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

𝙼𝚊𝚝𝚑.𝚑𝚢𝚙𝚘𝚝 ( v 1 , v 2 , , v n ) = i = 1 n v i 2 = v 1 2 + v 2 2 + + v n 2 \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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Math.hypot(value0, value1)
Math.hypot(value0, value1, /* … ,*/ valueN)


value1, …, valueN


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.


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).


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)


ECMAScript Language Specification
# sec-math.hypot

Browser compatibility

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See also