Math.hypot()

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

$$\mathtt{\operatorname{Math.hypot}(v_1, v_2, \dots, v_n)} = \sqrt{\sum_{i=1}^n v_i^2} = \sqrt{v_1^2 + v_2^2 + \dots + v_n^2}$$

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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:

if (!Math.hypot) Math.hypot = function() {
  var y = 0, i = arguments.length;
  while (i--) y += arguments[i] * arguments[i];
  return Math.sqrt(y);
};

A polyfill that avoids underflows and overflows:

if (!Math.hypot) Math.hypot = function (x, y) {
  // https://bugzilla.mozilla.org/show_bug.cgi?id=896264#c28
  var max = 0;
  var s = 0;
  for (var i = 0; i < arguments.length; i += 1) {
    var arg = Math.abs(Number(arguments[i]));
    if (arg > max) {
      s *= (max / arg) * (max / arg);
      max = arg;
    }
    s += arg === 0 && max === 0 ? 0 : (arg / max) * (arg / max);
  }
  return max === 1 / 0 ? 1 / 0 : max * Math.sqrt(s);
};

Specifications

Browser compatibility

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

See also

• Math.abs()
• Math.pow()
• Math.sqrt()