# Math

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Math is a built-in object that has properties and methods for mathematical constants and functions. Not a function object.

## Description

Unlike the other global objects, Math is not a constructor. 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.

## Properties

Math.E
Euler's constant and the base of natural logarithms, approximately 2.718.
Math.LN2
Natural logarithm of 2, approximately 0.693.
Math.LN10
Natural logarithm of 10, approximately 2.303.
Math.LOG2E
Base 2 logarithm of E, approximately 1.443.
Math.LOG10E
Base 10 logarithm of E, approximately 0.434.
Math.PI
Ratio of the circumference of a circle to its diameter, approximately 3.14159.
Math.SQRT1_2
Square root of 1/2; equivalently, 1 over the square root of 2, approximately 0.707.
Math.SQRT2
Square root of 2, approximately 1.414.

## Methods

Note that the trigonometric functions (sin(), cos(), tan(), asin(), acos(), atan(), atan2()) expect or return angles in radians. To convert radians to degrees, divide by (Math.PI / 180), and multiply by this to convert the other way.

Note that many math functions have a precision that's implementation-dependent. This means that different browsers can give a different result, and even the same JS engine on a different OS or architecture can give different results.

Math.abs(x)
Returns the absolute value of a number.
Math.acos(x)
Returns the arccosine of a number.
Math.acosh(x)
Returns the hyperbolic arccosine of a number.
Math.asin(x)
Returns the arcsine of a number.
Math.asinh(x)
Returns the hyperbolic arcsine of a number.
Math.atan(x)
Returns the arctangent of a number.
Math.atanh(x)
Returns the hyperbolic arctangent of a number.
Math.atan2(y, x)
Returns the arctangent of the quotient of its arguments.
Math.cbrt(x)
Returns the cube root of a number.
Math.ceil(x)
Returns the smallest integer greater than or equal to a number.
Math.clz32(x)
Returns the number of leading zeroes of a 32-bit integer.
Math.cos(x)
Returns the cosine of a number.
Math.cosh(x)
Returns the hyperbolic cosine of a number.
Math.exp(x)
Returns Ex, where x is the argument, and E is Euler's constant (2.718…), the base of the natural logarithm.
Math.expm1(x)
Returns subtracting 1 from exp(x).
Math.floor(x)
Returns the largest integer less than or equal to a number.
Math.fround(x)
Returns the nearest single precision float representation of a number.
Math.hypot([x[, y[, …]]])
Returns the square root of the sum of squares of its arguments.
Math.imul(x, y)
Returns the result of a 32-bit integer multiplication.
Math.log(x)
Returns the natural logarithm (loge, also ln) of a number.
Math.log1p(x)
Returns the natural logarithm (loge, also ln) of 1 + x for a number x.
Math.log10(x)
Returns the base 10 logarithm of a number.
Math.log2(x)
Returns the base 2 logarithm of a number.
Math.max([x[, y[, …]]])
Returns the largest of zero or more numbers.
Math.min([x[, y[, …]]])
Returns the smallest of zero or more numbers.
Math.pow(x, y)
Returns base to the exponent power, that is, baseexponent.
Math.random()
Returns a pseudo-random number between 0 and 1.
Math.round(x)
Returns the value of a number rounded to the nearest integer.
Math.sign(x)
Returns the sign of the x, indicating whether x is positive, negative or zero.
Math.sin(x)
Returns the sine of a number.
Math.sinh(x)
Returns the hyperbolic sine of a number.
Math.sqrt(x)
Returns the positive square root of a number.
Math.tan(x)
Returns the tangent of a number.
Math.tanh(x)
Returns the hyperbolic tangent of a number.
Math.toSource()
Returns the string "Math".
Math.trunc(x)
Returns the integral part of the number x, removing any fractional digits.

## Extending the Math object

As most of the built-in objects in JavaScript, the Math object can be extended with custom properties and methods. To extend the Math object, you do not use 'prototype'. Instead, you directly extend Math:

Math.propName = propValue;
Math.methodName = methodRef;

For instance, the following example adds a method to the Math object for calculating the greatest common divisor of a list of arguments.

/* Variadic function -- Returns the greatest common divisor of a list of arguments */
Math.gcd = function() {
if (arguments.length == 2) {
if (arguments[1] == 0)
return arguments[0];
else
return Math.gcd(arguments[1], arguments[0] % arguments[1]);
} else if (arguments.length > 2) {
var result = Math.gcd(arguments[0], arguments[1]);
for (var i = 2; i < arguments.length; i++)
result = Math.gcd(result, arguments[i]);
return result;
}
};

Try it:

console.log(Math.gcd(20, 30, 15, 70, 40)); // `5`

## Specifications

Specification Status Comment
ECMAScript 1st Edition (ECMA-262) Standard Initial definition. Implemented in JavaScript 1.1.
ECMAScript 5.1 (ECMA-262)
The definition of 'Math' in that specification.
Standard
ECMAScript 2015 (6th Edition, ECMA-262)
The definition of 'Math' in that specification.
Standard New methods log10(), log2(), log1p(), expm1(), cosh(), sinh(), tanh(), acosh(), asinh(), atanh(), hypot(), trunc(), sign(), imul(), fround(), cbrt() and clz32() added.
ECMAScript Latest Draft (ECMA-262)
The definition of 'Math' in that specification.
Draft

