Quick reference table
Common angle conversions
| From | To |
|---|---|
| 1 ° | 0.01745329252 rad |
| 1 rad | 57.29577951 ° |
| 1 ° | 1.111111111 grad |
| 1 grad | 0.9 ° |
| 1 turn | 360 ° |
| 1 ′ | 0.01666666667 ° |
How to convert angle
Angles are measured in degrees in everyday life and navigation, in radians in mathematics and programming, and in gradians in some surveying. A full turn is 360 degrees, 2π radians or 400 gradians.
Every angle unit is a fixed multiple of one base unit, the °. To convert a value, multiply it by the size of the starting unit and divide by the size of the target unit. For example, to convert ° to rad, multiply by 0.01745329252. To go the other way, divide by 0.01745329252.
The converter above does this for you and shows the exact formula under the result.
Worked examples
Degrees to Radians
| Degrees (°) | Radians (rad) |
|---|---|
| 1 ° | 0.01745329252 rad |
| 2 ° | 0.03490658504 rad |
| 5 ° | 0.08726646260 rad |
| 10 ° | 0.1745329252 rad |
| 25 ° | 0.4363323130 rad |
| 50 ° | 0.8726646260 rad |
| 100 ° | 1.745329252 rad |
| 1,000 ° | 17.45329252 rad |
Radians to Degrees
| Radians (rad) | Degrees (°) |
|---|---|
| 1 rad | 57.29577951 ° |
| 2 rad | 114.5915590 ° |
| 5 rad | 286.4788976 ° |
| 10 rad | 572.9577951 ° |
| 25 rad | 1,432.394488 ° |
| 50 rad | 2,864.788976 ° |
| 100 rad | 5,729.577951 ° |
| 1,000 rad | 57,295.77951 ° |
Angle units explained
| Unit | Symbol | Equals |
|---|---|---|
| Degrees | ° | 1 ° = 1 ° |
| Radians | rad | 1 rad = 57.2957795131 ° |
| Gradians | grad | 1 grad = 0.9 ° |
| Arcminutes | ′ | 1 ′ = 0.0166666666667 ° |
| Arcseconds | ″ | 1 ″ = 0.000277777777778 ° |
| Turns | turn | 1 turn = 360 ° |
| Milliradians | mrad | 1 mrad = 0.0572957795131 ° |
| Mils (NATO) | mil | 1 mil = 0.05625 ° |
Popular conversions: degrees to radians, radians to degrees.
Frequently asked questions
How many degrees is one radian?
One radian is about 57.29578 degrees, because 180° equals π radians.
How do I convert degrees to radians?
Multiply the degrees by π/180. For example, 90° is π/2, or about 1.5708 rad.
How many rad is 1 °?
1 ° = 0.01745329252 rad, and 1 rad = 57.29577951 °.
Does this angle converter work offline?
Yes. After the page has loaded once, all calculations run in your browser, so it keeps working without an internet connection.