Degrees to radians – and radians to degrees
1 ° = 0.017453293 rad
All units in this category
- 90°
- 1.5707963rad
- 1,570.7963mrad
- 100gon
- 5,400′
- 324,000″
- 0.25rev
Formula
Multiply the value in degrees by 0.017453293 to get radians.rad = ° × 0.017453293
Multiply the value in radians by 57.29578 to get degrees.° = rad × 57.29578
How to convert degrees to radians
Type a value in the field above and the result is calculated instantly. Use the arrow button to swap direction, or pick other units from the lists.
Doing it in your head
A rough conversion for when the calculator is not to hand. The error comes last, and it holds in both directions at that order of magnitude.
- Radians to degrees: × 50 + 15%. That gives 57.5 instead of 57.2958, an error of 0.36%.
Degrees to radians – common values
| Degrees (°) | Radians (rad) |
|---|---|
| 1 | 0.0174533 |
| 15 | 0.261799 |
| 30 | 0.523599 |
| 45 | 0.785398 |
| 60 | 1.0472 |
| 90 | 1.5708 |
| 120 | 2.0944 |
| 180 | 3.14159 |
| 270 | 4.71239 |
| 360 | 6.28319 |
Radians to degrees – common values
| Radians (rad) | Degrees (°) |
|---|---|
| 1 | 57.2958 |
| 15 | 859.437 |
| 30 | 1,718.87 |
| 45 | 2,578.31 |
| 60 | 3,437.75 |
| 90 | 5,156.62 |
| 120 | 6,875.49 |
| 180 | 10,313.2 |
| 270 | 15,469.9 |
| 360 | 20,626.5 |
About the units
Degrees. A degree is one 360th of a turn, π/180 radians. The degree is not an SI unit, but it is one of the long-standing units of angle in the SI Brochure, and it is a legal unit throughout the EU. It is used for maps, coordinates, building angles and compass bearings. Coordinates can be written in decimal degrees, in degrees with decimal minutes or in degrees, minutes and seconds: 15.51° is 15°30.6′, that is 15°30′36″. And there is the trap: 15.51° is not 15°51′.
Radians. The radian is the SI coherent unit of plane angle and a legal unit throughout the EU. One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius; a right angle is π/2 radians. That makes one radian 180/π degrees, 57.29578°, and a full turn 2π radians. All mathematics and physics count in radians, and angular velocity is given in radians per second. The trap is the calculator mode: sin(30) is 0.5 in degrees but −0.988 in radians.