Math.hypot()

Baseline Widely available

This feature is well established and works across many devices and browser versions. It’s been available across browsers since July 2015.

The Math.hypot() static method returns the square root of the sum of squares of its arguments. That is,

𝙼𝚊𝚝𝚑.𝚑𝚢𝚙𝚘𝚝(v1,v2,…,vn)=∑i=1nvi2=v12+v22+…+vn2\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

js
Math.hypot()
Math.hypot(value1)
Math.hypot(value1, value2)
Math.hypot(value1, value2, /* …, */ valueN)

Parameters

value1, …, valueN

Numbers.

Return value

The square root of the sum of squares of the given arguments. Returns Infinity if any of the arguments is ±Infinity. Otherwise, if at least one of the arguments is or is converted to NaN, returns NaN. Returns 0 if no arguments are given or all arguments are ±0.

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 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 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 a 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.

With one argument, Math.hypot() is equivalent to Math.abs(). Math.hypot.length is 2, which weakly signals that it's designed to handle at least two parameters.

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).

Examples

Using Math.hypot()

js
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 Language Specification
# sec-math.hypot

Browser compatibility

BCD tables only load in the browser

See also