---
name: "acosh"
section: "3"
platform: "linux"
package: "man-pages"
version: "6.19-1"
release: "Arch Linux 2026-11-01"
platforms: ["linux", "freebsd"]
url: "https://new.carta.tech/acosh"
---

# acosh(3)

inverse hyperbolic cosine function

## NAME

acosh, acoshf, acoshl - inverse hyperbolic cosine function

## LIBRARY

Math library (*libm*, *-lm*)

## SYNOPSIS

```
#include <math.h>
```

**double acosh(double** *x***);** **float acoshf(float** *x***);** **long double acoshl(long double** *x***);**

Feature Test Macro Requirements for glibc (see [**feature\_test\_macros**(7)](/feature_test_macros/7.md)):

**acosh**():

```
    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
        || _XOPEN_SOURCE >= 500
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
```

**acoshf**(), **acoshl**():

```
    _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
        || /* Since glibc 2.19: */ _DEFAULT_SOURCE
        || /* glibc <= 2.19: */ _BSD_SOURCE || _SVID_SOURCE
```

## DESCRIPTION

These functions calculate the inverse hyperbolic cosine of *x*; that is the value whose hyperbolic cosine is *x*.

## RETURN VALUE

On success, these functions return the inverse hyperbolic cosine of *x*.

If *x* is a NaN, a NaN is returned.

If *x* is +1, +0 is returned.

If *x* is positive infinity, positive infinity is returned.

If *x* is less than 1, a domain error occurs, and the functions return a NaN.

## ERRORS

See [**math\_error**(7)](/math_error/7.md) for information on how to determine whether an error has occurred when calling these functions.

The following errors can occur:

- Domain error: *x* is less than 1

  *errno* is set to **EDOM**. An invalid floating-point exception (**FE\_INVALID**) is raised.

## ATTRIBUTES

For an explanation of the terms used in this section, see [**attributes**(7)](/attributes/7.md).

| | | |
| --- | --- | --- |
| **Interface** | **Attribute** | **Value** |
| **acosh**(), **acoshf**(), **acoshl**() | Thread safety | MT-Safe |

## STANDARDS

C11, POSIX.1-2008.

## HISTORY

C99, POSIX.1-2001.

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

## SEE ALSO

[**asinh**(3)](/asinh/3.md), [**atanh**(3)](/atanh/3.md), [**cacosh**(3)](/cacosh/3.md), [**cosh**(3)](/cosh/3.md), [**sinh**(3)](/sinh/3.md), [**tanh**(3)](/tanh/3.md)