## Browser compatibility

FeatureChromeEdgeFirefoxInternet ExplorerOperaSafari
E Yes Yes Yes Yes Yes Yes
LN2 Yes Yes Yes Yes Yes Yes
LN10 Yes Yes Yes Yes Yes Yes
LOG2E Yes Yes Yes Yes Yes Yes
LOG10E Yes Yes Yes Yes Yes Yes
PI Yes Yes Yes Yes Yes Yes
SQRT1_2 Yes Yes Yes Yes Yes Yes
SQRT2 Yes Yes Yes Yes Yes Yes
abs Yes Yes Yes Yes Yes Yes
acos Yes Yes Yes Yes Yes Yes
acosh38 Yes25 No258
asin Yes Yes Yes Yes Yes Yes
asinh38 Yes25 No258
atan Yes Yes Yes Yes Yes Yes
atan2 Yes Yes Yes Yes Yes Yes
atanh38 Yes25 No258
cbrt38 Yes25 No258
ceil Yes Yes Yes Yes Yes Yes
clz3238 Yes31 No25 Yes
cos Yes Yes Yes Yes Yes Yes
cosh38 Yes25 No258
exp Yes Yes Yes Yes Yes Yes
expm138 Yes25 No258
floor Yes Yes Yes Yes Yes Yes
fround38 Yes26 No258
hypot38 Yes27 No258
imul28 Yes20 No167
log Yes Yes Yes Yes Yes Yes
log1p38 Yes25 No258
log238 Yes25 No258
log1038 Yes25 No258
max Yes Yes Yes Yes Yes Yes
min Yes Yes Yes Yes Yes Yes
pow Yes Yes Yes Yes Yes Yes
random Yes Yes Yes Yes Yes Yes
round Yes Yes Yes Yes Yes Yes
sign38 Yes25 No259
sin Yes Yes Yes Yes Yes Yes
sinh38 Yes25 No258
sqrt Yes Yes Yes Yes Yes Yes
tan Yes Yes Yes Yes Yes Yes
tanh38 Yes25 No258
trunc38 Yes25 No258
FeatureAndroid webviewChrome for AndroidEdge mobileFirefox for AndroidOpera AndroidiOS SafariSamsung Internet
E Yes Yes Yes Yes Yes Yes ?
LN2 Yes Yes Yes Yes Yes Yes ?
LN10 Yes Yes Yes Yes Yes Yes ?
LOG2E Yes Yes Yes Yes Yes Yes ?
LOG10E Yes Yes Yes Yes Yes Yes ?
PI Yes Yes Yes Yes Yes Yes ?
SQRT1_2 Yes Yes Yes Yes Yes Yes ?
SQRT2 Yes Yes Yes Yes Yes Yes ?
abs Yes Yes Yes Yes Yes Yes ?
acos Yes Yes Yes Yes Yes Yes ?
acosh Yes Yes Yes25 Yes8 ?
asin Yes Yes Yes Yes Yes Yes ?
asinh Yes Yes Yes25 Yes8 ?
atan Yes Yes Yes Yes Yes Yes ?
atan2 Yes Yes Yes Yes Yes Yes ?
atanh Yes Yes Yes25 Yes8 ?
cbrt Yes Yes Yes25 Yes8 ?
ceil Yes Yes Yes Yes Yes Yes ?
clz32 Yes Yes Yes31 Yes Yes ?
cos Yes Yes Yes Yes Yes Yes ?
cosh Yes Yes Yes25 Yes8 ?
exp Yes Yes Yes Yes Yes Yes ?
expm1 Yes Yes Yes25 Yes8 ?
floor Yes Yes Yes Yes Yes Yes ?
fround Yes Yes Yes26 Yes8 ?
hypot Yes Yes Yes27 Yes8 ?
imul Yes Yes Yes20 Yes7 ?
log Yes Yes Yes Yes Yes Yes ?
log1p Yes Yes Yes25 Yes8 ?
log2 Yes Yes Yes25 Yes8 ?
log10 Yes Yes Yes25 Yes8 ?
max Yes Yes Yes Yes Yes Yes ?
min Yes Yes Yes Yes Yes Yes ?
pow Yes Yes Yes Yes Yes Yes ?
random Yes Yes Yes Yes Yes Yes ?
round Yes Yes Yes Yes Yes Yes ?
sign Yes Yes Yes25 Yes Yes ?
sin Yes Yes Yes Yes Yes Yes ?
sinh Yes Yes Yes25 Yes8 ?
sqrt Yes Yes Yes Yes Yes Yes ?
tan Yes Yes Yes Yes Yes Yes ?
tanh Yes Yes Yes25 Yes8 ?
trunc Yes Yes Yes25 Yes8 ?