Math.hypot

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

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

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

See also

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