# Documentation/Calc Functions/ACOS

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## Function name:

ACOS

## Category:

Mathematical

## Summary:

Returns the inverse trigonometric cosine (the arccosine) of a number. This function calculates the principal value.

## Syntax:

ACOS(**Number**)

## Returns:

This function returns the inverse trigonometric cosine of **Number**, that is the angle (in radians) whose cosine is **Number**. The angle returned is between 0 and PI, i.e. [0,π].

## Arguments:

**Number** is the real number, or a reference to a cell containing that number, *between -1 and +1*, whose inverse trigonometric cosine value is to be calculated.

If the value of **Number** is outside this range, the function returns an invalid numeric value (#NUM!) error.

## Additional details:

- To return the angle in degrees, use the DEGREES function.
- Alternatively multiply by 180/PI() to convert the result from radians to degrees.

The figure below illustrates the function ACOS.

## Examples:

Formula | Description | Returns |
---|---|---|

=ACOS(-1) | Inverse trigonometric cosine of -1 | 3.14159265358979 (PI radians or π) |

=ACOS(0.5) | Inverse trigonometric cosine of 0.5 | 1.0471975511966 (radians) |

=DEGREES(ACOS(0.5)) | Inverse trigonometric cosine of 0.5. Further, converting angle in radians to degrees. | 60° (degrees) |

=ACOS(-0.5)*180/PI() | Inverse trigonometric cosine of -0.5. Further, converting angle in radians to degrees by multiplying by 180/PI(). | 120° (degrees) |

=ACOS(2) | Inverse trigonometric cosine of 2 will return an invalid numeric value (#NUM!) error because 2 is out of its domain. | #NUM! |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

ACOS