Degrees to Radians Converter
To convert degrees to radians, multiply by π/180 ≈ 0.017453. Example: 90° × π/180 = π/2 ≈ 1.5708 radians.
Inverse conversion
To convert radians to degrees, multiply by 180/π ≈ 57.2958. Example: π/2 radians × 180/π = 90°.
Formula
Formula
radians = degrees × π ÷ 180
Worked example
Convert 270° to radians: 270 × π/180 = 270π/180 = 3π/2 ≈ 4.7124 radians.
Quick reference table
| ° | rad |
|---|---|
| 0 | 0 |
| 30 | 0.523599 |
| 45 | 0.785398 |
| 60 | 1.047198 |
| 90 | 1.570796 |
| 120 | 2.094395 |
| 135 | 2.356194 |
| 180 | 3.141593 |
| 270 | 4.712389 |
| 360 | 6.283185 |
Unit definitions
Degree (°)
The degree (°) divides a circle into 360 equal parts. Widely used in everyday geometry, navigation, and engineering.
Radian (rad)
The radian (rad) is the SI unit of angle. 1 radian is the angle subtended by an arc equal in length to the circle's radius. 2π radians = 360°.
Common use cases
- Trigonometry and calculus
- Computer graphics and game development
- Physics and engineering formulas
- Navigation and surveying