# Documentation/Calc Functions/ATAN2

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ATAN2

Mathematical

## Summary:

Returns the angle (in radians) between the x-axis and a line from the origin to the point (Number X | Number Y). This function calculates the principal value. Note: Programming languages have usually the opposite order of arguments for their atan2() function.

## Syntax:

ATAN2(Number X; Number Y)

## Returns:

ATAN2 returns the angle (in radians) between the x-axis and a line from the origin to the point ( Number X | Number Y). The angle returned is between -PI and PI, i.e. [-π,π].

## Arguments:

Number X is the value of the x coordinate.

Number Y is the value of the y coordinate.

Number X and Number Y both can be 0 upon which function returns 0.

Programming languages have usually the opposite order of arguments for their atan2() function.

• To return the angle in degrees, use the DEGREES function.
• If the function returns a positive angle it represents a counterclockwise angle from the x-axis while a negative result represents a clockwise angle. This function is part of the Open Document Format for Office Applications (OpenDocument) standard Version 1.2. (ISO/IEC 26300:2-2015)

## Examples:

Formula Description Returns
=ATAN2(-5;9) The angle (in radians) between the x-axis and a line from the origin to the point having X = -5 and Y = 9. 2.07789 (radians)
=DEGREES(ATAN2(12.3;12.3)) The angle (in radians) between the x-axis and a line from the origin to the point having X = 12.3 and Y = 12.3. To get the angle in degrees apply the DEGREES function to the result. The tangent of 45 degrees is 1. 45° (degrees)
=ATAN2(0;0) The angle (in radians) between the x-axis and a line from the origin to the point having X = 0 and Y = 0. 0 (radians)
=ATAN2(-5;-3)*180/PI() The angle (in radians) between the x-axis and a line from the origin to the point having X = -5 and Y = -3. Further, converting angle in radians to degrees by multiplying by 180/PI(). -149.036243467926° (degrees)
=DEGREES(ATAN2(-8;5)) The angle (in radians) between the x-axis and a line from the origin to the point having X = -8 and Y = 5. The function can be used in converting cartesian coordinates to polar coordinates. See the Fig. below 147.994616791916° (degrees)

DEGREES

ATAN

TANH

TAN

## ODF standard:

Section 6.16.10, part 2

ATAN2