Web/JavaScript/Reference/Global objects/Math/hypot

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

<math display="block">\mathtt{\operatorname{Math.hypot}(v_{1},v_{2},\ldots,v_{n})} = \sqrt{\sum\limits_{i = 1}^{n}v_{i}^{2}} = \sqrt{v_{1}^{2} + v_{2}^{2} + \ldots + v_{n}^{2}}</math>

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 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 simply call Math.hypot(v1, v2) , or Math.hypot(v1, v2, v3, v4, ...).

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 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.

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 any of the arguments is ±Infinity, the result is Infinity. If any of the arguments is NaN (unless another argument is ±Infinity), the result is NaN. If at least one of the arguments cannot be converted to a number, the result is NaN.

With one argument, Math.hypot() is equivalent to 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(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)

Polyfill

A naive approach that does not handle overflow/underflow issues:

if (!Math.hypot) Math.hypot = function() {
  var y = 0, i = arguments.length, containsInfinity = false;
  while (i--) {
    var arg = arguments[i];
    if (arg === Infinity || arg === -Infinity)
      containsInfinity = true
    y += arg * arg 
  }
  return containsInfinity ? Infinity : Math.sqrt(y)
}

A polyfill that avoids underflows and overflows:

if (!Math.hypot) Math.hypot = function () {
  var max = 0;
  var s = 0;
  var containsInfinity = false;
  for (var i = 0; i < arguments.length; ++i) {
    var arg = Math.abs(Number(arguments[i]));
    if (arg === Infinity)
      containsInfinity = true
    if (arg > max) {
      s *= (max / arg) * (max / arg);
      max = arg;
    }
    s += arg === 0 && max === 0 ? 0 : (arg / max) * (arg / max);
  }
  return containsInfinity ? Infinity : (max === 1 / 0 ? 1 / 0 : max * Math.sqrt(s));
};

Specifications

Specification
ECMAScript (ECMA-262)The definition of 'Math.hypot' in that specification.

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	Safari on iOS	Samsung Internet	Node.js
`hypot`	Chrome Full support 38	Edge Full support 12	Firefox Full support 27	IE No support No	Opera Full support 25	Safari Full support 8	WebView Android Full support 38	Chrome Android Full support 38	Firefox Android Full support 27	Opera Android Full support 25	Safari iOS Full support 8	Samsung Internet Android Full support 3.0	nodejs Full support 0.12

Legend

Full support: Full support
No support: No support