# رياضيات

`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` (en-US)
Euler's constant and the base of natural logarithms, approximately 2.718.
`Math.LN2` (en-US)
Natural logarithm of 2, approximately 0.693.
`Math.LN10` (en-US)
Natural logarithm of 10, approximately 2.303.
`Math.LOG2E` (en-US)
Base 2 logarithm of E, approximately 1.443.
`Math.LOG10E` (en-US)
Base 10 logarithm of E, approximately 0.434.
`Math.PI` (en-US)
Ratio of the circumference of a circle to its diameter, approximately 3.14159.
`Math.SQRT1_2` (en-US)
Square root of 1/2; equivalently, 1 over the square root of 2, approximately 0.707.
`Math.SQRT2` (en-US)
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)` (en-US)
Returns the absolute value of a number.
`Math.acos(x)` (en-US)
Returns the arccosine of a number.
`Math.acosh(x)` (en-US)
Returns the hyperbolic arccosine of a number.
`Math.asin(x)` (en-US)
Returns the arcsine of a number.
`Math.asinh(x)` (en-US)
Returns the hyperbolic arcsine of a number.
`Math.atan(x)` (en-US)
Returns the arctangent of a number.
`Math.atanh(x)` (en-US)
Returns the hyperbolic arctangent of a number.
`Math.atan2(y, x)` (en-US)
Returns the arctangent of the quotient of its arguments.
`Math.cbrt(x)` (en-US)
Returns the cube root of a number.
`Math.ceil(x)` (en-US)
Returns the smallest integer greater than or equal to a number.
`Math.clz32(x)` (en-US)
Returns the number of leading zeroes of a 32-bit integer.
`Math.cos(x)` (en-US)
Returns the cosine of a number.
`Math.cosh(x)` (en-US)
Returns the hyperbolic cosine of a number.
`Math.exp(x)` (en-US)
Returns Ex, where x is the argument, and E is Euler's constant (2.718…), the base of the natural logarithm.
`Math.expm1(x)` (en-US)
Returns subtracting 1 from `exp(x)`.
`Math.floor(x)` (en-US)
Returns the largest integer less than or equal to a number.
`Math.fround(x)` (en-US)
Returns the nearest single precision float representation of a number.
`Math.hypot([x[, y[, …]]])` (en-US)
Returns the square root of the sum of squares of its arguments.
`Math.imul(x, y)` (en-US)
Returns the result of a 32-bit integer multiplication.
`Math.log(x)` (en-US)
Returns the natural logarithm (loge, also ln) of a number.
`Math.log1p(x)` (en-US)
Returns the natural logarithm (loge, also ln) of `1 + x` for a number x.
`Math.log10(x)` (en-US)
Returns the base 10 logarithm of a number.
`Math.log2(x)` (en-US)
Returns the base 2 logarithm of a number.
`Math.max([x[, y[, …]]])` (en-US)
Returns the largest of zero or more numbers.
`Math.min([x[, y[, …]]])` (en-US)
Returns the smallest of zero or more numbers.
`Math.pow(x, y)` (en-US)
Returns base to the exponent power, that is, `baseexponent`.
`Math.random()` (en-US)
Returns a pseudo-random number between 0 and 1.
`Math.round(x)` (en-US)
Returns the value of a number rounded to the nearest integer.
`Math.sign(x)` (en-US)
Returns the sign of the x, indicating whether x is positive, negative or zero.
`Math.sin(x)` (en-US)
Returns the sine of a number.
`Math.sinh(x)` (en-US)
Returns the hyperbolic sine of a number.
`Math.sqrt(x)` (en-US)
Returns the positive square root of a number.
`Math.tan(x)` (en-US)
Returns the tangent of a number.
`Math.tanh(x)` (en-US)
Returns the hyperbolic tangent of a number.
`Math.toSource()`
Returns the string `"Math"`.
`Math.trunc(x)` (en-US)
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()` (en-US), `log2()` (en-US), `log1p()` (en-US), `expm1()` (en-US), `cosh()` (en-US), `sinh()` (en-US), `tanh()` (en-US), `acosh()` (en-US), `asinh()` (en-US), `atanh()` (en-US), `hypot()` (en-US), `trunc()` (en-US), `sign()` (en-US), `imul()` (en-US), `fround()` (en-US), `cbrt()` (en-US) and `clz32()` (en-US) added.
ECMAScript (ECMA-262)
The definition of 'Math' in that specification.
Living Standard

## Browser compatibility

BCD tables only load in the browser