This free angle converter changes radians (rad) to degrees (°) and back again, useful for students, engineers, and anyone working with trigonometry, robotics, or graphics where one unit system is required but a value is given in the other. Type a value in either field and the result updates instantly.
How it works
An angle measured in radians is the arc length it subtends on a circle of radius 1. A full turn around that circle has circumference 2π, and a full turn is 360°, so 2π radians = 360°, which simplifies to π radians = 180°. Solving for degrees gives the exact conversion formula:
degrees = radians × 180 ÷ π
To go the other way, radians = degrees × π ÷ 180. The constant 180 ÷ π ≈ 57.29578 is the number of degrees in a single radian. The tool applies these formulas directly with full floating-point precision and rounds the displayed result for readability.
Example
Convert 2.5 radians to degrees:
degrees = 2.5 × 180 ÷ π = 450 ÷ 3.14159265 ≈ 143.2394°
Going back: 143.2394 × π ÷ 180 = 143.2394 × 0.0174533 ≈ 2.5 radians, confirming the round trip.
| Radians (rad) | Degrees (°) |
|---|---|
| 0.523599 rad | 30° |
| 0.785398 rad | 45° |
| 1.570796 rad | 90° |
| 3.141593 rad | 180° |
| 6.283185 rad | 360° |
All calculations run entirely in your browser — nothing you type is uploaded or stored.