Angle Converter Formula

Understand the math behind the angle converter. Each variable explained with a worked example.

Use the Angle Converter

Formulas Used

Radians

radians = degrees * pi / 180

Gradians

gradians = degrees * 10 / 9

Turns

turns = degrees / 360

Arcminutes

arcminutes = degrees * 60

Variables

VariableDescriptionDefault
degreesAngle(°)180

How It Works

Angle Converter

Conversion Factors from Degrees

  • Radians: degrees × pi / 180
  • Gradians: degrees × 10/9
  • Turns: degrees / 360
  • Arcminutes: degrees × 60

    • Worked Example

    Convert 180 degrees to radians, gradians, and turns.

    degrees = 180
    1. 01Radians = 180 × pi / 180 = 3.14159 rad
    2. 02Gradians = 180 × 10/9 = 200 grad
    3. 03Turns = 180 / 360 = 0.5 turns
    4. 04Arcminutes = 180 × 60 = 10800 arcminutes

    Ready to run the numbers?

    Open Angle Converter