Convert plane angle from radians (rad) to degrees (°) with this tool using the exact relationship between the SI unit radian and the degree. Suitable for trigonometry, robotics joints, graphics rotations, surveying notes, and spec sheets that report angles in degrees.
Radians (rad) to Degrees (°) Converter
Enter a value in the field below and press the button
Radians (rad)
Result in Degrees (°)
How to use
- Enter an angle in radians.
- Choose the number of decimal places.
- Select Convert to display degrees and the calculation line.
- Use Copy Result to copy the number.
- Use Clear All to reset all fields.
- The Swap control opens the degrees to radians calculator.
Definitions and unit facts
Radian (rad) — SI unit of plane angle. One radian subtends an arc equal to the circle’s radius. A full turn is 2π rad. Abbreviation: rad. System: SI. Exact relation used here: 1 rad = 180/π degrees ≈ 57.29577951°.
Degree (°) — Non-SI unit of plane angle historically dividing a turn into 360 equal parts. Abbreviation: °. System: non-SI. Exact relation used here: 1° = π/180 radians ≈ 0.01745329252 rad.
Conversion formula
radians = degrees × π ÷ 180
Sources: NIST — Guide to the SI, Chapter 5 (degree: 1° = π/180 rad)
Conversion table
| Radians (rad) | Exact in π | Degrees (°) |
|---|---|---|
| 0 | 0 | 0 |
| 0.174533 | π/18 | 10 |
| 0.261799 | π/12 | 15 |
| 0.314159 | π/10 | 18 |
| 0.392699 | π/8 | 22.5 |
| 0.523599 | π/6 | 30 |
| 0.785398 | π/4 | 45 |
| 0.872665 | 5π/18 | 50 |
| 1.047198 | π/3 | 60 |
| 1.221730 | 7π/18 | 70 |
| 1.308997 | 5π/12 | 75 |
| 1.396263 | 4π/9 | 80 |
| 1.570796 | π/2 | 90 |
| 1.745329 | π/ \u22481.80 | 100 |
| 2.094395 | 2π/3 | 120 |
| 2.356194 | 3π/4 | 135 |
| 2.617994 | 5π/6 | 150 |
| 3.141593 | π | 180 |
| 4.712389 | 3π/2 | 270 |
| 6.283185 | 2π | 360 |
Real-world examples
- Right angle in a square corner: 1.570796 rad = 90°
- Straight angle along a line: 3.141593 rad = 180°
- Full revolution: 6.283185 rad = 360°
- Clock hands at 3:00: 1.570796 rad = 90°
- Clock minute tick spacing: 0.104720 rad = 6°
- Equilateral triangle interior angle: 1.047198 rad = 60°
- Regular pentagon central angle: 1.256637 rad = 72°
- Regular hexagon interior angle: 2.094395 rad = 120°
- Regular octagon interior angle: 2.356194 rad = 135°
- ACME screw thread included angle: 0.506146 rad = 29°
If you are willing, tell us how you use this calculator. If another online tool would help your work or studies, please mention it in the comments and we will gladly consider building it.
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