---
name: "erf"
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/erf"
---

# erf(3)

error function

## NAME

erf, erff, erfl - error function

## LIBRARY

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

## SYNOPSIS

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

**double erf(double** *x***);** **float erff(float** *x***);** **long double erfl(long double** *x***);**

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

**erf**():

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

**erff**(), **erfl**():

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

## DESCRIPTION

These functions return the error function of *x*, defined as

```
erf(x) = 2/sqrt(pi) * integral from 0 to x of exp(-t*t) dt
```

## RETURN VALUE

On success, these functions return the value of the error function of *x*, a value in the range \[-1, 1\].

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

If *x* is +0 (-0), +0 (-0) is returned.

If *x* is positive infinity (negative infinity), +1 (-1) is returned.

If *x* is subnormal, a range error occurs, and the return value is 2\*x/sqrt(pi).

## 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:

- Range error: result underflow (*x* is subnormal)

  An underflow floating-point exception (**FE\_UNDERFLOW**) is raised.

These functions do not set *errno*.

## ATTRIBUTES

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

| | | |
| --- | --- | --- |
| **Interface** | **Attribute** | **Value** |
| **erf**(), **erff**(), **erfl**() | 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

[**cerf**(3)](/cerf/3.md), [**erfc**(3)](/erfc/3.md), [**exp**(3)](/exp/3.md)