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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 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 () {
  var d = Math.min.apply(Math, arguments);
  for (let n = arguments.length, i = 0; d > 1 && n > i; arguments[i] % d === 0 ? i++ : (d--, i = 0));
  return d;
}

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.
Living Standard  

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 (Yes)25 No257.1
asin (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
asinh38 (Yes)25 No257.1
atan (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
atan2 (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
atanh38 (Yes)25 No257.1
cbrt38 (Yes)25 No257.1
ceil (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
clz3238 (Yes)31 No25 (Yes)
cos (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
cosh38 (Yes)25 No257.1
exp (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
expm138 (Yes)25 No257.1
floor (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
fround38 (Yes)26 No257.1
hypot38 (Yes)27 No257.1
imul28 (Yes)20 No167
log (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
log1p38 (Yes)25 No257.1
log238 (Yes)25 No257.1
log1038 (Yes)25 No257.1
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 (Yes)25 No259
sin (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
sinh38 (Yes)25 No257.1
sqrt (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
tan (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
tanh38 (Yes)25 No257.1
trunc38 (Yes)25 No257.1
FeatureAndroidChrome for AndroidEdge mobileFirefox for AndroidIE mobileOpera AndroidiOS Safari
E (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
LN2 (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
LN10 (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
LOG2E (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
LOG10E (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
PI (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
SQRT1_2 (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
SQRT2 (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
abs (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
acos (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
acosh (Yes) (Yes) (Yes)25 No (Yes)8
asin (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
asinh (Yes) (Yes) (Yes)25 No (Yes)8
atan (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
atan2 (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
atanh (Yes) (Yes) (Yes)25 No (Yes)8
cbrt (Yes) (Yes) (Yes)25 No (Yes)8
ceil (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
clz32 (Yes) (Yes) (Yes)31 No (Yes) (Yes)
cos (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
cosh (Yes) (Yes) (Yes)25 No (Yes)8
exp (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
expm1 (Yes) (Yes) (Yes)25 No (Yes)8
floor (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
fround (Yes) (Yes) (Yes)26 No (Yes)8
hypot (Yes) (Yes) (Yes)27 No (Yes)8
imul (Yes) (Yes) (Yes)20 No (Yes)7
log (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
log1p (Yes) (Yes) (Yes)25 No (Yes)8
log2 (Yes) (Yes) (Yes)25 No (Yes)8
log10 (Yes) (Yes) (Yes)25 No (Yes)8
max (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
min (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
pow (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
random (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
round (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
sign (Yes) (Yes) (Yes)25 No (Yes) (Yes)
sin (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
sinh (Yes) (Yes) (Yes)25 No (Yes)8
sqrt (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
tan (Yes) (Yes) (Yes) (Yes) (Yes) (Yes) (Yes)
tanh (Yes) (Yes) (Yes)25 No (Yes)8
trunc (Yes) (Yes) (Yes)25 No (Yes)8

See also