Function & Syntax Reference — Scientific Calculator Input

Operators and precedence

Higher-precedence operations are evaluated first. Within the same level, evaluation goes left to right, except powers, which go right to left.

Level	Operation	Example	Result
1	Brackets `( )`, function calls	`(1+2)×3`	9
2	Postfix `!` `%` `°`	`3!²`	36
3	Power `^` (right-associative)	`2^3^2`	512
4	Unary sign `-` `+`	`-2^2`	−4
5	`×` `÷` `mod`, implied multiplication	`6÷2(1+2)`	9
6	`+` `−`	`10−4−3`	3

-2^2 = −4 follows the same convention as the mathematical notation −2². To square a negative number, bracket it: (-2)^2. A sign in the exponent works as written (2^-3 = 0.125).

Implied multiplication (2π, 3(4+5), 2x) has the same precedence as ordinary multiplication. So 1/2π is (1/2)×π; for 1/(2π) you need brackets. Two numbers separated by a space, as in 2 3, is an error.

% only divides by 100: 200×15% = 30, 100+10% = 100.1 (the desk-calculator markup rule is not applied).

° converts a value in degrees to the current angle unit. Even in RAD mode, sin(30°) = 0.5.

Numbers and input rules

Decimal point: 3.5, .5 · Exponent notation: 6.02E23, 1.6e-19 (E or e immediately after a number, followed by an integer)
Without an integer after e, as in 2e, it means multiplication by Euler's number e (2e ≈ 5.43656).
Base literals: 0x1F = 31, 0b1011 = 11, 0o17 = 15
You can type multiplication as × or *, division as ÷ or /, and subtraction as − or -.
Functions always need brackets (sin(30)). Separate multiple arguments with commas.
Unclosed brackets at the end of an expression are closed automatically: sin(30 → sin(30).
Names are case-sensitive; when written together, the longest name is matched first (2πx = 2·π·x).
Starting with an operator, as in ×2, puts the previous result Ans in front.

Trigonometric and inverse trig functions (angle unit applies)

Syntax	Description	Example	Result (DEG)
`sin(x)`	Sine	`sin(30)`	0.5
`cos(x)`	Cosine	`cos(60)`	0.5
`tan(x)`	Tangent. Undefined at odd multiples of 90°	`tan(45)`	1
`asin(x)`	Inverse sine, −1 ≤ x ≤ 1. Result in the current angle unit	`asin(0.5)`	30
`acos(x)`	Inverse cosine, −1 ≤ x ≤ 1	`acos(-0.5)`	120
`atan(x)`	Inverse tangent	`atan(1)`	45
`atan2(y, x)`	Argument of point (x, y). Quadrant-aware (−180° to 180°)	`atan2(1, -1)`	135

Hyperbolic functions (independent of angle unit)

Syntax	Description	Example	Result (DEG)
`sinh(x)`	Hyperbolic sine	`sinh(1)`	1.17520119364
`cosh(x)`	Hyperbolic cosine	`cosh(1)`	1.54308063482
`tanh(x)`	Hyperbolic tangent	`tanh(0.5)`	0.46211715726
`asinh(x)`	Inverse hyperbolic sine	`asinh(1)`	0.88137358702
`acosh(x)`	Inverse hyperbolic cosine, x ≥ 1	`acosh(2)`	1.31695789692
`atanh(x)`	Inverse hyperbolic tangent, −1 < x < 1	`atanh(0.5)`	0.549306144334

Exponentials and logarithms

Syntax	Description	Example	Result (DEG)
`log(x)`	Common logarithm (base 10), x > 0	`log(1000)`	3
`ln(x)`	Natural logarithm (base e), x > 0	`ln(e^2)`	2
`log(a, x)`	Logarithm to base a, logₐx — base comes first	`log(2, 8)`	3
`log2(x)`	Binary logarithm	`log2(1024)`	10
`exp(x)`	eˣ (same as e^x)	`exp(1)`	2.71828182846
`10^x`	Power of ten	`10^-3`	0.001

