Degrees and radians
A full circle is 360 degrees, 2π radians or 400 gradians. Degrees are used in everyday geometry and navigation; radians are the natural unit in mathematics, physics and programming, where functions such as sin() and cos() expect radians.
- Radians = degrees × π ÷ 180
- Degrees = radians × 180 ÷ π
| Degrees | Radians | Turns |
|---|---|---|
| 30° | π/6 ≈ 0.5236 | 1/12 |
| 45° | π/4 ≈ 0.7854 | 1/8 |
| 90° | π/2 ≈ 1.5708 | 1/4 |
| 180° | π ≈ 3.1416 | 1/2 |
| 360° | 2π ≈ 6.2832 | 1 |
One degree divides into 60 arcminutes, and one arcminute into 60 arcseconds.