Radians to Degrees Converter Formula

Understand the math behind the radians to degrees converter. Each variable explained with a worked example.

Use the Radians to Degrees Converter

Formulas Used

Degrees

degrees = rad * 180 / pi

Turns

turns = rad / (2 * pi)

Variables

VariableDescriptionDefault
radRadians(rad)3.14159

How It Works

How to Convert Radians to Degrees

Formula

Degrees = Radians × (180 / pi)

Since pi radians equals 180 degrees, multiply the radian value by 180/pi (approximately 57.2958) to get degrees.

Worked Example

Convert pi radians to degrees.

rad = 3.14159
  1. 01Degrees = 3.14159 × (180 / pi)
  2. 02= 3.14159 × 57.2958
  3. 03≈ 180.0 degrees

Frequently Asked Questions

What is 1 radian in degrees?

1 radian equals approximately 57.2958 degrees (180/pi).

What is pi/4 radians in degrees?

pi/4 radians equals 45 degrees.

When should I use radians vs degrees?

Use radians in calculus, physics formulas, and most mathematical contexts. Use degrees for everyday angles, navigation, and geometry class.

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Open Radians to Degrees Converter