Math.hypot()

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

Syntax

Math.hypot()
Math.hypot(value0)
Math.hypot(value0, value1)
Math.hypot(value0, value1, /* … ,*/ 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).