---
name: "hypot"
section: "3"
platform: "freebsd"
package: "base"
version: "16.0-CURRENT-20261027-61c70dc16a79"
release: "FreeBSD 16.0-CURRENT (2026-10-27)"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/cabs"
---

# hypot(3)

Euclidean distance and complex absolute value functions

Part of [cabs(3)](/cabs/3.md).

## NAME

**hypot**, **hypotf**, **hypotl**, **cabs**, **cabsf**, **cabsl** – Euclidean distance and complex absolute value functions

## LIBRARY

Math Library (libm, -lm)

## 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*);

**#include \<complex.h\>**

*double*\

**cabs**(*double complex z*);

*float*\

**cabsf**(*float complex z*);

*long double*\

**cabsl**(*long double complex z*);

## DESCRIPTION

The **hypot**(), **hypotf**() and **hypotl**() functions compute the sqrt(x\*x+y\*y) in such a way that underflow will not happen, and overflow occurs only if the final result deserves it. The **cabs**(), **cabsf**() and **cabsl**() functions compute the complex absolute value of *z*.

**hypot**(, *v*) = **hypot**(*v*, ) = + for all *v*, including .

## ERROR (due to Roundoff, etc.)

Below 0.97 *ulps*. Consequently **hypot**(*5.0*, *12.0*) = 13.0 exactly; in general, hypot and cabs return an integer whenever an integer might be expected.

## NOTES

As might be expected, **hypot**(*v*, ) and **hypot**(, *v*) are  for all *finite* *v*. But programmers might be surprised at first to discover that **hypot**(*±*, ) = +. This is intentional; it happens because **hypot**(, *v*) = + for *all* *v*, finite or infinite. Hence **hypot**(, *v*) is independent of *v*. Unlike the reserved operand fault on a VAX, the IEEE\
  is designed to disappear when it turns out to be irrelevant, as it does in **hypot**(, ).

## SEE ALSO

[carg(3)](/carg/3.md), [math(3)](/math/3.md), [sqrt(3)](/sqrt/3.md)

## STANDARDS

The **hypot**(), **hypotf**(), **hypotl**(), **cabs**(), **cabsf**(), and **cabsl**() functions conform to ISO/IEC 9899:1999 (“ISO C99”).

## HISTORY

Both a **hypot**() function and a **cabs**() function appeared in Version 7 AT&T UNIX.