Radians to Degrees Converter
Convert radians to degrees instantly with this free radians to degrees converter. Enter any value to get an accurate angle conversion, plus the formula, the conversion factor and a full reference table.
What is 1 radian in degrees?
1 radian is equal to 57.2957795 degrees.
1 × 57.2957795 = 57.2957795 degrees
Result
1 radian = 57.29577951 degrees
Radians to Degrees formula
° = rad × 57.2957795
The radians to degrees conversion factor is 57.2957795131, which is exact by definition. 1 radian = 57.2957795131 degrees, and 1 degree = 0.01745329252 radians.
Worked examples
- 5 radians = 286.478898 degrees — 5 × 57.2957795 = 286.478898 degrees
- 45 radians = 2,578.31008 degrees — 45 × 57.2957795 = 2,578.31008 degrees
- 180 radians = 10,313.2403 degrees — 180 × 57.2957795 = 10,313.2403 degrees
Radians to Degrees conversion table
Every value below is calculated with the exact conversion factor and rounded for display.
| Radians (rad) | Degrees (°) |
|---|---|
| 1 rad | 57.29578 ° |
| 5 rad | 286.4789 ° |
| 10 rad | 572.9578 ° |
| 15 rad | 859.43669 ° |
| 30 rad | 1,718.8734 ° |
| 45 rad | 2,578.3101 ° |
| 60 rad | 3,437.7468 ° |
| 90 rad | 5,156.6202 ° |
| 120 rad | 6,875.4935 ° |
| 180 rad | 10,313.24 ° |
| 270 rad | 15,469.86 ° |
| 360 rad | 20,626.481 ° |
When you need to convert radians to degrees
- Comparing specifications written for a different market.
- Checking a figure quoted in an unfamiliar unit before acting on it.
- Converting values consistently across a spreadsheet, report or shopping list.
Common mistakes to avoid
- Dividing when you should multiply. Because 1 radian = 57.2958 degrees, the answer should be larger than the number you started with.
- Rounding too early. Convert first at full precision, then round the final answer to the precision the task actually needs.
How precise does the answer need to be?
Round only at the end, and only to the precision your task actually needs. The converter above keeps full double precision internally and rounds for display.
How these units are defined
- Radian (rad): The SI angle unit: the angle subtending an arc equal to the radius. This unit's relationship to the SI base unit is exact by definition, so no rounding enters the conversion factor.
- Degree (°): 1/360 of a full turn. This unit's relationship to the SI base unit is exact by definition, so no rounding enters the conversion factor.
Related conversions
Frequently asked questions
- What is 1 radian in degrees?
- 1 radian is equal to 57.2957795 degrees.
- How many radians are in one degree?
- There are 0.017453293 radians in 1 degree.
- How do you convert radians to degrees?
- Multiply the number of radians by 57.2957795 — or use the formula ° = rad × 57.2957795.
- What is 45 radians in degrees?
- 45 radians is 2,578.31008 degrees. 45 × 57.2957795 = 2,578.31008 degrees.
- Is the radians to degrees conversion exact?
- Yes. The relationship is fixed by definition, so 57.2957795131 is an exact conversion factor — only the displayed result is rounded.