250 in every base
Base-N→ 250 →HEX/OCT/BIN
250 in every base
Base
Value
DEC
250
HEX
FA
OCT
372
BIN
11111010
Enter 250 in DEC, then tap each base key. The single quantity 250 is FA in hexadecimal, 372 in octal and 11111010 in binary.
Example 2To convert hexadecimal FF to decimal
Base-N▸HEX→ FF →DEC
Base HEX → DEC
FF
255
Type FF while the base is HEX — the hex digits A–F are typed with the sincostanloglnx² keys (A, B, C, D, E, F respectively) — then switch to DEC to read 255.
Arithmetic in the active base
The four operations + − × ÷ (and parentheses) work directly on numbers in the current base; the result is displayed in that base. Only digits the base allows can be entered (0–1 for BIN, 0–7 for OCT, 0–9 and A–F for HEX).
Example 3To add 1F + 1 in hexadecimal
HEX→ 1F + 1 →EXE
Base HEX
1F + 1
20
In HEX, 1F (= 31) plus 1 is 20 (= 32). Division discards any remainder, since Base-N is integer-only.
Mixing bases with per-value prefixes
From the CATALOG you can tag an individual number with the base to read it in, whatever the active base: d→ (decimal), h→ (hexadecimal), b→ (binary) and o→ (octal). This lets you combine values written in different bases in one calculation.
Example 4To add h→FF and 1 while the display base is DEC
DECCATALOGh→FF + 1 →EXE
Base DEC
h→FF + 1
256
The prefix h→ reads FF as hexadecimal (255) even though the display base is decimal, so h→FF + 1 = 256. Use d→, b→ or o→ the same way to drop in a decimal, binary or octal literal.
Bitwise logic operators
Press CATALOG in Base-N to insert a logic operator: and, or, xor, xnor, not and Neg (two's-complement negate). These operate on the binary bit patterns.
Example 51100 and 1010 (in binary)
BIN→ 1100and1010 →EXE
Base BIN
1100 and 1010
1000
and keeps bits that are set in BOTH operands: only the leading bit is set in both, so the result is 1000.
Example 61100 or 1010 (in binary)
BIN→ 1100or1010 →EXE
Base BIN
1100 or 1010
1110
or keeps bits set in EITHER operand, giving 1110.
Example 71100 xor 1010 (in binary)
BIN→ 1100xor1010 →EXE
Base BIN
1100 xor 1010
110
xor keeps bits set in EXACTLY ONE operand: 1100 xor 1010 = 0110 (shown as 110).
Note
xnor is the complement of xor (matching bits give 1); not inverts every bit of the 32-bit pattern; Neg forms the two's-complement negative — Neg 5 = −5. Because not and Neg flip all 32 bits, their results show as a long high-bit pattern in HEX/BIN, exactly like the negative value below.
Negative values
Decimal shows a signed value; the other bases show the 32-bit two's-complement bit pattern, so a negative number prints as its unsigned pattern.
Example 8To view −5 in two's-complement form
Base-N→ −5 →HEX/BIN
−5 in two's complement
Base
Value
DEC
−5
HEX
FFFFFFFB
BIN
…11111011
In DEC, −5 keeps its sign. In HEX it is FFFFFFFB, and in BIN the full 32-bit pattern ends in …11111011.
Important!
Base-N is integer-only: fractions, decimals and roots are not available, and a result outside the signed 32-bit range (−2 147 483 648 … 2 147 483 647) is a Math ERROR.
Matrix App Reference
MatrixMatrix arithmetic up to 4×4
The Matrix app performs calculations with matrices of up to four rows and four columns (and rectangular m×n matrices). You store values in the matrix memories MatA, MatB, MatC and MatD, then build an expression from them. The result of every matrix calculation is retained in a special memory called MatAns, which you can feed straight into the next calculation.
Creating and entering a matrix
When you open an operation, the calculator first asks for the dimensions (rows × columns), then shows an empty grid. Fill it cell by cell, pressing EXE after each value to advance to the next cell. This grid holds MatA = 2111:
MatA 2×2
c1
c2
r1
2
1
r2
1
1
Choose 2 rows and 2 columns, then key in the four values:
2›EXE›1›EXE›1›EXE›1›EXE
Important!
A matrix memory keeps its contents until you overwrite it or clear the app, so you can reuse MatA in several calculations without re-entering it.
The examples below all use these four matrices: MatA = 2111MatB = 2321MatC = 10−10−11MatD = 123456789
Addition and Subtraction
Example 1To add two matrices (MatA + MatB)
Matrix▸MatA + MatB→ enter MatA, MatB →EXE
MatAns=
4432
Corresponding entries are added: the (1,1) entries 2 + 2 = 4, the (1,2) entries 1 + 3 = 4, and so on, giving 4432.
Example 2To subtract two matrices (MatA − MatB)
Matrix▸MatA − MatB→ enter MatA, MatB →EXE
MatAns=
0−2−10
Subtraction is also entry by entry: 2 − 2 = 0, 1 − 3 = −2, and so on.
Note
The two matrices must have the same dimensions in order to be added or subtracted. An error occurs if you try to add or subtract matrices of different dimensions.
Multiplication
Example 3To multiply two matrices (MatA × MatB)
Matrix▸MatA × MatB→ enter MatA, MatB →EXE
MatAns=
6744
Each result entry is a row × column dot product. The (1,1) entry is (row 1 of MatA)·(column 1 of MatB) = 2·2 + 1·2 = 6; the (1,2) entry is 2·3 + 1·1 = 7.
Example 4To multiply matrices of different sizes (MatA × MatC)
Matrix▸MatA × MatB→ MatA (2×2), MatC (2×3) →EXE
MatAns=
2−1−11−10
A 2×2 times a 2×3 gives a 2×3 result, because MatA has 2 columns and MatC has 2 rows.
Important!
Matrix multiplication is only possible when the number of columns of the left matrix equals the number of rows of the right matrix. Note that MatA × MatB and MatB × MatA are generally not the same.
