How to convert degrees to radians
1 ° ≈ 0.0174533 rad
1° = π/180 rad exactly (SI Brochure, Table 8). Multiply degrees by π/180, about 0.01745329.
Examples
- 90 ° = 1.5707963 rad: a right angle
- 45 ° = 0.78539816 rad: half a right angle
- 360 ° = 6.2831853 rad: one full turn
Degrees to radians chart
| Degrees (°) | Radians (rad) |
|---|---|
| 1 ° | 0.017453293 rad |
| 2 ° | 0.034906585 rad |
| 3 ° | 0.052359878 rad |
| 4 ° | 0.06981317 rad |
| 5 ° | 0.087266463 rad |
| 10 ° | 0.17453293 rad |
| 15 ° | 0.26179939 rad |
| 20 ° | 0.34906585 rad |
| 25 ° | 0.43633231 rad |
| 45 ° | 0.78539816 rad |
| 50 ° | 0.87266463 rad |
| 75 ° | 1.3089969 rad |
| 90 ° | 1.5707963 rad |
| 100 ° | 1.7453293 rad |
| 360 ° | 6.2831853 rad |
Common mistakes
- A calculator in the wrong angle mode gives wrong trigonometry answers even when your conversion is right.
- π/180 is irrational, so decimal radian values are rounded; keep answers like π/3 in terms of π when exactness matters.