How to convert Trigonometric Angles in Radians using C#?

To convert trigonometric angles from degrees to radians in C#, multiply the degree value by Math.PI/180. Most trigonometric functions in C# expect angles in radians, so this conversion is essential for accurate calculations.

Syntax

Following is the syntax for converting degrees to radians −

double radians = degrees * (Math.PI / 180.0);

Following is the syntax for converting radians to degrees −

double degrees = radians * (180.0 / Math.PI);

Converting Degrees to Radians

Example

The following example shows how to properly convert degrees to radians before using trigonometric functions −

using System;

class Program {
   static void Main() {
      double angleInDegrees = 45;
      
      // Incorrect: using degrees directly
      Console.WriteLine("Cos(45 degrees directly): " + Math.Cos(45));
      
      // Correct: convert degrees to radians first
      double angleInRadians = angleInDegrees * (Math.PI / 180.0);
      Console.WriteLine("Cos(45 degrees converted): " + Math.Cos(angleInRadians));
      
      // Alternative using Math.PI constant
      double result = Math.Cos(Math.PI * 45 / 180.0);
      Console.WriteLine("Using Math.PI formula: " + result);
   }
}

The output of the above code is −

Cos(45 degrees directly): 0.525321988818042
Cos(45 degrees converted): 0.7071067811865476
Using Math.PI formula: 0.7071067811865476

Converting Radians to Degrees

Example

You can also convert radians back to degrees for display purposes −

using System;

class Program {
   static void Main() {
      double radiansValue = Math.PI / 4; // 45 degrees in radians
      
      // Convert radians to degrees
      double degreesValue = radiansValue * (180.0 / Math.PI);
      
      Console.WriteLine("Radians: " + radiansValue);
      Console.WriteLine("Degrees: " + degreesValue);
      
      // Verify with trigonometric function
      Console.WriteLine("Sin(" + degreesValue + "°) = " + Math.Sin(radiansValue));
   }
}

The output of the above code is −

Radians: 0.7853981633974483
Degrees: 45
Sin(45°) = 0.7071067811865475

Common Angle Conversions

Example

Here are some commonly used angle conversions −

using System;

class Program {
   static void Main() {
      double[] commonAngles = {0, 30, 45, 60, 90, 180, 270, 360};
      
      Console.WriteLine("Degrees\tRadians\t\tSin\t\tCos");
      Console.WriteLine("-------\t-------\t\t---\t\t---");
      
      foreach(double angle in commonAngles) {
         double radians = angle * (Math.PI / 180.0);
         Console.WriteLine($"{angle}°\t{radians:F4}\t\t{Math.Sin(radians):F4}\t\t{Math.Cos(radians):F4}");
      }
   }
}

The output of the above code is −

Degrees	Radians		Sin		Cos
-------	-------		---		---
0°	0.0000		0.0000		1.0000
30°	0.5236		0.5000		0.8660
45°	0.7854		0.7071		0.7071
60°	1.0472		0.8660		0.5000
90°	1.5708		1.0000		0.0000
180°	3.1416		0.0000		-1.0000
270°	4.7124		-1.0000		-0.0000
360°	6.2832		-0.0000		1.0000

Conclusion

Converting degrees to radians in C# is essential for accurate trigonometric calculations. Use the formula radians = degrees * (Math.PI / 180.0) to convert degrees to radians, and degrees = radians * (180.0 / Math.PI) to convert back to degrees when needed for display or user interface purposes.