C# / .NET - Math.Atan2() method example

The Math.Atan2() function returns the angle in radians in the range -Math.PI/2 to +Math.PI/2 between the positive x-axis and the ray to the point (x, y) ≠ (0, 0).

using System;

public class Program
{
    public static void Main(string[] args) 
    {
        //                            y   x         angle in radians
        Console.WriteLine(Math.Atan2( 2,  4)); //  0.4636476090008061 <-   ~26.6 degrees
        Console.WriteLine(Math.Atan2( 4, -2)); //  2.0344439357957027 <-  ~116.6 degrees
        Console.WriteLine(Math.Atan2(-2, -4)); // -2.677945044588987  <- ~-153.4 degrees
        Console.WriteLine(Math.Atan2(-4,  2)); // -1.1071487177940904 <-  ~-63.4 degrees
    }
}

Atan2() method has been visualized on below image:

1. Documentation

namespace System
{
    public static class Math
    {
        // ...
        public static double Atan2(double y, double x) { ... }
        // ...
    }
}

2. Working with degrees

using System;

public class Program
{
    static double CalculateAngle(double y, double x)
    {
        double angle = Math.Atan2(y, x);
        return (180 / Math.PI) * angle; // rad to deg conversion
    }

    public static void Main(string[] args)
    {
        //                                  y   x           degrees
        Console.WriteLine(  CalculateAngle( 2,  4)); //  26.56505117707799 
        Console.WriteLine(  CalculateAngle( 4, -2)); // 116.56505117707799 
        Console.WriteLine(  CalculateAngle(-2, -4)); // -153.434948822922  
        Console.WriteLine(  CalculateAngle(-4,  2)); // -63.43494882292201 
    }
}

3.  Conversion to only clockwise angles in degrees

This section shows how to convert angles to clockwise angles (from 0 to 360 degrees).

using System;

public class Program
{
    static double CalculateAngle(double y, double x)
    {
        double angle = Math.Atan2(y, x);
        if (angle < 0.0)
        {
            angle += 2.0 * Math.PI;
        }
        return (180 / Math.PI) * angle; // rad to deg conversion
    }

    public static void Main(string[] args)
    {
        //                                  y   x           degrees
        Console.WriteLine(  CalculateAngle( 2,  4)); //  26.56505117707799
        Console.WriteLine(  CalculateAngle( 4, -2)); // 116.56505117707799
        Console.WriteLine(  CalculateAngle(-2, -4)); // 206.565051177078
        Console.WriteLine(  CalculateAngle(-4,  2)); // 296.565051177078
    }
}

4.  Conversion to only counterclockwise angles in degrees

This section shows how to convert angles to counterclockwise angles (from -360 to 0 degrees).

using System;

public class Program
{
    static double CalculateAngle(double y, double x)
    {
        double angle = Math.Atan2(y, x);
        if (angle > 0.0)
        {
            angle -= 2.0 * Math.PI;
        }
        return (180 / Math.PI) * angle; // rad to deg conversion
    }

    public static void Main(string[] args)
    {
        //                                  y   x            degrees
        Console.WriteLine(  CalculateAngle( 2,  4)); // -333.434948822922 
        Console.WriteLine(  CalculateAngle( 4, -2)); // -243.434948822922 
        Console.WriteLine(  CalculateAngle(-2, -4)); // -153.434948822922 
        Console.WriteLine(  CalculateAngle(-4,  2)); // -63.43494882292201
    }
}

References

1. atan2 - Wikipedia
2. Inverse trigonometric functions - Wikipedia