Lua Math Library

math

Standard Lua 5.1 math library.

`math.pi`

field

math.pi

The value of pi.

Usage

math.pi

Returns

number

Example

print(math.pi)  -- 3.1415926535898

`math.huge`

field

math.huge

A value larger than any other numeric value.

A value larger than or equal to any other numeric value (floating-point infinity).

Usage

math.huge

Returns

number

Example

print(math.huge)  -- inf

`math.abs`

function

math.abs(x)

Absolute value.

Returns the absolute value of x.

Usage

math.abs(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

number

Example

print(math.abs(-5))  -- 5

`math.ceil`

function

math.ceil(x)

Round up to an integer.

Returns the smallest integer larger than or equal to x.

Usage

math.ceil(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

integer

Example

print(math.ceil(4.1))  -- 5

`math.floor`

function

math.floor(x)

Round down to an integer.

Returns the largest integer smaller than or equal to x.

Usage

math.floor(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

integer

Example

print(math.floor(4.9))  -- 4

`math.sqrt`

function

math.sqrt(x)

Square root.

Returns the square root of x.

Usage

math.sqrt(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

number

Example

print(math.sqrt(16))  -- 4

`math.pow`

function

math.pow(x, y)

Exponentiation.

Returns x raised to the power y. Equivalent to the x^y operator.

Usage

math.pow(x, y)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Base.
`y`	number	Yes	Exponent.

Returns

number

Example

print(math.pow(2, 10))  -- 1024

`math.exp`

function

math.exp(x)

e raised to a power.

Returns the value e^x.

Usage

math.exp(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Exponent.

Returns

number

Example

print(math.exp(1))  -- 2.718281828459

`math.log`

function

math.log(x)

Natural logarithm.

Returns the natural logarithm of x.

Usage

math.log(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

number

Example

print(math.log(math.exp(1)))  -- 1

`math.log10`

function

math.log10(x)

Base-10 logarithm.

Returns the base-10 logarithm of x.

Usage

math.log10(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

number

Example

print(math.log10(100))  -- 2

`math.fmod`

function

math.fmod(x, y)

Remainder of x/y.

Returns the remainder of the division of x by y that rounds the quotient towards zero.

Usage

math.fmod(x, y)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Dividend.
`y`	number	Yes	Divisor.

Returns

number

Example

print(math.fmod(7, 3))   -- 1
print(math.fmod(-7, 3))  -- -1

`math.modf`

function

math.modf(x)

Split a number into integral and fractional parts.

Returns the integral part of x and the fractional part of x; both have the same sign as x.

Usage

local ip, fp = math.modf(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

integralPart, fractionalPart

Example

local Ip, Fp = math.modf(3.75)
print(Ip, Fp)  -- 3  0.75

`math.max`

function

math.max(x, ...)

Largest of the given numbers.

Returns the argument with the maximum value, among a list of one or more numbers.

Usage

math.max(x, ...)

Parameters

Name	Type	Required	Description
`...`	number	Yes	One or more numbers.

Returns

number

Example

print(math.max(3, 7, 2))  -- 7

`math.min`

function

math.min(x, ...)

Smallest of the given numbers.

Returns the argument with the minimum value, among a list of one or more numbers.

Usage

math.min(x, ...)

Parameters

Name	Type	Required	Description
`...`	number	Yes	One or more numbers.

Returns

number

Example

print(math.min(3, 7, 2))  -- 2

`math.random`

function

math.random([m [, n]])

Pseudo-random number.

With no arguments, returns a float in [0, 1). With one integer argument m, returns an integer in [1, m]. With two integer arguments m, n, returns an integer in [m, n].

Usage

math.random(m, n)

Parameters

Name	Type	Required	Description
`m`	integer	No	Lower bound (or upper bound when n is omitted).
`n`	integer	No	Upper bound.

Returns

number

Example

print(math.random())        -- e.g. 0.6046602879796
print(math.random(6))       -- integer in [1, 6]
print(math.random(10, 20))  -- integer in [10, 20]

`math.randomseed`

function

math.randomseed(x)

Seed the pseudo-random generator.

Sets x as the seed for the pseudo-random generator used by math.random.

Usage

math.randomseed(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Seed value.

Returns

none

Example

math.randomseed(os.time())

`math.sin`

function

math.sin(x)

Sine.

Returns the sine of x (radians).

Usage

math.sin(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Angle in radians.

