Convert Degrees to Radians
° to rad · angle conversion
What are degrees and radians?
A degree is 1/360 of a full circle, the most common everyday angle unit. A radian is the angle where the arc length equals the radius; a full circle is 2π radians. For reference: a right angle is 90° (π/2 radians), and a full turn is 360° (2π radians).
How to convert degrees to radians
1 ° = 0.0174533 rad. To convert, multiply the number of degrees by 0.0174533. For example, 5 ° = 0.0872665 rad, and 20 ° = 0.349066 rad. To go the other way, multiply radians by 57.2958 (since 1 rad = 57.2958 °).
Degrees to Radians conversion table
| Degrees (°) | Radians (rad) |
|---|---|
| 1 | 0.0174533 |
| 15 | 0.261799 |
| 30 | 0.523599 |
| 45 | 0.785398 |
| 90 | 1.5708 |
| 180 | 3.14159 |
| 360 | 6.28319 |
FAQ
What is 1 ° in rad?
1 ° = 0.0174533 rad. To convert any amount, multiply the number of degrees by 0.0174533.
How do I convert radians back to degrees?
Go the other way: 1 rad = 57.2958 °, so multiply radians by 57.2958 to get degrees.
Is a degree bigger than a radian?
No — 1 ° is the smaller unit, equal to 0.0174533 rad (it takes 57.2958 ° to make one rad).
Are these angle conversions exact?
They use the standard internationally-defined conversion factors. Results are rounded to six significant figures for readability, which is accurate enough for everyday and most technical use.