Powers — Square and Cube
A square matrix can be raised to a power. MatA² means MatA × MatA, and MatA³ means MatA × MatA × MatA.
Example 5To square and cube MatA (MatA², MatA³)
Matrix▸MatA²/MatA³→EXE
MatAns=
5332
MatA² = 5332. Cubing goes one step further: MatA³ = MatA² × MatA = 13885.
Inverse
The inverse MatA⁻¹ is the matrix that satisfies MatA × MatA⁻¹ = I (the identity). It exists only for a square matrix whose determinant is non-zero.
Because det(MatA) = 1, the inverse is 1−1−12. You can check it: MatA × MatA⁻¹ returns the identity matrix.
Note
Only square matrices (same number of rows and columns) can be inverted. Trying to invert a matrix that is not square produces an error.
A matrix with a determinant of zero cannot be inverted — for example MatD above has det 0, so MatD⁻¹ is an error.
Calculation precision is affected for matrices whose determinant is near zero.
Determinant
The determinant is a single number describing a square matrix. For 1×1, 2×2 and 3×3 matrices it is computed as:
det a₁₁= a₁₁ det a₁₁a₁₂a₂₁a₂₂= a₁₁a₂₂ − a₁₂a₂₁ det a₁₁a₁₂a₁₃a₂₁a₂₂a₂₃a₃₁a₃₂a₃₃= a₁₁a₂₂a₃₃ + a₁₂a₂₃a₃₁ + a₁₃a₂₁a₃₂ − a₁₃a₂₂a₃₁ − a₁₂a₂₁a₃₃ − a₁₁a₂₃a₃₂
Example 7To obtain the determinant of MatA (Det(MatA))
Matrix▸MatA det / inv / trans▸Determinant→EXE
MatAns=
1
det(MatA) = a₁₁a₂₂ − a₁₂a₂₁ = 2·1 − 1·1 = 1. A determinant is a scalar, so the result is a single value.
Note
Determinants can be obtained only for square matrices. Trying to obtain a determinant for a non-square matrix produces an error. The determinant of MatD (above) is 0, which is why it has no inverse.
Transpose
The transpose Mᵀ turns rows into columns. It works for any matrix, including rectangular ones.
Example 8To transpose MatC (Trn(MatC))
Matrix▸MatA det / inv / trans▸Transpose→ MatC →EXE
MatAns=
100−1−11
The 2×3 matrix MatC becomes a 3×2 matrix — row 1 (1, 0, −1) becomes column 1, and row 2 (0, −1, 1) becomes column 2.
Identity Matrix
Identity(n) creates the n×n identity matrix — 1s on the main diagonal and 0s everywhere else. Multiplying any matrix by the identity leaves it unchanged. The size n may be 1 to 10; a value outside that range gives an Argument ERROR.
Example 9To create the 3×3 identity matrix (Identity(3))
Matrix▸Identity(n)→ 3 →EXE
MatAns=
100010001
Enter the size n = 3. Larger results that overflow the screen can be scrolled with the ▲▼◀▶ keys.
Reusing a result — MatAns
Every matrix result is held in MatAns. On a result screen press EXE to carry it straight into the next calculation as operand A, without re-entering it.
Example 10To verify an inverse — MatA × MatAns after inverting MatA
MatA⁻¹→EXE→MatA × MatAns→EXE
MatAns=
1001
Invert MatA first (MatAns becomes 1−1−12). Press EXE to reuse it, pick MatA × MatAns, and the product is the identity 1001 — confirming the inverse is correct.
Note
MatAns always holds the most recent matrix result, so you can chain calculations. A scalar result such as a determinant is kept in the ordinary Ans instead.
Copying a result into MatA–MatD
MatAns is overwritten by the next matrix calculation. To keep a result, copy it into one of the named matrices. On a matrix result screen press VARIABLE and choose the destination — MatA, MatB, MatC or MatD; the whole matrix (its dimensions and every element) is stored there.
Example 11To save the inverse of MatA into MatB
MatA⁻¹→EXE→VARIABLEMatB
MatAns=
1−1−12
With the inverse 1−1−12 on screen, VARIABLE ▸ MatB copies it into MatB. It now survives further calculations, so you can build an expression such as MatA × MatB later without recomputing the inverse.
Absolute value of a matrix
Applying Abs to a matrix takes the absolute value of every element, returning a matrix of the same size. Insert Abs from the FUNCTION menu (or the CATALOG) and put the matrix inside.
Example 12To take the element-wise absolute value of a matrix
FUNCTIONAbsMatA→EXE
MatAns=
1234
With MatA = −12−34, Abs(MatA) returns 1234 — each entry made non-negative. (For a vector, Abs instead gives its magnitude |v|.)
Vector App Reference
Vector2D & 3D vector operations
The Vector app stores two vectors, VctA and VctB, in 2 or 3 dimensions and computes their sum, difference, dot product, cross product, magnitudes, the angle between them and their unit vectors.
Choosing dimensions
Vector Dimension
12D vectors (x, y)
23D vectors (x, y, z)
Pick 2D or 3D, then enter the components of VctA and VctB. The cross product is always a vector: for 2D vectors it is (0, 0, z) — the calculator treats them as lying in the z = 0 plane — and for 3D it is the usual perpendicular vector.
A · B = AxBx + AyBy + AzBz |A| = √(Ax² + Ay² + Az²) cos θ =A · B|A| |B|
The dot product is 1·4 + 2·5 + 3·6 = 32; the cross product (−3, 6, −3) is perpendicular to both; |VctA| = √14 ≈ 3.742; and the angle is about 12.93° (Degree mode).
Key operation:
1›EXE›2›EXE›3›EXE›4›EXE›5›EXE›6›EXE›FUNCTION
Example 22D vectors VctA = (3, 4), VctB = (1, 0)
Vector▸2D vectors→ enter A, B →FUNCTION
2D Result
VctA · VctB3
VctA × VctB(0, 0, −4)
|VctA|5
Angle53.1301023542
In 2D the cross product is the vector (0, 0, −4): the z-component −4 is the signed area of the parallelogram (3·0 − 4·1). |VctA| = √(3² + 4²) = 5, and the angle between the vectors is 53.13°.
