Math Functions
Quick Reference:
General Math
Abs Absolute value
Value := Abs(Number)
Returns the absolute value of Number.
The return value is the same type as Number (integer or floating point).
MsgBox, % Abs(-1.2) ; Returns 1.2
Ceil Rounding up
Value := Ceil(Number)
Returns Number rounded up to the nearest integer (without any .00 suffix).
MsgBox, % Ceil(1.2) ; Returns 2 MsgBox, % Ceil(-1.2) ; Returns -1
Exp Exponential
Value := Exp(N)
Returns e (which is approximately 2.71828182845905) raised to the Nth power.
N may be negative and may contain a decimal point. To raise numbers other than e to a power, use the ** operator.
MsgBox, % Exp(1.2) ; Returns 3.320117
Floor Rounding down
Value := Floor(Number)
Returns Number rounded down to the nearest integer (without any .00 suffix).
MsgBox, % Floor(1.2) ; Returns 1 MsgBox, % Floor(-1.2) ; Returns -2
Log Decimal logarithm
Value := Log(Number)
Returns the logarithm (base 10) of Number.
The result is formatted as floating point. If Number is negative, an empty string is returned.
MsgBox, % Log(1.2) ; Returns 0.079181
Ln Natural logarithm
Value := Ln(Number)
Returns the natural logarithm (base e) of Number.
The result is formatted as floating point. If Number is negative, an empty string is returned.
MsgBox, % Ln(1.2) ; Returns 0.182322
Max Highest value [v1.1.27+]
Value := Max(Number1 [, Number2, ...])
Returns the highest value of one or more numbers.
If one of the input values is non-numeric, an empty string is returned.
MsgBox, % Max(2.11, -2, 0) ; Returns 2.11
You can also specify a variadic parameter to compare multiple values within an array. For example:
array := [1, 2, 3, 4] MsgBox, % Max(array*) ; Returns 4
Min Lowest value [v1.1.27+]
Value := Min(Number1 [, Number2, ...])
Returns the lowest value of one or more numbers.
If one of the input values is non-numeric, an empty string is returned.
MsgBox, % Min(2.11, -2, 0) ; Returns -2
You can also specify a variadic parameter to compare multiple values within an array. For example:
array := [1, 2, 3, 4] MsgBox, % Min(array*) ; Returns 1
Mod Remainder after division (Modulo)
Value := Mod(Dividend, Divisor)
Returns the remainder when Dividend is divided by Divisor.
The sign of the result is always the same as the sign of the first parameter. If either input is a floating point number, the result is also a floating point number. If the second parameter is zero, the function yields a blank result (empty string).
MsgBox, % Mod(7.5, 2) ; Returns 1.5 (2 x 3 + 1.5)
Round Rounding
Value := Round(Number [, N])
Returns Number rounded to N decimal places.
If N is omitted or 0, Number is rounded to the nearest integer:
MsgBox, % Round(3.14) ; Returns 3
If N is positive number, Number is rounded to N decimal places:
MsgBox, % Round(3.14, 1) ; Returns 3.1
If N is negative, Number is rounded by N digits to the left of the decimal point:
MsgBox, % Round(345, -1) ; Returns 350 MsgBox, % Round(345, -2) ; Returns 300
Unlike Transform Round, the result has no .000 suffix whenever N is omitted or less than 1. [v1.0.44.01+]: A value of N greater than zero displays exactly N decimal places rather than obeying SetFormat. To avoid this, perform another math operation on Round()'s return value; for example: Round(3.333, 1)+0.
Sqrt Square root
Value := Sqrt(Number)
Returns the square root of Number.
The result is formatted as floating point. If Number is negative, the function yields a blank result (empty string).
MsgBox, % Sqrt(16) ; Returns 4
Trigonometry
Note: To convert a radians value to degrees, multiply it by 180/pi (approximately 57.29578). To convert a degrees value to radians, multiply it by pi/180 (approximately 0.01745329252). The value of pi (approximately 3.141592653589793) is 4 times the arctangent of 1.
Sin Sine
Value := Sin(Number)
Returns the trigonometric sine of Number.
Number must be expressed in radians.
MsgBox, % Sin(1.2) ; Returns 0.932039
Cos Cosine
Value := Cos(Number)
Returns the trigonometric cosine of Number.
Number must be expressed in radians.
MsgBox, % Cos(1.2) ; Returns 0.362358
Tan Tangent
Value := Tan(Number)
Returns the trigonometric tangent of Number.
Number must be expressed in radians.
MsgBox, % Tan(1.2) ; Returns 2.572152
ASin Arcsine
Value := ASin(Number)
Returns the arcsine (the number whose sine is Number) in radians.
If Number is less than -1 or greater than 1, the function yields a blank result (empty string).
MsgBox, % ASin(0.2) ; Returns 0.201358
ACos Arccosine
Value := ACos(Number)
Returns the arccosine (the number whose cosine is Number) in radians.
If Number is less than -1 or greater than 1, the function yields a blank result (empty string).
MsgBox, % ACos(0.2) ; Returns 1.369438
ATan Arctangent
Value := ATan(Number)
Returns the arctangent (the number whose tangent is Number) in radians.
MsgBox, % ATan(1.2) ; Returns 0.876058
Error-Handling
Invalid operations such as divide by zero generally yield a blank result (empty string).
Abs, Max, Min and Mod return an empty string if any of their incoming parameters are non-numeric. Most math functions do not perform strict type-checking, so may treat non-numeric values as zero or another number. For example, Round("1.0foo") produces 1. However, this is expected to change in AutoHotkey v2.