---
title: رياضيات
slug: Web/JavaScript/Reference/Global_Objects/Math
translation_of: Web/JavaScript/Reference/Global_Objects/Math
---
<div>{{JSRef}}</div>

<p><strong><code>Math</code></strong> is a built-in object that has properties and methods for mathematical constants and functions. Not a function object.</p>

<h2 id="Description">Description</h2>

<p>Unlike the other global objects, <code>Math</code> is not a constructor. All properties and methods of <code>Math</code> are static. You refer to the constant pi as <code>Math.PI</code> and you call the sine function as <code>Math.sin(x)</code>, where <code>x</code> is the method's argument. Constants are defined with the full precision of real numbers in JavaScript.</p>

<h2 id="Properties">Properties</h2>

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

<h2 id="Methods">Methods</h2>

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

<div class="note">
<p>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.</p>
</div>

<dl>
 <dt>{{jsxref("Global_Objects/Math/abs", "Math.abs(x)")}}</dt>
 <dd>Returns the absolute value of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/acos", "Math.acos(x)")}}</dt>
 <dd>Returns the arccosine of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/acosh", "Math.acosh(x)")}}</dt>
 <dd>Returns the hyperbolic arccosine of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/asin", "Math.asin(x)")}}</dt>
 <dd>Returns the arcsine of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/asinh", "Math.asinh(x)")}}</dt>
 <dd>Returns the hyperbolic arcsine of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/atan", "Math.atan(x)")}}</dt>
 <dd>Returns the arctangent of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/atanh", "Math.atanh(x)")}}</dt>
 <dd>Returns the hyperbolic arctangent of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/atan2", "Math.atan2(y, x)")}}</dt>
 <dd>Returns the arctangent of the quotient of its arguments.</dd>
 <dt>{{jsxref("Global_Objects/Math/cbrt", "Math.cbrt(x)")}}</dt>
 <dd>Returns the cube root of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/ceil", "Math.ceil(x)")}}</dt>
 <dd>Returns the smallest integer greater than or equal to a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/clz32", "Math.clz32(x)")}}</dt>
 <dd>Returns the number of leading zeroes of a 32-bit integer.</dd>
 <dt>{{jsxref("Global_Objects/Math/cos", "Math.cos(x)")}}</dt>
 <dd>Returns the cosine of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/cosh", "Math.cosh(x)")}}</dt>
 <dd>Returns the hyperbolic cosine of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/exp", "Math.exp(x)")}}</dt>
 <dd>Returns E<sup>x</sup>, where <var>x</var> is the argument, and E is Euler's constant (2.718…), the base of the natural logarithm.</dd>
 <dt>{{jsxref("Global_Objects/Math/expm1", "Math.expm1(x)")}}</dt>
 <dd>Returns subtracting 1 from <code>exp(x)</code>.</dd>
 <dt>{{jsxref("Global_Objects/Math/floor", "Math.floor(x)")}}</dt>
 <dd>Returns the largest integer less than or equal to a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/fround", "Math.fround(x)")}}</dt>
 <dd>Returns the nearest <a href="http://en.wikipedia.org/wiki/Single-precision_floating-point_format" title="link to the wikipedia page on single precision">single precision</a> float representation of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/hypot", "Math.hypot([x[, y[, …]]])")}}</dt>
 <dd>Returns the square root of the sum of squares of its arguments.</dd>
 <dt>{{jsxref("Global_Objects/Math/imul", "Math.imul(x, y)")}}</dt>
 <dd>Returns the result of a 32-bit integer multiplication.</dd>
 <dt>{{jsxref("Global_Objects/Math/log", "Math.log(x)")}}</dt>
 <dd>Returns the natural logarithm (log<sub>e</sub>, also ln) of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/log1p", "Math.log1p(x)")}}</dt>
 <dd>Returns the natural logarithm (log<sub>e</sub>, also ln) of <code>1 + x</code> for a number x.</dd>
 <dt>{{jsxref("Global_Objects/Math/log10", "Math.log10(x)")}}</dt>
 <dd>Returns the base 10 logarithm of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/log2", "Math.log2(x)")}}</dt>
 <dd>Returns the base 2 logarithm of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/max", "Math.max([x[, y[, …]]])")}}</dt>
 <dd>Returns the largest of zero or more numbers.</dd>
 <dt>{{jsxref("Global_Objects/Math/min", "Math.min([x[, y[, …]]])")}}</dt>
 <dd>Returns the smallest of zero or more numbers.</dd>
 <dt>{{jsxref("Global_Objects/Math/pow", "Math.pow(x, y)")}}</dt>
 <dd>Returns base to the exponent power, that is, <code>base<sup>exponent</sup></code>.</dd>
 <dt>{{jsxref("Global_Objects/Math/random", "Math.random()")}}</dt>
 <dd>Returns a pseudo-random number between 0 and 1.</dd>
 <dt>{{jsxref("Global_Objects/Math/round", "Math.round(x)")}}</dt>
 <dd>Returns the value of a number rounded to the nearest integer.</dd>
 <dt>{{jsxref("Global_Objects/Math/sign", "Math.sign(x)")}}</dt>
 <dd>Returns the sign of the x, indicating whether x is positive, negative or zero.</dd>
 <dt>{{jsxref("Global_Objects/Math/sin", "Math.sin(x)")}}</dt>
 <dd>Returns the sine of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/sinh", "Math.sinh(x)")}}</dt>
 <dd>Returns the hyperbolic sine of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/sqrt", "Math.sqrt(x)")}}</dt>
 <dd>Returns the positive square root of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/tan", "Math.tan(x)")}}</dt>
 <dd>Returns the tangent of a number.</dd>
 <dt>{{jsxref("Global_Objects/Math/tanh", "Math.tanh(x)")}}</dt>
 <dd>Returns the hyperbolic tangent of a number.</dd>
 <dt><code>Math.toSource()</code> {{non-standard_inline}}</dt>
 <dd>Returns the string <code>"Math"</code>.</dd>
 <dt>{{jsxref("Global_Objects/Math/trunc", "Math.trunc(x)")}}</dt>
 <dd>Returns the integer part of the number x, removing any fractional digits.</dd>
</dl>

