Math
A builtin object that has properties and methods for mathematical constants and functions. For example, the Math object's PI property has the value of pi.
Core object

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Created by
The Math object is a toplevel, predefined JavaScript object. You can automatically access it without using a constructor or calling a method.
Description
All properties and methods of Math are static. You refer to the constant PI as Math.PI and you call the sine function as Math.sin(x), where x is the method's argument. Constants are defined with the full precision of real numbers in JavaScript.
It is often convenient to use the with statement when a section of code uses several Math constants and methods, so you don't have to type "Math" repeatedly. For example,
with (Math) {
a = PI * r*r
y = r*sin(theta)
x = r*cos(theta)
}
Property Summary
Property

Description

E

Euler's constant and the base of natural logarithms, approximately 2.718.

LN2

Natural logarithm of 2, approximately 0.693.

LN10

Natural logarithm of 10, approximately 2.302.

LOG2E

Base 2 logarithm of E (approximately 1.442).

LOG10E

Base 10 logarithm of E (approximately 0.434).

PI

Ratio of the circumference of a circle to its diameter, approximately 3.14159.

SQRT1_2

Square root of 1/2; equivalently, 1 over the square root of 2, approximately 0.707.

SQRT2

Square root of 2, approximately 1.414.

Method Summary
Method

Description

abs

Returns the absolute value of a number.

acos

Returns the arccosine (in radians) of a number.

asin

Returns the arcsine (in radians) of a number.

atan

Returns the arctangent (in radians) of a number.

atan2

Returns the arctangent of the quotient of its arguments.

ceil

Returns the smallest integer greater than or equal to a number.

cos

Returns the cosine of a number.

exp

Returns E^{number}, where number is the argument, and E is Euler's constant, the base of the natural logarithms.

floor

Returns the largest integer less than or equal to a number.

log

Returns the natural logarithm (base E) of a number.

max

Returns the greater of two numbers.

min

Returns the lesser of two numbers.

pow

Returns base to the exponent power, that is, base ^{exponent}.

random

Returns a pseudorandom number between 0 and 1.

round

Returns the value of a number rounded to the nearest integer.

sin

Returns the sine of a number.

sqrt

Returns the square root of a number.

tan

Returns the tangent of a number.

In addition, this object inherits the watch and unwatch methods from Object.
abs
Returns the absolute value of a number.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
abs(x)
Parameters
Examples
The following function returns the absolute value of the variable x:
function getAbs(x) {
return Math.abs(x)
}
Description
Because abs is a static method of Math, you always use it as Math.abs(), rather than as a method of a Math object you created.
acos
Returns the arccosine (in radians) of a number.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
acos(x)
Parameters
Description
The acos method returns a numeric value between 0 and pi radians. If the value of number is outside this range, it returns NaN.
Because acos is a static method of Math, you always use it as Math.acos(), rather than as a method of a Math object you created.
Examples
The following function returns the arccosine of the variable x:
function getAcos(x) {
return Math.acos(x)
}
If you pass 1 to getAcos, it returns 3.141592653589793; if you pass 2, it returns NaN because 2 is out of range.
See also
Math.asin, Math.atan, Math.atan2, Math.cos, Math.sin, Math.tan
asin
Returns the arcsine (in radians) of a number.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
asin(x)
Parameters
Description
The asin method returns a numeric value between pi/2 and pi/2 radians. If the value of number is outside this range, it returns NaN.
Because asin is a static method of Math, you always use it as Math.asin(), rather than as a method of a Math object you created.
Examples
The following function returns the arcsine of the variable x:
function getAsin(x) {
return Math.asin(x)
}
If you pass getAsin the value 1, it returns 1.570796326794897 (pi/2); if you pass it the value 2, it returns NaN because 2 is out of range.
See also
Math.acos, Math.atan, Math.atan2, Math.cos, Math.sin, Math.tan
atan
Returns the arctangent (in radians) of a number.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
atan(x)
Parameters
Description
The atan method returns a numeric value between pi/2 and pi/2 radians.
Because atan is a static method of Math, you always use it as Math.atan(), rather than as a method of a Math object you created.
Examples
The following function returns the arctangent of the variable x:
function getAtan(x) {
return Math.atan(x)
}
If you pass getAtan the value 1, it returns 0.7853981633974483; if you pass it the value .5, it returns 0.4636476090008061.
See also
Math.acos, Math.asin, Math.atan2, Math.cos, Math.sin, Math.tan
atan2
Returns the arctangent of the quotient of its arguments.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
atan2(y, x)
Parameters
Description
The atan2 method returns a numeric value between pi and pi representing the angle theta of an (x,y) point. This is the counterclockwise angle, measured in radians, between the positive X axis, and the point (x,y). Note that the arguments to this function pass the ycoordinate first and the xcoordinate second.
atan2 is passed separate x and y arguments, and atan is passed the ratio of those two arguments.
Because atan2 is a static method of Math, you always use it as Math.atan2(), rather than as a method of a Math object you created.
Examples
The following function returns the angle of the polar coordinate:
function getAtan2(x,y) {
return Math.atan2(x,y)
}
If you pass getAtan2 the values (90,15), it returns 1.4056476493802699; if you pass it the values (15,90), it returns 0.16514867741462683.
See also
Math.acos, Math.asin, Math.atan, Math.cos, Math.sin, Math.tan
ceil
Returns the smallest integer greater than or equal to a number.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
ceil(x)
Parameters
Description
Because ceil is a static method of Math, you always use it as Math.ceil(), rather than as a method of a Math object you created.
Examples
The following function returns the ceil value of the variable x:
function getCeil(x) {
return Math.ceil(x)
}
If you pass 45.95 to getCeil, it returns 46; if you pass 45.95, it returns 45.
See also
Math.floor
cos
Returns the cosine of a number.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
cos(x)
Parameters
Description
The cos method returns a numeric value between 1 and 1, which represents the cosine of the angle.
Because cos is a static method of Math, you always use it as Math.cos(), rather than as a method of a Math object you created.
Examples
The following function returns the cosine of the variable x:
function getCos(x) {
return Math.cos(x)
}
If x equals 2*Math.PI, getCos returns 1; if x equals Math.PI, the getCos method returns 1.
See also
Math.acos, Math.asin, Math.atan, Math.atan2, Math.sin, Math.tan
E
Euler's constant and the base of natural logarithms, approximately 2.718.
Property of