Powers and roots

Syntax	Description	Example	Result (DEG)
`x^y`	Power. A negative base gives a real result only for fractional exponents with an odd denominator	`(-8)^(1/3)`	−2
`x² x³`	Square and cube (x^2, x^3)	`12²`	144
`sqrt(x) · √x`	Square root, x ≥ 0. √ applies only to the number or bracket right after it	`√(2)`	1.41421356237
`cbrt(x)`	Cube root (negatives allowed)	`cbrt(-27)`	−3
`root(x, n)`	n-th root of x. Negative x only when n is odd	`root(81, 4)`	3
`x^(-1)`	Reciprocal	`4^(-1)`	0.25

Factorials and combinatorics

Syntax	Description	Example	Result (DEG)
`n!`	Factorial. Integers 0 to 170 (171! overflows)	`10!`	3628800
`nPr(n, r)`	Permutations n!/(n−r)!	`nPr(10, 3)`	720
`nCr(n, r)`	Combinations n!/(r!(n−r)!)	`nCr(45, 6)`	8145060
`gcd(a, b)`	Greatest common divisor (integers)	`gcd(84, 36)`	12
`lcm(a, b)`	Least common multiple (integers)	`lcm(4, 6)`	12

Rounding and more

Syntax	Description	Example	Result (DEG)
`round(x) · round(x, n)`	Round (to n decimal places). .5 rounds away from zero	`round(2.675, 2)`	2.68
`floor(x)`	Round down (floor)	`floor(-2.5)`	−3
`ceil(x)`	Round up (ceiling)	`ceil(-2.5)`	−2
`trunc(x)`	Drop the fractional part (toward zero)	`trunc(-2.7)`	−2
`frac(x)`	Fractional part	`frac(3.75)`	0.75
`abs(x)`	Absolute value	`abs(-7.5)`	7.5
`x mod y`	Remainder. Takes the sign of the divisor	`-7 mod 3`	2
`sign(x)`	Sign (−1, 0, 1)	`sign(-4)`	−1
`min(…) · max(…)`	Minimum and maximum (any number of arguments)	`max(3, 9, 4)`	9
`hypot(a, b)`	√(a²+b²)	`hypot(5, 12)`	13
`deg(x) · rad(x)`	Convert radians to degrees, degrees to radians	`deg(π/3)`	60
`x%`	x ÷ 100	`200×15%`	30
`x°`	Degree value in the current angle unit	`sin(30°)`	0.5

Constants and variables

Syntax	Description	Example	Result (DEG)
`π · pi`	Pi	`2π`	6.28318530718
`e`	Euler's number	`e^1`	2.71828182846
`φ · phi`	Golden ratio (1+√5)/2	`φ^2-φ`	1
`Ans`	Last confirmed result	`Ans`	0
`x · y · z`	Variables stored with STO	`x`	3
`M`	Independent memory (M+ · M−)	`M`	0
`c0 · hP · NA …`	20 physical constants (see the constants table)	`c0`	299792458

Example results were computed with this site's calculation engine at build time (2026-09-24) and are shown to 12 significant digits.

Display formats and precision

NORM: plain notation when the magnitude is at least 10⁻⁹ and below 10¹²; otherwise switches to scientific notation automatically.
SCI: always shows a.bcd×10ⁿ with the chosen number of significant digits.
ENG: keeps the exponent a multiple of 3 (×10³ = k, ×10⁻⁶ = μ). Convenient for engineering units.
Significant digits: 6 to 15 (default 12). Internal calculation uses IEEE 754 double precision; rounding happens only for display.
Fractions: if the result matches a fraction with a denominator up to 10,000 within display precision, the fraction is shown too (0.75 → 3/4).
Multiples of π: simple multiples of π are shown as well, e.g. π/2.
Number bases: integer results up to 2⁵³ also show binary, octal and hexadecimal values.

Error messages

Message	Cause	Example
Syntax error	Unmatched brackets or operators, function without brackets	`2+`, `sin 30`, `2 3`
Unknown name	Unsupported name	`r`, `sec(1)`
Math error	Outside the domain	`√(-1)`, `log(0)`, `asin(2)`, `1/0`
Undefined	The value does not exist at that point	`tan(90)` (DEG)
Overflow	Exceeds about 1.797×10³⁰⁸	`171!`, `10^400`

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