<h2 id="Extending_the_Math_object">Extending the <code>Math</code> object</h2>

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

<pre>Math.propName = propValue;
Math.methodName = methodRef;</pre>

<p>For instance, the following example adds a method to the <code>Math</code> object for calculating the <em>greatest common divisor</em> of a list of arguments.</p>

<pre class="brush: js">/* 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 &gt; 2) {
        var result = Math.gcd(arguments[0], arguments[1]);
        for (var i = 2; i &lt; arguments.length; i++)
            result = Math.gcd(result, arguments[i]);
        return result;
    }
};</pre>

<p>Try it:</p>

<pre class="brush: js">console.log(Math.gcd(20, 30, 15, 70, 40)); // `5`</pre>

<h2 id="Specifications">Specifications</h2>

<table class="standard-table">
 <tbody>
  <tr>
   <th scope="col">Specification</th>
   <th scope="col">Status</th>
   <th scope="col">Comment</th>
  </tr>
  <tr>
   <td>{{SpecName('ES1')}}</td>
   <td>{{Spec2('ES1')}}</td>
   <td>Initial definition. Implemented in JavaScript 1.1.</td>
  </tr>
  <tr>
   <td>{{SpecName('ES5.1', '#sec-15.8', 'Math')}}</td>
   <td>{{Spec2('ES5.1')}}</td>
   <td> </td>
  </tr>
  <tr>
   <td>{{SpecName('ES6', '#sec-math-object', 'Math')}}</td>
   <td>{{Spec2('ES6')}}</td>
   <td>New methods {{jsxref("Math.log10()", "log10()")}}, {{jsxref("Math.log2()", "log2()")}}, {{jsxref("Math.log1p()", "log1p()")}}, {{jsxref("Math.expm1()", "expm1()")}}, {{jsxref("Math.cosh()", "cosh()")}}, {{jsxref("Math.sinh()", "sinh()")}}, {{jsxref("Math.tanh()", "tanh()")}}, {{jsxref("Math.acosh()", "acosh()")}}, {{jsxref("Math.asinh()", "asinh()")}}, {{jsxref("Math.atanh()", "atanh()")}}, {{jsxref("Math.hypot()", "hypot()")}}, {{jsxref("Math.trunc()", "trunc()")}}, {{jsxref("Math.sign()", "sign()")}}, {{jsxref("Math.imul()", "imul()")}}, {{jsxref("Math.fround()", "fround()")}}, {{jsxref("Math.cbrt()", "cbrt()")}} and {{jsxref("Math.clz32()", "clz32()")}} added.</td>
  </tr>
  <tr>
   <td>{{SpecName('ESDraft', '#sec-math-object', 'Math')}}</td>
   <td>{{Spec2('ESDraft')}}</td>
   <td> </td>
  </tr>
 </tbody>
</table>

<h2 id="Browser_compatibility">Browser compatibility</h2>

<p class="hidden">The compatibility table in this page is generated from structured data. If you'd like to contribute to the data, please check out <a href="https://github.com/mdn/browser-compat-data">https://github.com/mdn/browser-compat-data</a> and send us a pull request.</p>

<p>{{Compat("javascript.builtins.Math")}}</p>

<h2 id="See_also">See also</h2>

<ul>
 <li>{{jsxref("Number")}}</li>
</ul>