Math.Atan2 Method

Returns the angle whose tangent is the quotient of two specified numbers.

Namespace:  System
Assembly:  mscorlib (in mscorlib.dll)

public static double Atan2(
	double y,
	double x


Type: System.Double
The y coordinate of a point.
Type: System.Double
The x coordinate of a point.

Return Value

Type: System.Double
An angle, θ, measured in radians, such that -π θ π, and tan(θ) = y / x, where (x, y) is a point in the Cartesian plane. Observe the following:
  • For (x, y) in quadrant 1, 0 < θ < π/2.

  • For (x, y) in quadrant 2, π/2 < θ π.

  • For (x, y) in quadrant 3, -π < θ < -π/2.

  • For (x, y) in quadrant 4, -π/2 < θ < 0.

For points on the boundaries of the quadrants, the return value is the following:
  • If y is 0 and x is not negative, θ = 0.

  • If y is 0 and x is negative, θ = π.

  • If y is positive and x is 0, θ = π/2.

  • If y is negative and x is 0, θ = -π/2.

If x or y is NaN, or if x and y are either PositiveInfinity or NegativeInfinity, the method returns NaN.

The return value is the angle in the Cartesian plane formed by the x-axis, and a vector starting from the origin, (0,0), and terminating at the point, (x,y).

The following example demonstrates how to calculate the arctangent of an angle and a vector. The resulting value is displayed in the console.

// This example demonstrates Math.Atan()
//                           Math.Atan2()
//                           Math.Tan()
using System;

class Example
   public static void Demo(System.Windows.Controls.TextBlock outputBlock)
      double x = 1.0;
      double y = 2.0;
      double angle;
      double radians;
      double result;

      // Calculate the tangent of 30 degrees.
      angle = 30;
      radians = angle * (Math.PI / 180);
      result = Math.Tan(radians);
      outputBlock.Text += String.Format("The tangent of 30 degrees is {0}.", result) + "\n";

      // Calculate the arctangent of the previous tangent.
      radians = Math.Atan(result);
      angle = radians * (180 / Math.PI);
      outputBlock.Text += String.Format("The previous tangent is equivalent to {0} degrees.", angle) + "\n";

      // Calculate the arctangent of an angle.
      String line1 = "{0}The arctangent of the angle formed by the x-axis and ";
      String line2 = "a vector to point ({0},{1}) is {2}, ";
      String line3 = "which is equivalent to {0} degrees.";

      radians = Math.Atan2(y, x);
      angle = radians * (180 / Math.PI);

      outputBlock.Text += String.Format(line1, "\n") + "\n";
      outputBlock.Text += String.Format(line2, x, y, radians) + "\n";
      outputBlock.Text += String.Format(line3, angle) + "\n";
This example produces the following results:

The tangent of 30 degrees is 0.577350269189626.
The previous tangent is equivalent to 30 degrees.

The arctangent of the angle formed by the x-axis and
a vector to point (1,2) is 1.10714871779409,
which is equivalent to 63.434948822922 degrees.


Supported in: 5, 4, 3

Silverlight for Windows Phone

Supported in: Windows Phone OS 7.1, Windows Phone OS 7.0

XNA Framework

Supported in: Xbox 360, Windows Phone OS 7.0

For a list of the operating systems and browsers that are supported by Silverlight, see Supported Operating Systems and Browsers.

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