How the conversion works
A full turn is 360° or 2π radians, so one radian is 180/π degrees and one degree is π/180 radians. To convert degrees to radians, multiply by π and divide by 180. To go the other way, multiply by 180 and divide by π. Because π is irrational, a decimal result is almost always an approximation — that is why the exact form is worth keeping.
Worked example: 45°
Multiply 45 by π/180. Both numbers divide by 45, which leaves π/4 — the exact answer. As a decimal that is about 0.785398 radians. Going back the other way, π/4 × 180/π cancels the π and leaves 180/4 = 45°.
Common angles
The angles that come up most often in trigonometry, with their exact and decimal radian values.
| Degrees | Radians (exact) | Radians (decimal) |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.523599 |
| 45° | π/4 | 0.785398 |
| 60° | π/3 | 1.047198 |
| 90° | π/2 | 1.570796 |
| 120° | 2π/3 | 2.094395 |
| 135° | 3π/4 | 2.356194 |
| 150° | 5π/6 | 2.617994 |
| 180° | π | 3.141593 |
| 270° | 3π/2 | 4.712389 |
| 360° | 2π | 6.283185 |