Example 3Sum and difference — VctA + VctB and VctA − VctB (3D vectors)
FUNCTION▸VctA + VctB/VctA − VctB
Sum & Difference
VctA + VctB(5, 7, 9)
VctA − VctB(−3, −3, −3)
Vectors add and subtract component by component. Using VctA = (1, 2, 3) and VctB = (4, 5, 6): VctA + VctB = (5, 7, 9) and VctA − VctB = (−3, −3, −3). Both operands must have the same dimension.
Example 4The unit vector  of VctA = (3, 4)
FUNCTION▸Unit Vector Â
Unit Vector
|VctA|5
 (unit)(0.6, 0.8)
The unit vector  = A / |A| = (3/5, 4/5) = (0.6, 0.8) has length 1 and points the same way as A.
Reusing a result — VctAns
Every vector result is kept in VctAns, exactly like MatAns for matrices. Insert it from the CATALOG (in the Calculate app) to carry a vector result straight into the next expression.
Example 5To take the magnitude of a sum — |VctAns| after VctA + VctB
FUNCTION▸VctA + VctB→EXE→CalculateCATALOGVctAns
VctAns chaining
VctA + VctB → VctAns(5, 7, 9)
|VctAns|12.449899598
Using VctA = (1, 2, 3), VctB = (4, 5, 6): the sum (5, 7, 9) is held in VctAns. Reuse it in the Calculate app — for example |VctAns| = √(5² + 7² + 9²) = √155 ≈ 12.45 — without re-entering the vector.
Note
The angle uses the current Angle Unit — in Radian mode the same vectors give the angle in radians. VctAns always holds the most recent vector result, and the Calculate app's CATALOG provides VctA–VctD and VctAns so a vector can be carried into a free expression.
Note
A scalar vector result (such as a dot product) can be stored into a memory: on the result screen press VARIABLE and pick A–F, x, y or z. See “Storing a result from another app” in the Calculate chapter.
Ratio App Reference
RatioSolving proportions
The Ratio app finds the missing term X in a proportion A : B = C : D. Choose which position is unknown, enter the three known values, and the calculator solves for X by cross-multiplication.
Choosing the form
Ratio Form
1A : B = X : D
2A : B = C : X
Form 1 solves for the third term; form 2 solves for the fourth. Both use the rule that equal ratios cross-multiply: A · D = B · C.
Example 1To solve 3 : 4 = X : 8
Ratio▸A : B = X : D→ 3, 4, 8 →FUNCTION
A : B = X : D
A3
B4
D8
X6
X = (A · D) / B = (3 · 8) / 4 = 6. This is just the proportion 3⁄4 = X⁄8, so 4X = 24.
Key operation:
3›EXE›4›EXE›8›EXE›FUNCTION
Example 2To solve 3 : 4 = 6 : X
Ratio▸A : B = C : X→ 3, 4, 6 →FUNCTION
A : B = C : X
A3
B4
C6
X8
X = (B · C) / A = (4 · 6) / 3 = 8.
Example 3A zero divisor is rejected (3 : 0 = X : 8)
Ratio▸A : B = X : D→ 3, 0, 8 →FUNCTION
A : B = X : D
A3
B0
D8
Math ERROR
Solving needs a division by B (form 1) or A (form 2), so a 0 in that position makes the proportion undefined and returns Math ERROR. Re-enter a non-zero value to continue.
Note
Each ratio box opens pre-filled with 1 (A = 1, B = 1, D = 1 or C = 1), so you only overwrite the terms you know. Two ratios are equal exactly when their cross-products match (A · D = B · C).
Spreadsheet App Reference
SpreadsheetA calculator spreadsheet
The Spreadsheet app is a grid of 5 columns (A–E) × 45 rows. Each cell holds either a number or a formula that begins with = and may reference other cells (A1, B2, …). Formulas recalculate automatically as you edit.
Entering constants
Move the cursor with the arrow keys and type a number to enter a constant into a cell. Press EXE to confirm and drop to the next row. The examples in this chapter build on column A holding the values 1 to 5.
Example 1To enter the values 1–5 into cells A1 to A5
Spreadsheet→ point to A1 →1EXE2EXE…
Spreadsheet
A
1
1
2
2
3
3
4
4
5
5
Each value is typed and confirmed with EXE, which moves down to the next cell. The reference of a cell is its column letter and row number, so the value 3 sits in A3.
Entering formulas
Start a cell with = to make it a formula. A formula may contain numbers, operators and cell references (A1, B2, …). A reference always tracks the current value of that cell, so the formula recalculates automatically whenever the referenced cell changes.
Example 2To put =A1×2 in cell B1
point to B1→=A1×2EXE
Spreadsheet
A
B
1
1
2
2
2
3
3
4
4
5
5
B1 shows its computed value 2 (= 1 × 2). If you later change A1, B1 updates by itself. Use Show Cell (TOOLS) to view the underlying formula =A1×2 instead of the value.
Note
Enter the column letters A–E of a reference with the sincostanlogln keys (A, B, C, D, E respectively) and the row number with the number keys — so A1 is sin1 and B2 is cos2.
Relative and absolute references
When a formula is copied or filled to another cell, its references shift with it — these are relative references. A $ locks part of a reference so it does not shift: $A$1 is fully locked, A$1 locks only the row and $A1 only the column.
Example 3To fill =A1×2 down column B (relative reference)
B1→TOOLS ▸ Fill Formula→ range B1:B5 →EXE
Spreadsheet
A
B
1
1
2
2
2
4
3
3
6
4
4
8
5
5
10
Filling adjusts the relative reference for each row: B2 becomes =A2×2, B3 becomes =A3×2, and so on — giving 2, 4, 6, 8, 10.