Returns

number

Example

print(math.sin(0))  -- 0

`math.cos`

function

math.cos(x)

Cosine.

Returns the cosine of x (radians).

Usage

math.cos(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Angle in radians.

Returns

number

Example

print(math.cos(0))  -- 1

`math.tan`

function

math.tan(x)

Tangent.

Returns the tangent of x (radians).

Usage

math.tan(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Angle in radians.

Returns

number

Example

print(math.tan(0))  -- 0

`math.asin`

function

math.asin(x)

Arc sine.

Returns the arc sine of x (in radians).

Usage

math.asin(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

number

Example

print(math.asin(1))  -- 1.5707963267949

`math.acos`

function

math.acos(x)

Arc cosine.

Returns the arc cosine of x (in radians).

Usage

math.acos(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

number

Example

print(math.acos(1))  -- 0

`math.atan`

function

math.atan(x)

Arc tangent.

Returns the arc tangent of x (in radians).

Usage

math.atan(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

number

Example

print(math.atan(1))  -- 0.78539816339745

`math.atan2`

function

math.atan2(y, x)

Arc tangent of y/x.

Returns the arc tangent of y/x (in radians), using the signs of both arguments to determine the quadrant.

Usage

math.atan2(y, x)

Parameters

Name	Type	Required	Description
`y`	number	Yes	Numerator.
`x`	number	Yes	Denominator.

Returns

number

Example

print(math.atan2(1, 1))  -- 0.78539816339745

`math.deg`

function

math.deg(x)

Radians to degrees.

Converts angle x from radians to degrees.

Usage

math.deg(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Angle in radians.

Returns

number

Example

print(math.deg(math.pi))  -- 180

`math.rad`

function

math.rad(x)

Degrees to radians.

Converts angle x from degrees to radians.

Usage

math.rad(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Angle in degrees.

Returns

number

Example

print(math.rad(180))  -- 3.1415926535898

`math.sinh`

function

math.sinh(x)

Hyperbolic sine.

Returns the hyperbolic sine of x.

Usage

math.sinh(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

number

Example

print(math.sinh(0))  -- 0.0

`math.cosh`

function

math.cosh(x)

Hyperbolic cosine.

Returns the hyperbolic cosine of x.

Usage

math.cosh(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

number

Example

print(math.cosh(0))  -- 1.0

`math.tanh`

function

math.tanh(x)

Hyperbolic tangent.

Returns the hyperbolic tangent of x.

Usage

math.tanh(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

number

Example

print(math.tanh(0))  -- 0.0

`math.frexp`

function

math.frexp(x)

Split a number into mantissa and exponent.

Returns m (a multiplier, |m| in [0.5, 1)) and e (an integer exponent) such that x = m * 2^e. Used for portable, precision-safe manipulation of floating-point values.

Usage

math.frexp(x)

Parameters

Name	Type	Required	Description
`x`	number	Yes	Input value.

Returns

m (mantissa), e (exponent)

Example

local M, E = math.frexp(8)
print(M, E)  -- 0.5  4

`math.ldexp`

function

math.ldexp(m, e)

Build a number from a mantissa and exponent.

Returns m * 2^e. The inverse of math.frexp.

Usage

math.ldexp(m, e)

Parameters

Name	Type	Required	Description
`m`	number	Yes	Mantissa.
`e`	integer	Yes	Exponent.

Returns

number

Example

print(math.ldexp(0.5, 4))  -- 8

math.pi​

math.huge​

math.abs​

math.ceil​

math.floor​

math.sqrt​

math.pow​

math.exp​

math.log​

math.log10​

math.fmod​

math.modf​

math.max​

math.min​

math.random​

math.randomseed​

math.sin​

math.cos​

math.tan​

math.asin​

math.acos​

math.atan​

math.atan2​

math.deg​

math.rad​

math.sinh​

math.cosh​

math.tanh​

math.frexp​

math.ldexp​

`math.pi`

`math.huge`

`math.abs`

`math.ceil`

`math.floor`

`math.sqrt`

`math.pow`

`math.exp`

`math.log`

`math.log10`

`math.fmod`

`math.modf`

`math.max`

`math.min`

`math.random`

`math.randomseed`

`math.sin`

`math.cos`

`math.tan`

`math.asin`

`math.acos`

`math.atan`

`math.atan2`

`math.deg`

`math.rad`

`math.sinh`

`math.cosh`

`math.tanh`

`math.frexp`

`math.ldexp`