# Documentation/Calc Functions/ATAN2

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## Function name:

ATAN2

## Category:

Mathematical

## Summary:

Calculates the inverse trigonometric tangent (arctangent or arctan) for the specified x and y coordinates. That is, the angle (in radians) between the x-axis and a line from the origin to the specified (x, y) point. The value returned is the principal value and lies in the range (-π, π] radians.

## Syntax:

ATAN2(**Number X**; **Number Y**)

## Returns:

Returns a real number in the range (-π, π] that is the inverse trigonometric cosine in radians for the specified x and y coordinates.

If the function returns a positive angle it represents a counterclockwise angle from the x-axis, while a negative result represents a clockwise angle.

## Arguments:

**Number X** is a real number, or a reference to a cell containing that number, that is the value of the x coordinate.

**Number Y** is a real number, or a reference to a cell containing that number, that is the value of the y coordinate.

- If either
**Number X**or**Number Y**is non-numeric, then ATAN2 returns a #VALUE! error.

**Number X**and**Number Y**are both equal to 0, then ATAN2 returns the value 0.

## Additional details:

The following illustration shows the geometry used by ATAN2 (φ is the angle calculated).

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

- Beware that computer programming languages often use the opposite order of arguments for their atan2() functions.

## Examples:

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

=ATAN2(-5; 9) | Here the function calculates the angle (in radians) between the x-axis and a line from the origin to the point (-5, 9). | 2.07789483118723 |

=DEGREES(ATAN2(12.3; 12.3)) | Here the function calculates the angle (in degrees) between the x-axis and a line from the origin to the point (12.3, 12.3). | 45 |

=ATAN2(D1; D2) where cells D1 and D2 both contain the value 0. | Here the function returns 0. | 0 |

=ATAN2(-5; -3)*180/PI() | Here the function calculates the angle (in degrees) between the x-axis and a line from the origin to the point (-5, -3). | -149.036243467926 |

=DEGREES(ATAN2(-8; 5)) | Here the function calculates the angle (in degrees) between the x-axis and a line from the origin to the point (-8, 5). | 147.994616791916 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

ATAN2