Example 4To fill =A1×$A$5 down column C (absolute reference)
C1→TOOLS ▸ Fill Formula→ range C1:C5 →EXE
Spreadsheet
A
C
1
1
5
2
2
10
3
3
15
4
4
20
5
5
25
The $A$5 part is locked to cell A5 (= 5) in every row, while A1 shifts to A2, A3, … So the column becomes A × 5 = 5, 10, 15, 20, 25.
Range commands — Sum, Min, Max, Mean
The commands Sum(, Min(, Max( and Mean( operate over a block of cells written as a range such as A1:A5. Insert them from the SHEET commands in the CATALOG.
Example 5To total column A with =Sum(A1:A5)
CATALOG▸SHEET ▸ Sum(→ A1:A5 →EXE
Sheet
=Sum(A1:A5)
15
Sum adds every value in the range: 1 + 2 + 3 + 4 + 5 = 15.
Example 6To find the mean, maximum and minimum of A1:A5
CATALOG▸SHEET ▸ Mean( / Max( / Min(→ A1:A5 →EXE
Range commands
=Mean(A1:A5)3
=Max(A1:A5)5
=Min(A1:A5)1
Mean returns the average (15 ÷ 5 = 3), while Max and Min return the largest and smallest values in the range.
Batch input — Fill Value
To put the same constant into many cells at once, use Fill Value instead of typing it row by row.
Example 7To write the constant 100 into D1:D3 with Fill Value
TOOLS▸Fill Value→ Value 100, range D1:D3 →EXE
Spreadsheet
D
1
100
2
100
3
100
Fill Value writes the constant into every cell of the range in one step. Its companion Fill Formula (Examples 3–4) does the same for a formula, adjusting the relative references as it goes.
The spreadsheet TOOLS menu
Press TOOLS inside the sheet for editing commands that act on the pointed cell or range:
Command
What it does
Fill Formula
Copies a formula across a range, adjusting relative references (locked $ parts stay put).
Fill Value
Writes the same constant into every cell of a range.
Copy & Paste
Duplicates a cell, adjusting its relative references at the destination.
Cut & Paste
Moves a cell; references are kept and the source is cleared.
Grab
Point to a cell to insert its reference into the formula you are editing.
Show Cell
Toggles the grid between showing computed values and the underlying formulas.
Auto Calc
Turns automatic recalculation on or off; Recalculate refreshes on demand.
Delete All
Clears the whole spreadsheet.
Important!
The spreadsheet holds up to 5 × 45 = 225 cells. Turning Auto Calc off freezes the displayed values — useful while entering a large sheet — until you Recalculate.
Math Box App Reference
Math BoxLearning-support tools
The Math Box app is a set of interactive learning aids: probability experiments and visual number tools. Choose a tool from the menu.
The Math Box menu
Math Box
1Dice Roll
2Coin Toss
3Number Line
4Circle
Each tool runs an experiment or draws a figure you can explore. Point to a tool and press OK.
Example 1Dice Roll — 2 dice, 20 rolls, tallied by Sum
Math Box▸Dice Roll→ dice 2, attempts 20 →EXE▸Frequency
Dice Roll · Sum
Sum
Freq
5
3
6
5
7
6
8
4
Rolls 1–3 dice for a chosen number of attempts and tallies each outcome — a hands-on way to see experimental probability approach the theoretical values. After the run, choose List (every roll) or the Frequency table shown here. The Same Result setting (Off / #1 / #2 / #3) replays a fixed random sequence, so a whole class sees identical rolls (the dice count, attempts and Same Result slot must match on every calculator).
Example 2Dice Roll — the same 2 dice tallied by Difference
With two dice a second menu asks whether to tally by Sum (2–12) or by Difference (0–5) — the absolute gap between the two dice. Difference 1 is the most common, difference 5 the rarest, matching the theoretical shape. (This is one 20-roll run; your frequencies will differ unless Same Result is set.)
Example 3Coin Toss — 2 coins, 20 tosses
Math Box▸Coin Toss→ coins 2, attempts 20 →EXE▸Frequency
Coin Toss
Heads
Freq
0
5
1
11
2
4
With two coins the middle outcome (one head, one tail) is about twice as likely as two heads or two tails — visible directly in the tally. Coin Toss offers the same List / Frequency choice as the dice.
Example 4Number Line — draw 2 ≤ x < 5
Math Box▸Number Line▸a ≤ x < b→ 2, 5
Number Line
2 ≤ x < 5
●━━━━○ [2, 5)
Draws the solution of a simple inequality: a filled circle for an inclusive bound, an open circle for a strict one. Nine expression types are available, from x < a to a ≤ x ≤ b.
Example 5Number Line — up to three regions at once
Number Line→ slot 1, slot 2, slot 3 →EXE
Number Line ×3
x < 1 ; 2 ≤ x < 4 ; x ≥ 5
○─── ●━━○ ━●
The Number Line holds up to three expression slots and draws them on one axis, so regions can be compared side by side — here x < 1, the band 2 ≤ x < 4, and x ≥ 5. Any of the nine expression types can go in any slot.
Example 6Number Line — pan and zoom the view-window
on the drawn line:◀▶ pan · ▲▼ zoom · DEL reset
Number Line
2 ≤ x < 5 (zoomed in)
●━━━━━━━━○
The line first auto-fits to show every region with a little margin. On the drawn line you can then adjust the view-window: ◀▶ pan left / right, ▲ zoom in and ▼ zoom out (about the centre), and DEL snaps back to the automatic fit. Zooming in spreads a tight cluster of bounds apart so they are easier to read; zooming out reveals a region that sits far off to one side.
Example 7Circle — the Unit Circle at 30°
Math Box▸Circle▸Unit Circle→ θ 30 →EXE
Circle · Unit
θ₁30°
sin0.5
cos0.8660254038
tan0.5773502692
The point on the unit circle at 30° is (x, y) = (cos θ, sin θ) = (0.866, 0.5). The read-out lists sin, cos and tan of the angle — a visual link between an angle and its trig ratios. The three Circle types are Unit Circle, Half Circle and Clock.
