# Section (3) hypot

## Name

hypot, hypotf, hypotl — Euclidean distance function

## Synopsis

`#include <math.h>`
 ```double hypot(``` double x, double y`)`;

 ```float hypotf(``` float x, float y`)`;

 ```long double hypotl(``` long double x, long double y`)`; Note
Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
`hypot`():
`_ISOC99_SOURCE` || `_POSIX_C_SOURCE` >= 200112L || `_XOPEN_SOURCE` || /* Since glibc 2.19:
*/ `_DEFAULT_SOURCE` || /* Glibc versions <= 2.19:
*/ `_BSD_SOURCE` || `_SVID_SOURCE`
`hypotf`(), `hypotl`():
`_ISOC99_SOURCE` || `_POSIX_C_SOURCE` >= 200112L || /* Since glibc 2.19:
*/ `_DEFAULT_SOURCE` || /* Glibc versions <= 2.19:
*/ `_BSD_SOURCE` || `_SVID_SOURCE`
Note Link with `−lm`.

## DESCRIPTION

These functions return sqrt(`x`*`x`+`y`*`y`). This is the length of the hypotenuse of a right-angled triangle with sides of length `x` and `y`, or the distance of the point (`x`,`y`) from the origin.

The calculation is performed without undue overflow or underflow during the intermediate steps of the calculation.

## RETURN VALUE

On success, these functions return the length of a right-angled triangle with sides of length `x` and `y`.

If `x` or `y` is an infinity, positive infinity is returned.

If `x` or `y` is a NaN, and the other argument is not an infinity, a NaN is returned.

If the result overflows, a range error occurs, and the functions return `HUGE_VAL`, `HUGE_VALF`, or `HUGE_VALL`, respectively.

If both arguments are subnormal, and the result is subnormal, a range error occurs, and the correct result is returned.

## ERRORS

See math_error(7) for information on how to determine whether an error has occurred when calling these functions.

The following errors can occur:

Range error: result overflow

`errno` is set to ERANGE. An overflow floating-point exception (`FE_OVERFLOW`) is raised.

Range error: result underflow

An underflow floating-point exception (`FE_UNDERFLOW`) is raised.

These functions do not set `errno` for this case.

## ATTRIBUTES

For an explanation of the terms used in this section, see attributes(7).

 Interface Attribute Value `hypot`(), `hypotf`(), `hypotl`() Thread safety MT-Safe

## CONFORMING TO

C99, POSIX.1-2001, POSIX.1-2008.

The variant returning double also conforms to SVr4, 4.3BSD.

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