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

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Created by:

Dharman

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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).

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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:

atan2(y, x) function visualization - C# Math Object. — Atan2(y, x) function visualization - C# Math Object.

1. Documentation

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Syntax	xxxxxxxxxx 1 namespace System 2 { 3 public static class Math 4 { 5 // ... 6 public static double Atan2(double y, double x) { ... } 7 // ... 8 } 9 }
Parameters	`y`, `x` - double values that are coordinates of the point (primitive value).
Result	`number` value of angle between two lines `OP` and `OX` in radians in the range `-Math.PI/2` to `+Math.PI/2` (primitive value). Where: `O=(0, 0)` - intersection point of coordinate system axes, `P=(x, y)` - out point, `OX` - positive part of x-axis. If point is in the 1st (I) or 2nd (II) quadrant angle is measured in a counterclockwise direction. If point is in the 3rd (III) or 4th (IV) quadrant angle is measured in a clockwise direction. Note: angle arrows show measured angles for points located in different quadrants.
Description	`Atan2` is a static method that takes two parameters and returns an approximation of the arctangent(y/x) function taking into account quadrants of a point location (`P=(x, y)`).

2. Working with degrees

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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

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

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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

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

xxxxxxxxxx
 
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
    }
}