# Documentation/Calc Functions/ATAN2

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ATAN2

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

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)

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))

Calculate 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.

The function returns 0.

0
=ATAN2(−5; −3)*180/PI()

Calculate 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))

Calculate the angle (in degrees) between the x-axis and a line from the origin to the point (−8, 5).

147.994616791916

ATAN2