Angle Converter
Convert degrees, radians, gradians, arcminutes, arcseconds and turns.
About the Angle Converter
A full turn is 360°, 2π radians or 400 gradians. One radian is the angle where the arc equals the radius, about 57.2958°. Maths and programming use radians; maps and everyday use degrees.
The formula
Result = Value × (size of the “from” unit ÷ size of the “to” unit)
- 1 °
- 0.01745329252 °
- 1 rad
- 1 °
- 1 gon
- 0.01570796327 °
- 1 ′
- 0.0002908882087 °
- 1 ″
- 0.000004848136811 °
- 1 turn
- 6.283185307 °
Every angle unit is converted through degree using its exact definition.
Common conversions
| From | To |
|---|---|
| 90 ° | 1.570796327 rad |
| 180 ° | 3.141592654 rad |
| 1 rad | 57.29577951 ° |
| 1 turn | 360 ° |
| 90 ° | 100 gon |
How to read your result
- Negative angles are allowed (clockwise rotation).
Worked example
Example: 99 degree = 1.727875959 rad
- Inputs: Value: 99; From: Degree (°); To: Radian (rad).
- Formula: Result = Value × (size of the “from” unit ÷ size of the “to” unit)
- Multiply by the number of rad in one ° 99 × 0.01745329252 = 1.727875959 rad
- Result: 99 degree = 1.727875959 rad
- 1 ° = 0.01745329252 rad
- 1 rad = 57.29577951 °
Questions people ask
How do I convert degrees to radians?
Multiply by π/180. 90° × π/180 = π/2 ≈ 1.5708 rad.
What are arcminutes used for?
Map coordinates and astronomy: 1° = 60′ and 1′ = 60″.