How to Convert Radians to Degrees (rad to °)
Angle conversions show up in maths and physics lessons, surveying and navigation. This guide shows how to convert radians into degrees by hand, with examples and a quick-reference table.
The conversion
To convert radians to degrees, multiply the value by 57.2957795131. To go the other way, divide by the same number (or multiply by 0.0174532925). For a quick estimate, multiply by about 57.
Degrees = radians × 57.2957795131
Worked examples
- 3 rad = 171.8873 °
- 12.5 rad = 716.1972 °
- 75 rad = 4,297.18 °
Radians to Degrees table
| Radians | Degrees |
|---|---|
| 1 rad | 57.2958 ° |
| 2 rad | 114.5916 ° |
| 5 rad | 286.4789 ° |
| 10 rad | 572.9578 ° |
| 20 rad | 1,145.92 ° |
| 25 rad | 1,432.39 ° |
| 50 rad | 2,864.79 ° |
| 100 rad | 5,729.58 ° |
| 250 rad | 14,323.94 ° |
| 500 rad | 28,647.89 ° |
| 1,000 rad | 57,295.78 ° |
Common questions
Is rad to ° exact?
The factors used here are the internationally defined values where they exist; results are rounded for display only.
How do I convert back?
Use the Degrees to Radians converter.
Mistakes to avoid
Mixing similar-sounding units
US and imperial gallons, pints and tons are different sizes, and decimal kilobytes differ from binary kibibytes.
Forgetting squared and cubed units
Area and volume factors are the length factor squared or cubed, so 1 m² is about 10.76 sq ft, not 3.28.
Rounding the factor too early
Using 3 instead of 3.28 for feet per metre introduces an error of almost 9% before you have started.
Background
Unit conversion is simply multiplication by a fixed ratio. The ratio between two units of the same quantity never changes, so once you know it you can convert any value in either direction.
For everyday use, three or four significant figures are usually enough. Engineering, science and trade documents may need more, and rounding should happen only at the end of a calculation.
Singapore adopted the metric system in the 1970s, replacing imperial units and traditional Chinese measures in most official uses. Metric units are now standard in schools, trade and government, but older units survive in property, markets and imported goods.
For any value, use the Radians to Degrees Converter or browse all angle converters.
Run your own numbers: Radians to Degrees Converter