# Core JavaScript 1.5 Reference - Math Object

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Core JavaScript Reference 1.5

Math

A built-in 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 ECMA-262

Created by
The Math object is a top-level, 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 Enumber, 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 pseudo-random 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 Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
abs(x)

Parameters

 x A number

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 Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
acos(x)

Parameters

 x A number

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.

Math.asin, Math.atan, Math.atan2, Math.cos, Math.sin, Math.tan

asin

Returns the arcsine (in radians) of a number.

 Method of Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
asin(x)

Parameters

 x A number

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.

Math.acos, Math.atan, Math.atan2, Math.cos, Math.sin, Math.tan

atan

Returns the arctangent (in radians) of a number.

 Method of Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
atan(x)

Parameters

 x A number

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.

Math.acos, Math.asin, Math.atan2, Math.cos, Math.sin, Math.tan

atan2

Returns the arctangent of the quotient of its arguments.

 Method of Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
atan2(y, x)

Parameters

 y, x Number

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 y-coordinate first and the x-coordinate 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.

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 Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
ceil(x)

Parameters

 x A number

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.

Math.floor

cos

Returns the cosine of a number.

 Method of Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
cos(x)

Parameters

 x A number

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.

E

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

 Property of Static, Read-only Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

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 Ex, where x is the argument, and E is Euler's constant, the base of the natural logarithms.

 Method of Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
exp(x)

Parameters

 x A number

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.

Math.E, Math.log, Math.pow

floor

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

 Method of Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
floor(x)

Parameters

 x A number

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.

Math.ceil

LN2

The natural logarithm of 2, approximately 0.693.

 Property of Static, Read-only Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

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 Static, Read-only Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

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 Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
log(x)

Parameters

 x A number

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.

Math.exp, Math.pow

LOG2E

The base 2 logarithm of E (approximately 1.442).

 Property of Static, Read-only Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

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 Static, Read-only Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

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 Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
max(x,y)

Parameters

 x, y Numbers.

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.

Math.min

min

Returns the smaller of two numbers.

 Method of Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
min(x,y)

Parameters

 x, y Numbers

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.

Math.max

PI

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

 Property of Static, Read-only Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

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 Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

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).

Math.exp, Math.log

random

Returns a pseudo-random number between 0 and 1. The random number generator is seeded from the current time, as in Java.

 Method of Static Implemented in JavaScript 1.0, NES 2.0: Unix only JavaScript 1.1, NES 2.0: all platforms ECMA version ECMA-262

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 1function getRandom() {   return Math.random()}  `

round

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

 Method of Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
round(x)

Parameters

 x A number

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 Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
sin(x)

Parameters

 x A number

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.

sqrt

Returns the square root of a number.

 Method of Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
sqrt(x)

Parameters

 x A number

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 Static, Read-only Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

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 Static, Read-only Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

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 Static Implemented in JavaScript 1.0, NES 2.0 ECMA version ECMA-262

Syntax
tan(x)

Parameters

 x A number

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)   }  `