Math

Static, Readonly

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Description
Because E is a static property of Math, you always use it as Math.E, rather than as a property of a Math object you created.
Examples
The following function returns Euler's constant:
function getEuler() {
return Math.E
}
exp
Returns E^{x}, where x is the argument, and E is Euler's constant, the base of the natural logarithms.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
exp(x)
Parameters
Description
Because exp is a static method of Math, you always use it as Math.exp(), rather than as a method of a Math object you created.
Examples
The following function returns the exponential value of the variable x:
function getExp(x) {
return Math.exp(x)
}
If you pass getExp the value 1, it returns 2.718281828459045.
See also
Math.E, Math.log, Math.pow
floor
Returns the largest integer less than or equal to a number.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
floor(x)
Parameters
Description
Because floor is a static method of Math, you always use it as Math.floor(), rather than as a method of a Math object you created.
Examples
The following function returns the floor value of the variable x:
function getFloor(x) {
return Math.floor(x)
}
If you pass 45.95 to getFloor, it returns 45; if you pass 45.95, it returns 46.
See also
Math.ceil
LN2
The natural logarithm of 2, approximately 0.693.
Property of

Math

Static, Readonly

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Examples
The following function returns the natural log of 2:
function getNatLog2() {
return Math.LN2
}
Description
Because LN2 is a static property of Math, you always use it as Math.LN2, rather than as a property of a Math object you created.
LN10
The natural logarithm of 10, approximately 2.302.
Property of

Math

Static, Readonly

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Examples
The following function returns the natural log of 10:
function getNatLog10() {
return Math.LN10
}
Description
Because LN10 is a static property of Math, you always use it as Math.LN10, rather than as a property of a Math object you created.
log
Returns the natural logarithm (base E) of a number.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
log(x)
Parameters
Description
If the value of number is negative, the return value is always NaN.
Because log is a static method of Math, you always use it as Math.log(), rather than as a method of a Math object you created.
Examples
The following function returns the natural log of the variable x:
function getLog(x) {
return Math.log(x)
}
If you pass getLog the value 10, it returns 2.302585092994046; if you pass it the value 0, it returns Infinity; if you pass it the value 1, it returns NaN because 1 is out of range.
See also
Math.exp, Math.pow
LOG2E
The base 2 logarithm of E (approximately 1.442).
Property of

Math

Static, Readonly

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Examples
The following function returns the base 2 logarithm of E:
function getLog2e() {
return Math.LOG2E
}
Description
Because LOG2E is a static property of Math, you always use it as Math.LOG2E, rather than as a property of a Math object you created.
LOG10E
The base 10 logarithm of E (approximately 0.434).
Property of

