files/en-us/web/javascript/reference/global_objects/math/hypot/index.md

metadata

title: Math.hypot()
short-title: hypot()
slug: Web/JavaScript/Reference/Global_Objects/Math/hypot
page-type: javascript-static-method
browser-compat: javascript.builtins.Math.hypot
sidebar: jsref

The Math.hypot() static method returns the square root of the sum of squares of its arguments. That is,

$$𝙼𝚊𝚝𝚑.𝚑𝚢𝚙𝚘𝚝(v_1,v_2,\dots ,v_n)=\sqrt{\sum _{i=1}^n{v}_i^2}=\sqrt{v_1^2+v_2^2+\dots +v_n^2}\backslash mathtt\{\backslash operatorname\{Math.hypot\}(v\_1,\; v\_2,\; \backslash dots,\; v\_n)\}\; =\; \backslash sqrt\{\backslash sum\_\{i=1\}^n\; v\_i^2\}\; =\; \backslash sqrt\{v\_1^2\; +\; v\_2^2\; +\; \backslash dots\; +\; v\_n^2\}$$

{{InteractiveExample("JavaScript Demo: Math.hypot()")}}

console.log(Math.hypot(3, 4));
// Expected output: 5

console.log(Math.hypot(5, 12));
// Expected output: 13

console.log(Math.hypot(3, 4, 5));
// Expected output: 7.0710678118654755

console.log(Math.hypot(-5));
// Expected output: 5

Syntax

Math.hypot()
Math.hypot(value1)
Math.hypot(value1, value2)
Math.hypot(value1, value2, /* …, */ valueN)

Parameters

• value1, …, valueN
  • : Numbers.

Return value

The square root of the sum of squares of the given arguments. Returns {{jsxref("Infinity")}} if any of the arguments is ±Infinity. Otherwise, if at least one of the arguments is or is converted to {{jsxref("NaN")}}, returns {{jsxref("NaN")}}. Returns 0 if no arguments are given or all arguments are ±0.

Description

Calculating the hypotenuse of a right triangle, or the magnitude of a complex number, uses the formula Math.sqrt(v1*v1 + v2*v2), where v1 and v2 are the lengths of the triangle's legs, or the complex number's real and complex components. The corresponding distance in 2 or more dimensions can be calculated by adding more squares under the square root: Math.sqrt(v1*v1 + v2*v2 + v3*v3 + v4*v4).

This function makes this calculation easier and faster; you call Math.hypot(v1, v2), or Math.hypot(v1, /* …, */, vN).

Math.hypot also avoids overflow/underflow problems if the magnitude of your numbers is very large. The largest number you can represent in JS is Number.MAX_VALUE, which is around 10³⁰⁸. If your numbers are larger than about 10¹⁵⁴, taking the square of them will result in Infinity. For example, Math.sqrt(1e200*1e200 + 1e200*1e200) = Infinity. If you use hypot() instead, you get a better answer: Math.hypot(1e200, 1e200) = 1.4142...e+200. This is also true with very small numbers. Math.sqrt(1e-200*1e-200 + 1e-200*1e-200) = 0, but Math.hypot(1e-200, 1e-200) = 1.4142...e-200.

With one argument, Math.hypot() is equivalent to Math.abs(). Math.hypot.length is 2, which weakly signals that it's designed to handle at least two parameters.

Because hypot() is a static method of Math, you always use it as Math.hypot(), rather than as a method of a Math object you created (Math is not a constructor).

Examples

Using Math.hypot()

Math.hypot(3, 4); // 5
Math.hypot(3, 4, 5); // 7.0710678118654755
Math.hypot(); // 0
Math.hypot(NaN); // NaN
Math.hypot(NaN, Infinity); // Infinity
Math.hypot(3, 4, "foo"); // NaN, since +'foo' => NaN
Math.hypot(3, 4, "5"); // 7.0710678118654755, +'5' => 5
Math.hypot(-3); // 3, the same as Math.abs(-3)

Specifications

{{Specifications}}

Browser compatibility

{{Compat}}

See also

• Polyfill of Math.hypot in core-js
• {{jsxref("Math.abs()")}}
• {{jsxref("Math.pow()")}}
• {{jsxref("Math.sqrt()")}}