Angle conversion chart
Convert between degrees and radians, the two main ways to measure angles. Degrees split a full turn into 360; radians measure the angle by arc length, with a full turn equal to two pi.
Conversion formulas
| Conversion | Formula |
|---|---|
| Degrees to radians | radians = degrees × π / 180 |
| Radians to degrees | degrees = radians × 180 / π |
Common angles
| Degrees | Radians |
|---|---|
| 0° | 0 |
| 30° | π/6 |
| 45° | π/4 |
| 60° | π/3 |
| 90° | π/2 |
| 120° | 2π/3 |
| 135° | 3π/4 |
| 150° | 5π/6 |
| 180° | π |
| 270° | 3π/2 |
| 360° | 2π |
A full circle is 360 degrees or 2 pi radians, so 180 degrees equals pi radians. To convert degrees to radians, multiply by pi over 180; to go the other way, multiply by 180 over pi. Radians are the natural unit in higher mathematics because they tie an angle directly to arc length.
Need the unit circle?
See the Unit Circle Chart and the Circle Formula Chart.
Degrees and radians
Degrees are familiar from everyday use, dividing a full turn into 360 equal parts. Radians measure an angle by how far you travel around a unit circle, so a full turn of circumference 2 pi equals 2 pi radians. Because 360 degrees and 2 pi radians describe the same full turn, you can convert between them with a single ratio.
Why radians matter
In calculus and physics, radians are the natural choice because they make formulas for arc length, angular speed, and the derivatives of trig functions clean and factor-free. An arc length is simply the radius times the angle in radians, with no extra constants, which is why higher mathematics defaults to radians.
FAQ
How do I convert degrees to radians?
Multiply the degrees by π / 180. So 90 degrees is 90 × π/180 = π/2 radians.
How many radians are in a full circle?
2π radians, which equals 360 degrees. Half a circle is π radians, or 180 degrees.
Why use radians instead of degrees?
Radians link angle directly to arc length, making calculus and physics formulas simpler and free of extra conversion constants.