# Math.hypot()

The Math.hypot() function returns the square root of the sum of squares of its arguments, that is

$Math.hypot(v1,v2,…,vn)=∑i=1nvi2=v12+v22+…+vn2\mathtt{\operatorname{Math.hypot}(v_1, v_2, \dots, v_n)} = \sqrt{\sum_{i=1}^n v_i^2} = \sqrt{v_1^2 + v_2^2 + \dots + v_n^2}$

## Syntax

Math.hypot([value1[, value2[, ...]]])

### Parameters

value1, value2, ...
Numbers.

### Return value

The square root of the sum of squares of the given arguments. If at least one of the arguments cannot be converted to a number, NaN is returned.

## 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 either the sides of the triangle, or the real and complex values.  For calculating distance in 2 or more dimensions, simply add in more squares inside the square root sign, like Math.sqrt(v1*v1 + v2*v2 + v3*v3 + v4*v4) .

This function makes it a little easier and faster, you just call Math.hypot(v1, v2) , or Math.hypot(v1, v2, v3, v4, ...) .

It also avoids a problem if the magnitude of your numbers is huge.  The largest number you can represent in JS's double floats is Number.MAX_VALUE = 1.797...e+308 .  If your numbers are larger  than about 1e154, taking the square of them will result in Infinity, demolishing your results.  For example, Math.sqrt(1e200*1e200 + 1e200*1e200) = Infinity .  If you use hypot() instead, you get a good 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, a good answer.

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).

If no arguments are given, the result is +0.

If at least one of the arguments cannot be converted to a number, the result is NaN.

With one argument, Math.hypot() returns the same as Math.abs().

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


## Polyfill

This can be emulated using the following function:

Math.hypot = Math.hypot || function() {
var y = 0;
var length = arguments.length;

for (var i = 0; i < length; i++) {
if (arguments[i] === Infinity || arguments[i] === -Infinity) {
return Infinity;
}
y += arguments[i] * arguments[i];
}
return Math.sqrt(y);
};


## Specifications

Specification Status Comment
ECMAScript 2015 (6th Edition, ECMA-262)
The definition of 'Math.hypot' in that specification.
Standard Initial definition.
ECMAScript 2017 Draft (ECMA-262)
The definition of 'Math.hypot' in that specification.
Draft

## Browser compatibility

Feature Chrome Firefox (Gecko) Internet Explorer Opera Safari
Basic support 38 27 (27) No support 25 7.1
Feature Android Chrome for Android Firefox Mobile (Gecko) IE Mobile Opera Mobile Safari Mobile
Basic support No support No support 27.0 (27) No support No support 8

## License

© 2016 Mozilla Contributors
Licensed under the Creative Commons Attribution-ShareAlike License v2.5 or later.
https://developer.mozilla.org/en-us/docs/web/javascript/reference/global_objects/math/hypot