# 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.

Math works with the `Number` type. It doesn't work with `BigInt`.

## 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 integer part of the number x, removing any fractional digits.

## Extending the `Math` object

As with 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

Update compatibility data on GitHub
Desktop Mobile Server Chrome Edge Firefox Internet Explorer Opera Safari Android webview Chrome for Android Firefox for Android Opera for Android Chrome Full support 1 Edge Full support 12 Firefox Full support 1 IE Full support 3 Opera Full support Yes Safari Full support Yes WebView Android Full support 1 Chrome Android Full support 18 Firefox Android Full support 4 Opera Android Full support Yes Safari iOS Full support Yes Samsung Internet Android Full support 1.0 nodejs Full support Yes Chrome Full support 1 Edge Full support 12 Firefox Full support 1 IE Full support 3 Opera Full support Yes Safari Full support Yes WebView Android Full support 1 Chrome Android Full support 18 Firefox Android Full support 4 Opera Android Full support Yes Safari iOS Full support Yes Samsung Internet Android Full support 1.0 nodejs Full support Yes Chrome Full support 1 Edge Full support 12 Firefox Full support 1 IE Full support 3 Opera Full support Yes Safari Full support Yes WebView Android Full support 1 Chrome Android Full support 18 Firefox Android Full support 4 Opera Android Full support Yes Safari iOS Full support Yes Samsung Internet Android Full support 1.0 nodejs Full support Yes Chrome Full support 1 Edge Full support 12 Firefox Full support 1 IE Full support 3 Opera Full support Yes Safari Full support Yes WebView Android Full support 1 Chrome Android Full support 18 Firefox Android Full support 4 Opera Android Full support Yes Safari iOS Full support Yes Samsung Internet Android Full support 1.0 nodejs Full support Yes Chrome Full support 1 Edge Full support 12 Firefox Full support 1 IE Full support 3 Opera Full support Yes Safari Full support Yes WebView Android Full support 1 Chrome Android Full support 18 Firefox Android Full support 4 Opera Android Full support Yes Safari iOS Full support Yes Samsung Internet Android Full support 1.0 nodejs Full support Yes Chrome Full support 1 Edge Full support 12 Firefox Full support 1 IE Full support 3 Opera Full support Yes Safari Full support Yes WebView Android Full support 1 Chrome Android Full support 18 Firefox Android Full support 4 Opera Android Full support Yes Safari iOS Full support Yes Samsung Internet Android Full support 1.0 nodejs Full support Yes Chrome Full support 1 Edge Full support 12 Firefox Full support 1 IE Full support 3 Opera Full support Yes Safari Full support Yes WebView Android Full support 1 Chrome Android Full support 18 Firefox Android Full support 4 Opera Android Full support Yes Safari iOS Full support Yes Samsung Internet Android Full support 1.0 nodejs Full support Yes Chrome Full support 1 Edge Full support 12 Firefox Full support 1 IE Full support 3 Opera Full support Yes Safari Full support Yes WebView Android Full support 1 Chrome Android Full support 18 Firefox Android Full support 4 Opera Android Full support Yes Safari iOS Full support Yes Samsung Internet Android Full support 1.0 nodejs Full support Yes Chrome Full support 1 Edge Full support 12 Firefox Full 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