Example 8Circle — two angles at once (45° and 135°)
Circle▸Unit Circle→ θ₁ 45, θ₂ 135 →EXE
Circle · two angles
θ₁45°
sin0.7071067812
cos0.7071067812
tan1
Enter a second angle θ₂ to draw two radii together; the selected one is drawn thicker and its sin/cos/tan are shown. Press ▲▼ to switch to θ₂ = 135° (sin 0.7071, cos −0.7071, tan −1). Half Circle works the same way but restricts angles to 0°–180° (0–π in Radian mode).
Example 9Circle — the Clock at 3:00
Circle▸Clock→ hour 3 →EXE
Circle · Clock
Time3:00
θ₁ (smaller)90°
θ₂ (larger)270°
The Clock shows the two angles between the hour and minute hands: at 3:00 they are θ₁ = 90° (the smaller) and θ₂ = 270° (the larger, θ₁ + θ₂ = 360°). Press ▲▼ to advance or rewind the hour one step at a time.
Note
Math Box tools are for exploration and teaching; they don't feed results into the other apps, but the frequency tables and coordinates can be read off directly.
The floating calculator (top) and its live extended display with the Big Number explain window (below).
The Big Number app does exact arithmetic on very large whole numbers — hundreds or thousands of digits — and shows the answer in full, never in exponential form. An ordinary calculator would round 102510000 to a short a × 10ⁿ value; Big Number prints every one of its 30,108 digits.
Opening Big NumberHOME ▸ Big Number
Press the ⌂ (HOME) key to open the app list and choose Big Number. (Big Number is opened from HOME — not from the blue MODE button, which only switches Normal / Step-by-Step in the Calculate app.) The screen shows the BIG NUMBER banner, an input line, and the result area.
Note
Results are exact integers. A division that does not come out evenly is carried to a set number of decimal places instead (see “Division precision”, below) — every other operation (+ − × and powers) is always exact.
Entering an expressionIntegers, + − × ÷, powers, parentheses
Type whole numbers with the digit keys and combine them with:
+−×÷ — add, subtract, multiply, divide;
▢^ — a power. The exponent is entered as a raised superscript, so 102510000 appears just as written; press ▶ to leave the exponent and continue;
() — parentheses for grouping.
Press EXE to evaluate. Use DEL to delete and AC to clear the line.
Important!
Big Number takes whole numbers only as input — there is no decimal point on entry. A decimal result can still appear (from division); it is shown to the chosen number of places.
Reading the resultDigit count, chips, quotient & remainder
After EXE the result area shows a digit count (for example “30,108 digits”) above the number itself. Three chips at the top-right of the display control how the answer is shown:
Chip
Meaning
1,000
Thousands grouping — inserts a comma every three digits so a long number is readable. On by default. This is display only; Copy always copies the plain, ungrouped digits.
×10ⁿ
Scientific form — adds an approximate ≈ a.bcde × 10ⁿ line beneath the full digits, giving the size of the number at a glance. Off by default.
÷ 20 dp
Division precision — how many decimal places a division is carried to. Press ▲ / ▼ to cycle 10 · 20 · 50 · 100.
For a plain whole-number division such as 100000 ÷ 7, a quotient and remainder line (= 14,285 R 5) is shown beneath the decimal value.
Example 1Whole-number division — decimal, quotient and remainder
100000÷7EXE
BIG NUMBER25 digits
100000 ÷ 7
14,285.71428571428571428571 = 14,285 R 5
At the default 20 dp the decimal is carried to twenty places; the reminder line gives the exact integer quotient (14,285) and remainder (5).
The extended display & explain windowPresent a big result
Press the ⧉ (cast) button to open the extended display — a large mirror of the calculator screen for a class or projector, marked LIVE DISPLAY. Below it, the explain window restates the expression, the digit count, and the complete grouped result in a scrolling panel, with a one-tap COPY that copies the raw digits. Both refresh automatically after each EXE (shown in the hero at the top of this chapter).
The FUNCTION menuNumber-theory operations with placeholder boxes
Press the FUNCTION key to insert a function. Each function is inserted as a template with empty ▢ boxes for its arguments — fill the first box, press ▶ (or ▼) to move to the next, and press ▶ once more to leave the closing bracket. You never type a comma.
Entry
Meaning
▢!
Factorial — n! = 1 × 2 × … × n.
a mod b
Remainder of a ÷ b.
gcd(▢, ▢)
Greatest common divisor.
lcm(▢, ▢)
Least common multiple.
nCr(▢, ▢)
Combinations — n choose r.
nPr(▢, ▢)
Permutations.
powmod(▢, ▢, ▢)
Modular power — ab mod m, computed without ever building the full power.
root(▢, ▢)
Integer n-th root — ⌊x1/n⌋.
isqrt(▢)
Integer square root — ⌊√x⌋.
digitsum(▢)
Sum of the decimal digits.
isprime(▢)
Primality test — 1 if prime, 0 if not.
sumeven(▢, ▢) · sumodd(▢, ▢)
Sum of the even / odd whole numbers in the range a…b.
factorize(▢)
Prime factorisation, as p^e × q × …
evens(▢, ▢) · odds(▢, ▢)
List the even / odd whole numbers in the range a…b (comma-separated).
primes(▢)
List the first n prime numbers.
fib(▢)
List the first n Fibonacci numbers (0, 1, 1, 2, 3, …).
pi(▢)
π to n decimal places (up to 50,000).
hex(▢) · bin(▢) · oct(▢)
Convert to base 16 / 2 / 8 (0x… / 0b… / 0o…).
Note
factorize, hex, bin, oct, evens, odds, primes, fib and pi produce text (a factor list, a based number, or a sequence), not a plain integer, so they can only be used on their own — not inside a larger sum. Their argument may itself be any expression, e.g. factorize(nCr(20, 10)). Every other function — including sumeven and sumodd — combines freely: gcd(48, 36) + 1 works.
