The Math.hypot()
function returns the square root of the sum of squares of its arguments, that is:
The Math.hypot()
function returns the square root of the sum of squares of its arguments, that is:
Math.hypot() Math.hypot(value0) Math.hypot(value0, value1) Math.hypot(value0, value1, /* … ,*/ valueN)
value1
, …, valueN
Numbers.
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.
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 call Math.hypot(v1, v2)
, or Math.hypot(v1, /* … ,*/, vN)
.
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 10^308. If your numbers are larger than about 10^154, 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()
.
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)
Specification |
---|
ECMAScript Language Specification # sec-math.hypot |
Desktop | Mobile | Server | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Chrome | Edge | Firefox | Internet Explorer | Opera | Safari | WebView Android | Chrome Android | Firefox for Android | Opera Android | Safari on IOS | Samsung Internet | Deno | Node.js | |
hypot |
38 |
12 |
27 |
No |
25 |
8 |
38 |
38 |
27 |
25 |
8 |
3.0 |
1.0 |
0.12.0 |
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https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/hypot