Math

Static, Readonly

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Examples
The following function returns the base 10 logarithm of E:
function getLog10e() {
return Math.LOG10E
}
Description
Because LOG10E is a static property of Math, you always use it as Math.LOG10E, rather than as a property of a Math object you created.
max
Returns the larger of two numbers.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
max(x,y)
Parameters
Description
Because max is a static method of Math, you always use it as Math.max(), rather than as a method of a Math object you created.
Examples
The following function evaluates the variables x and y:
function getMax(x,y) {
return Math.max(x,y)
}
If you pass getMax the values 10 and 20, it returns 20; if you pass it the values 10 and 20, it returns 10.
See also
Math.min
min
Returns the smaller of two numbers.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
min(x,y)
Parameters
Description
Because min is a static method of Math, you always use it as Math.min(), rather than as a method of a Math object you created.
Examples
The following function evaluates the variables x and y:
function getMin(x,y) {
return Math.min(x,y)
}
If you pass getMin the values 10 and 20, it returns 10; if you pass it the values 10 and 20, it returns 20.
See also
Math.max
PI
The ratio of the circumference of a circle to its diameter, approximately 3.14159.
Property of

Math

Static, Readonly

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Examples
The following function returns the value of pi:
function getPi() {
return Math.PI
}
Description
Because PI is a static property of Math, you always use it as Math.PI, rather than as a property of a Math object you created.
pow
Returns base to the exponent power, that is, base^{exponent}.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
pow(x,y)
Parameters
base

The base number

exponent

The exponent to which to raise base

Description
Because pow is a static method of Math, you always use it as Math.pow(), rather than as a method of a Math object you created.
Examples
function raisePower(x,y) {
return Math.pow(x,y)
}
If x is 7 and y is 2, raisePower returns 49 (7 to the power of 2).
See also
Math.exp, Math.log
random
Returns a pseudorandom number between 0 and 1. The random number generator is seeded from the current time, as in Java.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0: Unix only
JavaScript 1.1, NES 2.0: all platforms

ECMA version

ECMA262

Syntax
random()
Parameters
None.
Description
Because random is a static method of Math, you always use it as Math.random(), rather than as a method of a Math object you created.
Examples
//Returns a random number between 0 and 1
function getRandom() {
return Math.random()
}
round
Returns the value of a number rounded to the nearest integer.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
round(x)
Parameters
Description
If the fractional portion of number is .5 or greater, the argument is rounded to the next higher integer. If the fractional portion of number is less than .5, the argument is rounded to the next lower integer.
Because round is a static method of Math, you always use it as Math.round(), rather than as a method of a Math object you created.
Examples
//Returns the value 20
x=Math.round(20.49)
//Returns the value 21
x=Math.round(20.5)
//Returns the value 20
x=Math.round(20.5)
//Returns the value 21
x=Math.round(20.51)
sin
Returns the sine of a number.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
sin(x)
Parameters
Description
The sin method returns a numeric value between 1 and 1, which represents the sine of the argument.
Because sin is a static method of Math, you always use it as Math.sin(), rather than as a method of a Math object you created.
Examples
The following function returns the sine of the variable x:
function getSine(x) {
return Math.sin(x)
}
If you pass getSine the value Math.PI/2, it returns 1.
See also
Math.acos, Math.asin, Math.atan, Math.atan2, Math.cos, Math.tan
sqrt
Returns the square root of a number.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
sqrt(x)
Parameters
Description
If the value of number is negative, sqrt returns NaN.
Because sqrt is a static method of Math, you always use it as Math.sqrt(), rather than as a method of a Math object you created.
Examples
The following function returns the square root of the variable x:
function getRoot(x) {
return Math.sqrt(x)
}
If you pass getRoot the value 9, it returns 3; if you pass it the value 2, it returns 1.414213562373095.
SQRT1_2
The square root of 1/2; equivalently, 1 over the square root of 2, approximately 0.707.
Property of

Math

Static, Readonly

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Examples
The following function returns 1 over the square root of 2:
function getRoot1_2() {
return Math.SQRT1_2
}
Description
Because SQRT1_2 is a static property of Math, you always use it as Math.SQRT1_2, rather than as a property of a Math object you created.
SQRT2
The square root of 2, approximately 1.414.
Property of

Math

Static, Readonly

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Examples
The following function returns the square root of 2:
function getRoot2() {
return Math.SQRT2
}
Description
Because SQRT2 is a static property of Math, you always use it as Math.SQRT2, rather than as a property of a Math object you created.
tan
Returns the tangent of a number.
Method of

Math

Static

Implemented in

JavaScript 1.0, NES 2.0

ECMA version

ECMA262

Syntax
tan(x)
Parameters
Description
The tan method returns a numeric value that represents the tangent of the angle.
Because tan is a static method of Math, you always use it as Math.tan(), rather than as a method of a Math object you created.
Examples
The following function returns the tangent of the variable x:
function getTan(x) {
return Math.tan(x)
}
See also
Math.acos, Math.asin, Math.atan, Math.atan2, Math.cos, Math.sin