Big Number can also list or add up a whole run of numbers and print π to any length. The list functions (evens, odds, primes, fib) return a comma-separated sequence; sumeven and sumodd return a single total; and pi(n) prints π to n decimal places. The list functions are capped so a huge request is refused rather than left to fill the screen.
Example 10Even & odd numbers in a range
evens(▢,▢)1▶20EXE
BIG NUMBER
evens(1, 20)
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
BIG NUMBER
odds(1, 20)
1, 3, 5, 7, 9, 11, 13, 15, 17, 19
Fill the low end (1), press ▶, fill the high end (20), then EXE. Up to 10,000 terms are listed.
Example 11Sum of the evens or odds in a range
sumeven(▢,▢)1▶100EXE
BIG NUMBER
sumeven(1, 100)
2,550
BIG NUMBER
sumodd(1, 100)
2,500
sumeven and sumodd add the even (or odd) whole numbers in the range. They return a plain integer, so they combine freely: sumeven(1, 100) + 1 works.
pi(n) gives π to n decimal places — up to 50,000 — computed with the fast Chudnovsky series.
Really big numbersThousands of digits, in full
Big Number handles results up to 50,000 digits. Powers are guarded so an over-large one is refused rather than left to hang the screen. Two examples that would overflow any ordinary calculator:
33,980 digits — the full number scrolls in the result area and the explain window.
Turn ×10ⁿ on to read the magnitude at a glance, keep 1,000 on to read the digits in groups, and use COPY to paste the exact number elsewhere — the copy is always the plain, ungrouped value.
Constants & Unit Conversions
Physical ConstantsCATALOG → CONST ▸
The CONST ▸ sub-menu inserts any of these 47 scientific constants (CODATA-based values) into a calculation. Point to a category, then to a constant, and press OK to insert its symbol and value. The six categories and their constants are:
Universal
Symbol
Constant
Value
Unit
h
Planck constant
6.62607015 × 10⁻³⁴
J·s
ħ
reduced Planck constant (h/2π)
1.054571817 × 10⁻³⁴
J·s
c
speed of light in vacuum
2.99792458 × 10⁸
m/s
ε₀
electric constant
8.8541878188 × 10⁻¹²
F/m
μ₀
magnetic constant
1.25663706127 × 10⁻⁶
N/A²
Z₀
vacuum impedance
376.730313412
Ω
G
gravitational constant
6.6743 × 10⁻¹¹
m³·kg⁻¹·s⁻²
lP
Planck length
1.616255 × 10⁻³⁵
m
tP
Planck time
5.391247 × 10⁻⁴⁴
s
Electromagnetic
Symbol
Constant
Value
Unit
μN
nuclear magneton
5.0507837393 × 10⁻²⁷
J/T
μB
Bohr magneton
9.2740100657 × 10⁻²⁴
J/T
e
elementary charge
1.602176634 × 10⁻¹⁹
C
Φ₀
magnetic flux quantum
2.067833848 × 10⁻¹⁵
Wb
G₀
conductance quantum
7.748091729 × 10⁻⁵
S
KJ
Josephson constant
4.835978484 × 10¹⁴
Hz/V
RK
von Klitzing constant
25812.80745
Ω
Atomic & Nuclear
Symbol
Constant
Value
Unit
mp
proton mass
1.67262192595 × 10⁻²⁷
kg
mn
neutron mass
1.67492750056 × 10⁻²⁷
kg
me
electron mass
9.1093837139 × 10⁻³¹
kg
mμ
muon mass
1.883531627 × 10⁻²⁸
kg
a₀
Bohr radius
5.29177210544 × 10⁻¹¹
m
α
fine-structure constant
0.0072973525643
—
re
classical electron radius
2.8179403205 × 10⁻¹⁵
m
λC
Compton wavelength
2.42631023538 × 10⁻¹²
m
γp
proton gyromagnetic ratio
2.6752218708 × 10⁸
s⁻¹·T⁻¹
λCp
proton Compton wavelength
1.3214098536 × 10⁻¹⁵
m
λCn
neutron Compton wavelength
1.31959090382 × 10⁻¹⁵
m
R∞
Rydberg constant
1.09737315682 × 10⁷
m⁻¹
μp
proton magnetic moment
1.41060679545 × 10⁻²⁶
J/T
μe
electron magnetic moment
−9.2847646917 × 10⁻²⁴
J/T
μn
neutron magnetic moment
−9.6623653 × 10⁻²⁷
J/T
μμ
muon magnetic moment
−4.4904483 × 10⁻²⁶
J/T
mτ
tau mass
3.16754 × 10⁻²⁷
kg
Physico-Chem
Symbol
Constant
Value
Unit
mu
atomic mass constant
1.66053906892 × 10⁻²⁷
kg
F
Faraday constant
96485.33212
C/mol
NA
Avogadro constant
6.02214076 × 10²³
mol⁻¹
k
Boltzmann constant
1.380649 × 10⁻²³
J/K
Vm
molar volume of ideal gas
0.02271095464
m³/mol
R
molar gas constant
8.314462618
J·mol⁻¹·K⁻¹
c₁
first radiation constant
3.741771852 × 10⁻¹⁶
W·m²
c₂
second radiation constant
0.01438776877
m·K
σ
Stefan-Boltzmann constant
5.670374419 × 10⁻⁸
W·m⁻²·K⁻⁴
Adopted Values
Symbol
Constant
Value
Unit
gn
std acceleration of gravity
9.80665
m/s²
atm
standard atmosphere
101325
Pa
RK-90
conventional von Klitzing
25812.807
Ω
KJ-90
conventional Josephson
4.835979 × 10¹⁴
Hz/V
Other
Symbol
Constant
Value
Unit
t
Celsius temperature (0 °C)
273.15
K
Note
Values follow the 2022 CODATA recommended set. A constant is inserted as its stored value; combine it with other terms just like any number.
