Degrees to Radians Converter
1 ° equals 0.017453293 rad, and 1 rad equals 57.29578 °. Enter a value in either box to convert degrees to radians and back. Formula: radians = degrees x pi / 180; 1 turn = 360 degrees = 400 gradians = 2 pi radians.
· CalcFlow Editorial
1 ° = 0.017453293 rad
Results shown are estimates for informational purposes only. Nothing on CalcFlow is financial, tax, legal, or medical advice. Always consult a qualified professional before making important decisions.
Degrees to Radians Conversion Table
| Degrees | Radians |
|---|---|
| 1 ° | 0.017453293 rad |
| 15 ° | 0.26179939 rad |
| 30 ° | 0.52359878 rad |
| 45 ° | 0.78539816 rad |
| 60 ° | 1.0471976 rad |
| 90 ° | 1.5707963 rad |
| 180 ° | 3.1415927 rad |
| 270 ° | 4.712389 rad |
| 360 ° | 6.2831853 rad |
Radians to Degrees Conversion Table
| Radians | Degrees |
|---|---|
| 1 rad | 57.29578 ° |
| 15 rad | 859.43669 ° |
| 30 rad | 1,718.8734 ° |
| 45 rad | 2,578.3101 ° |
| 60 rad | 3,437.7468 ° |
| 90 rad | 5,156.6202 ° |
| 180 rad | 10,313.24 ° |
| 270 rad | 15,469.86 ° |
| 360 rad | 20,626.481 ° |
Worked example: 15 ° = 0.26179939 rad. 180 degrees is pi radians (3.14159). A bearing of 45 degrees is 0.7854 radians, or 50 gradians.
Need other units? Open the full Angle Converter.
Popular Angle Conversions
Formula
radians = degrees x pi / 180; 1 turn = 360 degrees = 400 gradians = 2 pi radiansUnderstanding Angle Conversion
An angle can be measured in degrees, where a full circle is 360, in radians, where a full circle is 2 pi, or in gradians, where a full circle is 400. Radians are the natural unit in mathematics and physics because they make formulas such as arc length equal to radius times angle. Arcminutes and arcseconds are 1/60 and 1/3600 of a degree and are used in navigation and astronomy.
Tips and Best Practices
- 1Multiply degrees by 0.017453 to get radians; multiply radians by 57.2958 to get degrees.
- 2A right angle is 90 degrees, pi/2 radians or 100 gradians.
- 3Set your calculator to the right angle mode before using sine or cosine.
Real-World Example
180 degrees is pi radians (3.14159). A bearing of 45 degrees is 0.7854 radians, or 50 gradians.
Common Mistakes to Avoid
- Leaving a calculator in degree mode when the formula expects radians.
- Confusing arcminutes with minutes of time.
- Treating gradians as degrees; a gradian is 0.9 degrees.
How to Use
- Type a number in the Degrees box.
- The Radians result appears instantly; you can also edit the Radians box to convert backwards.
- Use the swap button to reverse the direction and Copy result to copy the answer.
Frequently Asked Questions
How many radians are in 1 °?
How many degrees are in 1 rad?
What is the formula to convert degrees to radians?
How many degrees in a full circle?
Sources: BIPM SI Brochure (radian; degree, arcminute, arcsecond as accepted units).