Degrees to Radians
Degrees and radians are two ways to measure an angle. A full turn is 360 degrees or 2 pi radians. Convert between them for trigonometry, physics and programming.
Your numbers
Result
- Unit
- radians
| Degrees | Radians |
|---|---|
| 30 | 0.52 |
| 45 | 0.79 |
| 90 | 1.57 |
| 180 | 3.14 |
| 360 | 6.28 |
How to convert
To go from degrees to radians, multiply by pi / 180: 180 x pi / 180 = pi (about 3.1416 rad). For the reverse, multiply by 180 / pi. The key reference: 180 degrees = pi radians, a half turn.
Why radians
The radian is the "natural" measure of an angle: 1 rad is the angle whose arc equals the radius. Trig functions in math and in programming languages (like Math.sin) expect radians, not degrees.
Frequently asked questions
Sources
- Trigonometry — angle measures (degree and radian)
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