Degrees to Radians
Convert degrees (°) to radians (rad) instantly — with formula and reference table.
Quick answer: 1 ° = 0.017453 rad. To convert degrees to radians, multiply by ° × 0.017453.
Converting degrees to radians
This converter changes a value in degrees (°) into radians (rad). One degree equals 0.017453 rad. A full circle is 360 degrees or 2 pi radians, so one degree equals pi/180 radians (about 0.01745 rad). The conversion runs entirely in your browser — enter a value and the result updates instantly, in either direction.
Formula
rad = ° × 0.017453
Example
Convert 10 ° to rad: 10 × 0.017453 = 0.174533 rad.
Degrees to Radians conversion table
| Degrees (°) | Radians (rad) |
|---|---|
| 1 ° | 0.017453 rad |
| 2 ° | 0.034907 rad |
| 3 ° | 0.05236 rad |
| 5 ° | 0.087266 rad |
| 10 ° | 0.174533 rad |
| 20 ° | 0.349066 rad |
| 25 ° | 0.436332 rad |
| 50 ° | 0.872665 rad |
| 100 ° | 1.745329 rad |
Popular degrees to radians conversions
Quick answers for the ° values people look up most often:
- 4 ° = 0.0698 rad
- 6 ° = 0.1047 rad
- 7 ° = 0.1222 rad
- 8 ° = 0.1396 rad
- 9 ° = 0.1571 rad
- 12 ° = 0.2094 rad
- 15 ° = 0.2618 rad
- 30 ° = 0.5236 rad
- 40 ° = 0.6981 rad
- 60 ° = 1.0472 rad
- 75 ° = 1.309 rad
- 80 ° = 1.3963 rad
- 90 ° = 1.5708 rad
- 150 ° = 2.618 rad
- 200 ° = 3.4907 rad
- 250 ° = 4.3633 rad
- 500 ° = 8.7266 rad
- 1000 ° = 17.4533 rad
How to use this converter
- Enter a value in the degrees (°) field.
- Read the converted value in radians (rad) below.
- Type into the rad field instead to convert in reverse, or use the swap button.
Frequently asked questions
How do I convert degrees to radians?
Multiply degrees by pi/180 (about 0.01745). 180 degrees = pi radians.
What is 90 degrees in radians?
90 degrees equals pi/2, about 1.5708 radians.
Why use radians?
Radians make calculus and trigonometry cleaner because arc length equals radius times angle in radians.