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# Math.hypot()

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

## Syntax

```js
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`](../Number/MAX_VALUE.mdx), which is around 10<sup>308</sup>. If your numbers are larger than about 10<sup>154</sup>, 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()`](./abs.mdx). [`Math.hypot.length`](../Function/prototype/length.mdx) 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).
