--- title: Math.hypot() short-title: hypot() slug: Web/JavaScript/Reference/Global_Objects/Math/hypot page-type: javascript-static-method browser-compat: javascript.builtins.Math.hypot sidebar: jsref --- The **`Math.hypot()`** static method returns the square root of the sum of squares of its arguments. That is,

\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}

{{InteractiveExample("JavaScript Demo: Math.hypot()")}} ```js interactive-example console.log(Math.hypot(3, 4)); // Expected output: 5 console.log(Math.hypot(5, 12)); // Expected output: 13 console.log(Math.hypot(3, 4, 5)); // Expected output: 7.0710678118654755 console.log(Math.hypot(-5)); // Expected output: 5 ``` ## Syntax ```js-nolint 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 {{jsxref("Infinity")}} if any of the arguments is ±Infinity. Otherwise, if at least one of the arguments is or is converted to {{jsxref("NaN")}}, returns {{jsxref("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`](/en-US/docs/Web/JavaScript/Reference/Global_Objects/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()`](/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/abs). [`Math.hypot.length`](/en-US/docs/Web/JavaScript/Reference/Global_Objects/Function/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 {{Specifications}} ## Browser compatibility {{Compat}} ## See also - [Polyfill of `Math.hypot` in `core-js`](https://github.com/zloirock/core-js#ecmascript-math) - {{jsxref("Math.abs()")}} - {{jsxref("Math.pow()")}} - {{jsxref("Math.sqrt()")}}