Convert degrees to radians in one step. Type a value, change the units if you need a different pair, and the answer updates as you type, with the reverse rate and a quick reference list.
Results are estimates for planning. Check the figures before you make a financial or health decision.
How to convert degrees to radians
Multiply the number of ° by 0.017453 to get rad:
rad = ° × 0.017453
To go the other way, divide by 0.017453 (or multiply by 57.29578). The converter stores each unit as a multiple of a base unit, so you can also pick any other pair of units from the same group.
Worked example
Using the default values in the converter above:
| Input | Value |
|---|---|
| Value | 90 |
| From | Degrees |
| To | Radians |
90 degrees equals 1.570796 radians
Degrees to Radians reference table
| Degrees | Radians |
|---|---|
| 1 ° | 0.017453 rad |
| 15 ° | 0.261799 rad |
| 30 ° | 0.523599 rad |
| 45 ° | 0.785398 rad |
| 60 ° | 1.047198 rad |
| 90 ° | 1.570796 rad |
| 180 ° | 3.141593 rad |
| 270 ° | 4.712389 rad |
| 360 ° | 6.283185 rad |
Tips and common mistakes
A full turn is 360 degrees or 2π radians, so 180° equals π radians (about 3.14159) and 90° equals π/2 (about 1.5708). To convert degrees to radians multiply by π ÷ 180, and to go back, multiply by 180 ÷ π.
The classic mistake is leaving a scientific calculator in the wrong mode, so that sin(90) gives 0.894 (radians) instead of 1 (degrees). Check the mode before trusting a trigonometric result.
Gradians (gon) divide a right angle into 100 parts and are used in some surveying, while turns are handy in rotations and animations.
Frequently asked questions
How many radians are in 1 °?
1 ° equals 0.017453 radians.
How do I convert ° to rad by hand?
Multiply the ° figure by 0.017453. For example, 90 ° × 0.017453 = 1.570796 rad.
How do I convert rad back to °?
Divide the rad figure by 0.017453, or multiply it by 57.29578. For example, 1.570796 rad is 90 °.
Is this conversion exact?
Yes. 180 degrees is exactly π radians.