Convert degrees to radians and radians to degrees instantly. Bidirectional angle converter with formula and common values.
To convert degrees to radians, multiply the angle in degrees by pi/180, which equals approximately 0.0174533. A full circle contains 360 degrees or 2pi radians.
| Degrees | Radians |
|---|---|
| 15 | 0.261799 |
| 30 | 0.523599 |
| 45 | 0.785398 |
| 90 | 1.570796 |
| 120 | 2.094395 |
| 180 | 3.141593 |
| 270 | 4.712389 |
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One degree equals approximately 0.0174533 radians. This comes from dividing pi by 180.
Radians simplify calculus and trigonometric formulas. Derivatives of sine and cosine only work cleanly when the angle is in radians.
180 degrees equals exactly pi radians, approximately 3.14159. This is the fundamental relationship between the two units.
Degrees are more intuitive for everyday measurements like navigation, construction, and geographic coordinates. Radians are preferred in pure mathematics and physics equations.