Unit ConversionsCATALOG → CONV ▸
The CONV ▸ sub-menu converts the value currently on the display. First compute or type a value, then choose a category and a conversion; the display is replaced by the converted value. There are 40 conversions in nine categories:
Length
Conversion
Factor
in ▶ cm
× 2.54
cm ▶ in
÷ 2.54
ft ▶ m
× 0.3048
m ▶ ft
÷ 0.3048
yd ▶ m
× 0.9144
m ▶ yd
÷ 0.9144
mile ▶ km
× 1.609344
km ▶ mile
÷ 1.609344
n mile ▶ m
× 1852
m ▶ n mile
÷ 1852
pc ▶ km
× 3.0856776 × 10¹³
km ▶ pc
÷ 3.0856776 × 10¹³
Area
Conversion
Factor
acre ▶ m²
× 4046.856422
m² ▶ acre
÷ 4046.856422
Volume
Conversion
Factor
gal(US) ▶ L
× 3.785411784
L ▶ gal(US)
÷ 3.785411784
gal(UK) ▶ L
× 4.54609
L ▶ gal(UK)
÷ 4.54609
Mass
Conversion
Factor
oz ▶ g
× 28.349523125
g ▶ oz
÷ 28.349523125
lb ▶ kg
× 0.45359237
kg ▶ lb
÷ 0.45359237
Velocity
Conversion
Factor
km/h ▶ m/s
÷ 3.6
m/s ▶ km/h
× 3.6
Pressure
Conversion
Factor
atm ▶ Pa
× 101325
Pa ▶ atm
÷ 101325
mmHg ▶ Pa
× 133.322387415
Pa ▶ mmHg
÷ 133.322387415
kgf/cm² ▶ Pa
× 98066.5
Pa ▶ kgf/cm²
÷ 98066.5
lbf/in² ▶ kPa
× 6.894757293
kPa ▶ lbf/in²
÷ 6.894757293
Energy
Conversion
Factor
kgf·m ▶ J
× 9.80665
J ▶ kgf·m
÷ 9.80665
J ▶ cal₁₅
÷ 4.1858
cal₁₅ ▶ J
× 4.1858
Power
Conversion
Factor
hp ▶ kW
× 0.745699872
kW ▶ hp
÷ 0.745699872
Temperature
Conversion
Factor
°F ▶ °C
(x − 32) × 5⁄9
°C ▶ °F
x × 9⁄5 + 32
Note
Factors follow NIST Special Publication 811. Each conversion has a matching reverse conversion (for example in ▶ cm and cm ▶ in), so you can convert in either direction.
Technical Reference
Calculation Priority SequenceOrder of operations
The calculator evaluates an expression according to a fixed priority sequence. Basically, calculations run from left to right, expressions inside parentheses have the highest priority, and each command has the priority shown below.
Priority
Commands
1
Parenthetical expressions
2
Functions that take parentheses — sin(, cos(, tan(, ln(, log(, √, ∛, log▢(, Abs(, GCD(, LCM(, d/dx, ∫dx, Σ, Π, Pol(, Rec( and similar
3
Functions that come after a value — x², x³, x⁻¹, x!, %, angle units ° ʳ ᵍ — and powers (x▢) and roots (▢√▢)
4
Negative sign (−) and Base-N prefixes (d, h, b, o)
5
Permutation (nPr), combination (nCr), complex polar symbol (∠)
6
Implicit multiplication — an omitted × before a value, constant or bracket (2π, 3(1+2))
7
Multiplication (×), division (÷), dot product (·)
8
Addition (+), subtraction (−)
9
and (logical operator, Base-N)
10
or, xor, xnor (logical operators, Base-N)
Important!
Implicit multiplication (priority 6) binds tighter than explicit × and ÷ (priority 7). This is why 6 ÷ 2(1 + 2) = 1 — the calculator reads it as 6 ÷ (2 × (1 + 2)) — and 6 ÷ 2π = 0.9549… reads as 6 ÷ (2π).
Precautions when a calculation contains negative values
Because a postfix function such as x² (priority 3) binds tighter than the negative sign (priority 4), a leading minus applies to the whole power. To square a negative value you must enclose it in parentheses.
−2²=−4
Math DEG
−2²
−4
reads −(2²): the square is taken first, then negated
(−2)²=4
Math DEG
(−2)²
4
the parentheses square the whole value −2
Calculation Ranges, Digits and PrecisionHow the emulator computes
The SC-991BF emulator performs every calculation in IEEE-754 double precision — the same arithmetic used throughout modern computing — and then formats the answer the way a scientific calculator would.
Property
Value
Internal precision
Double precision — about 15–16 significant digits
Displayed digits (Norm)
Decimal results shown to up to 6 decimal places (trailing zeros removed); integer part shown in full. Use Fix 7–9 / Sci for more
Switch to scientific form
When |x| ≥ 1×10¹⁰ or |x| < 1×10⁻⁹ (Norm 2, default); < 1×10⁻² in Norm 1
Fix setting
Fixed number of decimal places, 0 to 9
Sci setting
Fixed number of significant figures
Note
Errors are cumulative across consecutive calculations, and tend to be larger near a function's singular points and inflection points. Functions that need repeated internal calculation — xʸ, ˣ√y, x!, nPr, nCr, numerical d/dx and ∫dx — can accumulate error with each step.
Function input ranges
The following table lists the practical input range of the main functions. Values outside a range give a Math ERROR.
Function
Input range
sin x, cos x, tan x
Degree: |x| < 9×10⁹ · Radian: |x| < 157079632.7 · (tan x undefined at odd multiples of 90°)
sin⁻¹x, cos⁻¹x
0 ≤ |x| ≤ 1
tan⁻¹x
|x| ≤ 9.999999999×10⁹⁹
sinh x, cosh x
|x| ≤ 230.2585092
sinh⁻¹x
|x| ≤ 4.999999999×10⁹⁹
cosh⁻¹x
1 ≤ x ≤ 4.999999999×10⁹⁹
tanh x
|x| ≤ 9.999999999×10⁹⁹
tanh⁻¹x
|x| ≤ 9.999999999×10⁻¹
log x, ln x
0 < x ≤ 9.999999999×10⁹⁹
10ˣ
−9.999999999×10⁹⁹ ≤ x ≤ 99.99999999
eˣ
−9.999999999×10⁹⁹ ≤ x ≤ 230.2585092
√x
0 ≤ x < 1×10¹⁰⁰
x²
|x| < 1×10⁵⁰
x⁻¹
|x| < 1×10¹⁰⁰; x ≠ 0
x!
