How to Convert Degrees to Radians (° to rad)
Angle conversions show up in maths and physics lessons, surveying and navigation. This guide shows how to convert degrees into radians by hand, with examples and a quick-reference table.
The conversion
To convert degrees to radians, multiply the value by 0.0174532925. To go the other way, divide by the same number (or multiply by 57.2957795131). For a quick estimate, multiply by about 0.017.
Radians = degrees × 0.0174532925
Worked examples
- 3 ° = 0.05236 rad
- 12.5 ° = 0.218166 rad
- 75 ° = 1.309 rad
Degrees to Radians table
| Degrees | Radians |
|---|---|
| 1 ° | 0.017453 rad |
| 2 ° | 0.034907 rad |
| 5 ° | 0.087266 rad |
| 10 ° | 0.174533 rad |
| 20 ° | 0.349066 rad |
| 25 ° | 0.436332 rad |
| 50 ° | 0.872665 rad |
| 100 ° | 1.7453 rad |
| 250 ° | 4.3633 rad |
| 500 ° | 8.7266 rad |
| 1,000 ° | 17.4533 rad |
Common questions
Is ° to rad 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 Radians to Degrees converter.
Mistakes to avoid
Multiplying when you should divide
Converting to a smaller unit gives a bigger number, and converting to a larger unit gives a smaller one. If your answer moves the wrong way, you have inverted the factor.
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.
Background
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.
Many conversion factors are exact by definition. The inch has been defined as exactly 2.54 centimetres since 1959, and the pound as exactly 0.45359237 kilograms, so conversions involving them can be as precise as you need.
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.
For any value, use the Degrees to Radians Converter or browse all angle converters.
Run your own numbers: Degrees to Radians Converter