Degree to Radian
1 ° = 0.0174532925 rad
How to convert degree to radian
Enter the value in degree (°) above and the equivalent in radian (rad) updates as you type. This conversion comes up when programming: graphics libraries often want radians while design tools show degrees.
- A right angle: 90°, about 1.57 radians (π/2) → that is 1.570796 rad in radian.
- A 45° roof pitch is a 50% (100 gon/2) slope guide → that is 0.785398 rad in radian.
Typical situations: machining and carpentry specs mixing degrees and gradians; navigation: bearings and compass readings.
You can also convert in the other direction: Radian to Degree
Degree to Radian conversion table
| Degree (°) | Radian (rad) |
|---|---|
| 1 | 0.017453 |
| 2 | 0.034907 |
| 5 | 0.087266 |
| 10 | 0.174533 |
| 25 | 0.436332 |
| 50 | 0.872665 |
| 100 | 1.745329 |
Watch out for
- Radians are dimensionless, which is why calculus uses them; degree-based formulas break in derivatives
- Gradians (400 per circle) appear mainly on European construction calculators
Frequently asked questions
How many radians is 1 degree?
1 degree = 0.017453 radians.
What is the formula to convert degree to radians?
The formula is: rad = ° × 0.017453.
What is 10 degrees in radians?
10 degrees = 0.174533 radians.