The Math.hypot()
function returns the square root of the sum of squares of its arguments, that is:
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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 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()
.
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)); };
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
Specification |
---|
ECMAScript (ECMA-262) The definition of 'Math.hypot' in that specification. |
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.
Desktop | Mobile | Server | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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