Degrees to Radians Calculator
Convert any angle from degrees to radians using the formula radians = degrees x pi / 180. The calculator also shows the result as a fraction of pi, plus turns and gradians for engineering applications.
Degrees and radians are both units for measuring angles. Degrees divide a full circle into 360 parts, while radians define one full rotation as 2π (roughly 6.2832). Radians are the standard unit in mathematics and physics because they simplify many formulas.
Formula: radians = degrees x (π / 180)
Common Degree to Radian Conversions:
| Degrees | Radians | Pi Form |
|---|---|---|
| 0° | 0 | 0 |
| 30° | 0.5236 | π/6 |
| 45° | 0.7854 | π/4 |
| 60° | 1.0472 | π/3 |
| 90° | 1.5708 | π/2 |
| 120° | 2.0944 | 2π/3 |
| 180° | 3.1416 | π |
| 270° | 4.7124 | 3π/2 |
| 360° | 6.2832 | 2π |
Why radians matter: In calculus, the derivative of sin(x) is cos(x) only when x is measured in radians. If you use degrees, extra conversion factors appear in every derivative and integral. That is why virtually all scientific and engineering software defaults to radians.
To convert back: degrees = radians x (180 / π).