Unit converter
Degrees to radians.
Convert ° to rad and rad to °. Type in either box and the other follows. Trigonometric functions in almost every programming language expect radians, which is where the missing π usually goes.
| ° | rad |
|---|---|
| 1 ° | 0.0174533 rad |
| 5 ° | 0.0872665 rad |
| 10 ° | 0.174533 rad |
| 15 ° | 0.261799 rad |
| 30 ° | 0.523599 rad |
| 45 ° | 0.785398 rad |
| 60 ° | 1.0472 rad |
| 90 ° | 1.5708 rad |
| 120 ° | 2.0944 rad |
| 180 ° | 3.14159 rad |
| 270 ° | 4.71239 rad |
| 360 ° | 6.28319 rad |
- Conversion goes through rad in both directions, so neither figure is rounded on the way.
Definitions
- The degree divides a full turn into 360, a Babylonian convention that survives because 360 divides so many ways.
- The radian is the SI unit of angle: the angle subtending an arc equal to the radius. A full turn is 2π radians.
- This conversion is exact by definition. 1 ° = 0.01745329252 rad.
- Angle is converted through rad.
How it works
One direction multiplies and the other divides by the same number, so nothing is lost by going back and forth.
The value passes through rad, the unit every other angle unit on the site is defined against, rather than a number written into this page on its own. That is why the figure here, the figure in the table above and the general angle converter always agree.
Display precision sets a maximum number of significant figures and trims trailing zeroes, so it changes what you see and never what was calculated. The editable box always holds a plain number at full working precision, so you can carry on from either side.
Common questions this answers: how many radians in a degree (0.0174533), how many degrees in a radian (57.2958), and what 90 ° is in radians (1.5708 rad).
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