0 ≤ x ≤ 69 (x is an integer)
nPr, nCr
0 ≤ r ≤ n; n < 1×10¹⁰ (n, r integers)
Pol(x, y)
|x|, |y| ≤ 9.999999999×10⁹⁹
Rec(r, θ)
0 ≤ r ≤ 9.999999999×10⁹⁹; θ same as sin x
RanInt#(a, b)
a < b; |a|, |b| < 1×10¹⁰
GCD(a, b), LCM(a, b)
integers, |a|, |b| < 1×10¹⁰
Note
The Base-N app works only with integers in the signed 32-bit range −2 147 483 648 to 2 147 483 647; a result outside this range is a Math ERROR.
Important!
Tangent singularities. tan x is undefined at odd multiples of 90° (90°, 270°, …; π⁄2, 3π⁄2, … in Radian mode), where the curve goes to infinity. Entering tan 90° gives a Math ERROR rather than a huge finite number. The trigonometric functions also reject arguments beyond about |x| = 9×10⁹ degrees, where rounding would make the result meaningless — this too is reported as a Math ERROR.
Error MessagesCauses and remedies
When a calculation cannot be completed, the calculator shows an error message instead of a result and returns you to the expression with the cursor already placed on the item that caused the problem — so you can correct it immediately without searching. (Press ◀ or ▶ to move on from there.) The common messages are:
Message
Cause
Remedy
Syntax ERROR
The expression is not written correctly — for example mismatched parentheses, or an operator with a missing operand.
Check the input at the cursor and correct the format.
Math ERROR
The calculation is mathematically undefined or out of range — division by zero, √ of a negative in real mode, or a value outside a function's input range (see the table above).
Check the values. For a square root or power that gives a complex result, use the Complex app.
Dimension ERROR
A matrix or vector operation was attempted on incompatible sizes — for example adding matrices of different dimensions, or multiplying when the columns of the first do not equal the rows of the second.
Re-enter the matrices or vectors with compatible dimensions.
Square only
A determinant or inverse was requested for a matrix that is not square.
Use a square matrix (equal rows and columns).
Argument ERROR
A command was given an argument outside its allowed set — for example an identity-matrix size below 1 or above the supported maximum.
Re-enter the command with an argument in range.
Stack ERROR
The calculation nested too deeply — most often a user-defined f(x)/g(x) that refers back to itself, so the evaluation never bottoms out.
Simplify the expression or remove the circular reference between f and g.
Variable ERROR
SOLVE was started on an expression that contains no variable to solve for (every term is a constant).
Include the unknown in the equation before solving.
Time Out
A ∑, ∏, ∫ or d/dx calculation could not finish within its working range — for example a summation whose index spans far too many terms.
Narrow the range or simplify the summand/integrand.
Can't Solve
SOLVE / the Equation Solver could not find any root from the given starting value.
Store a starting value in the variable closer to the expected root and solve again.
Could not converge
SOLVE / the Equation Solver reached its iteration limit without settling on a root. The best value so far is shown with its residual (L − R).
Press OK to Continue iterating from that value, or AC to Exit and keep the near-solution. For a better start, store a value in x closer to the expected root and solve again.
Note
Some apps also show short guidance messages such as No data, No equation, f(x) empty or Empty. These are not errors — they simply mean the app needs you to enter its data or expression before it can calculate.
None required — the emulator is software and is always ready to use on the host device
Note
Because the SC-991BF is a software emulator, there is no battery to replace and no low-battery warning: it is available whenever the app or web page is open, and its speed depends on the host device.
Frequently Asked Questions
Frequently Asked Questions
How can I switch a result between decimal and exact (fraction) form?
By default (MathI/MathO) a result appears in its exact “Standard” form (fraction, π, √). Press ⇄ (FORMAT / S⇔D) to toggle to its decimal value and back. To make results appear as a decimal from the start instead, change Input/Output in SETTINGS to MathI/DecimalO.
What is the difference between Ans memory and variable memory?
Both store a single value. Ans holds the result of the last calculation, letting you carry it straight into the next one (press Ans). A variable (A–F, x, y, z, M) is a named container you fill yourself and reuse whenever you need the same value more than once.
How can I find a function from an older calculator model?
Almost every function lives on the CATALOG. Press CATALOG to open the catalog menu, then pick the function or constant you need. See Using the CATALOG earlier in this guide for the full list.
How do I change the calculation result display format?
Press ⇄ (FORMAT) after a result to toggle exact ⇄ decimal, or open the full FORMAT menu (SHIFT⇄) for Prime Factor, Recurring Decimal, Sexagesimal, Standard Form and Improper/Mixed Fraction. Result defaults are set in SETTINGS (Number Format, Fraction Result, Complex Result).
How can I tell which calculator app I am currently using?
Press ⌂ (HOME). The icon of the app you are in is highlighted on the HOME screen.
How do I calculate sin² x ?
sin²x means (sin x)². Enter it as the square of the sine — for example sin²30° = (sin 30°)² = ¼:
(›sin›3›0›)›▢²›EXE
Why can’t I input i or calculate with complex numbers in Calculate?
The Calculate app works with real numbers. To enter the imaginary unit i or perform complex arithmetic, switch to the Complex app.
How can I return the calculator to its initial default settings?
Open any app from HOME, then press ⚙ (SETTINGS) and choose Reset ▸ Settings & Data ▸ Yes. This restores the default settings and clears memories.
Do I need to worry about the battery?
No. The SC-991BF is a software emulator, so it has no battery, never shows a low-battery warning, and is ready whenever you open it.