Angle Converter
180 degrees equals pi radians, about 3.14159 radians. This angle converter switches a value between degrees, radians, and gradians. Enter an angle, pick the units, and read the result, whether you are turning radians into degrees for a graph or degrees into radians for a formula.
Quick answer
A full circle is 360 degrees, 2 pi radians, or 400 gradians.
Result
3.141593
What this tells you
- •A full circle is 360 degrees, 2 pi radians, or 400 gradians.
- •One radian is about 57.2958 degrees.
- •Degrees are common in geometry, radians in trigonometry and calculus.
- •Switch the from and to units to convert in either direction.
How to Use
- 1Enter the angle you want to convert.
- 2Choose the unit you are converting from.
- 3Choose the unit you are converting to.
- 4Read the converted angle below.
How It Works
Formula
radians = degrees x pi / 180Degrees and radians relate through pi: 180 degrees is pi radians. To go from degrees to radians, multiply by pi/180. To go from radians to degrees, multiply by 180/pi. Gradians use 400 to a full circle, so 90 degrees is 100 gradians.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Convert 180 degrees to radians
180 x pi / 180 = pi, which is about 3.141593 radians.
Convert 1 radian to degrees
1 x 180 / pi = 57.29578 degrees.
Common Angle Conversions
Degrees with their radian and gradian equivalents.
| Degrees | Radians | Gradians |
|---|---|---|
| 30 | pi/6 (0.5236) | 33.33 |
| 45 | pi/4 (0.7854) | 50 |
| 60 | pi/3 (1.0472) | 66.67 |
| 90 | pi/2 (1.5708) | 100 |
| 180 | pi (3.1416) | 200 |
| 360 | 2 pi (6.2832) | 400 |
Radians are shown both as a multiple of pi and as a decimal rounded to 4 places.
Common mistakes
- Using 3.14 for a half turn in degrees. Pi radians is 180 degrees, not 3.14 degrees.
- Forgetting to multiply by pi/180. Degrees and radians are not interchangeable as plain numbers.
- Mixing gradians with degrees. A right angle is 90 degrees but 100 gradians.