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).

ATAN2 arguments.png
  • 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:

ACOS

ACOT

ASIN

ATAN

TAN

ODF standard:

Section 6.16.10, part 2

Equivalent Excel functions:

ATAN2