Radians to Degrees Converter
Type a value in radians to see it in degrees as you type, with the exact formula and a reference chart.
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How this was calculated
- 1 radian = 57.29577951 degrees
- 2 × 57.29577951 = 114.59156 °
| rad | ° |
|---|---|
| 0.1 rad | 5.72958 ° |
| 0.25 rad | 14.3239 ° |
| 0.5 rad | 28.6479 ° |
| 1 rad | 57.2958 ° |
| 1.5 rad | 85.9437 ° |
| 2 rad | 114.592 ° |
| 2.5 rad | 143.239 ° |
| 3 rad | 171.887 ° |
| 3.14159 rad | 180 ° |
| 4 rad | 229.183 ° |
| 5 rad | 286.479 ° |
| 6 rad | 343.775 ° |
| 6.28319 rad | 360 ° |
| 10 rad | 572.958 ° |
| ° | rad |
|---|---|
| 1 ° | 0.0174533 rad |
| 5 ° | 0.0872665 rad |
| 10 ° | 0.174533 rad |
| 15 ° | 0.261799 rad |
| 30 ° | 0.523599 rad |
| 45 ° | 0.785398 rad |
| 60 ° | 1.0472 rad |
| 90 ° | 1.5708 rad |
| 120 ° | 2.0944 rad |
| 135 ° | 2.35619 rad |
| 150 ° | 2.61799 rad |
| 180 ° | 3.14159 rad |
How to convert radians to degrees
1 radian = 57.29577951 degrees. To convert radians to degrees, multiply by 57.29577951. A radian is the angle at the center of a circle that cuts off an arc as long as the radius; a full turn is 2π rad. A degree is 1/360 of a full turn, exactly π/180 radians (about 0.017453 rad).
Worked examples
- 1 radian = 57.2958 ° (1 × 57.29578)
- 2 radians = 114.592 ° (2 × 57.29578)
- 3.14159 radians = 180 ° (3.14159 × 57.29578)
Where this conversion comes up
Radians are used for trigonometry, calculus, physics and programming (sin, cos and tan take radians); degrees for maps, navigation, geometry, construction and everyday angles. Calculators, spreadsheets and programming languages (sin, cos, tan in Excel, Python and JavaScript) work in radians, while geometry and navigation use degrees. Half a turn is π rad = 180°, a full turn 2π rad = 360°, so 1 rad is about 57.2958°.
Quick estimate
Multiply by 57.3 (0.005% high): 2 rad ≈ 114.6°, exact 114.5916°. Or multiply by 180 and divide by π.
Common mistakes
- Dividing instead of multiplying. A degree is smaller than a radian, so the number of degrees must come out larger: 1 radian = 57.2958 °.
- Rounding too early. Keep the full factor until the last step; rounding 57.3 to 57 first puts large values noticeably off.
Going the other way? Use the degrees to radians converter.
Frequently asked questions
How do you convert radians to degrees?
Multiply the radians by 57.29577951. For example, 2 radians is 114.592 degrees.
How many degrees are in one radian?
One radian is 57.29577951 degrees. A radian is the angle at the center of a circle that cuts off an arc as long as the radius; a full turn is 2π rad.
What is 3.14159 radians in degrees?
3.14159 radians is 180 degrees.
Is there a quick way to estimate radians to degrees?
Multiply by 57.3 (0.005% high): 2 rad ≈ 114.6°, exact 114.5916°. Or multiply by 180 and divide by π.