Radians (rad) to Degrees (°) Conversion
Radians
The radian (rad) is the SI derived unit of plane angle, defined as the angle subtended at the centre of a circle by an arc whose length equals the radius. One full rotation equals exactly 2π radians (≈ 6.2832 rad), and one radian equals approximately 57.2958°. The radian is preferred in mathematics and physics because it makes the derivatives of trigonometric functions algebraically clean — d/dx(sin x) = cos x only when x is in radians. Rotational speed (rad/s) and angular frequency in oscillatory systems are always expressed in radians.
Degrees
The degree (°) is a unit of angular measurement equal to 1/360 of a full rotation, a convention inherited from ancient Babylonian astronomy which used a base-60 numeral system and approximated the year as 360 days — one degree for each day of apparent solar travel. The degree is subdivided into 60 arcminutes (′), each of which divides into 60 arcseconds (″), following the same sexagesimal tradition. It is the most widely used angle unit in everyday life, navigation, geography, and engineering outside of advanced mathematics.
| Radians (rad) | Degrees (°) |
|---|---|
| 0.1 rad | 5.7296 ° |
| 1 rad | 57.2958 ° |
| 2 rad | 114.5916 ° |
| 3 rad | 171.8873 ° |
| 5 rad | 286.4789 ° |
| 10 rad | 572.9578 ° |
| 20 rad | 1,145.9156 ° |
| 30 rad | 1,718.8734 ° |
| 50 rad | 2,864.789 ° |
| 100 rad | 5,729.578 ° |
| 1000 rad | 57,295.7795 ° |
Frequently Asked Questions (FAQ)
How many degrees are in 1 radians?
1 radians (rad) is exactly 57.296 degrees (°).
How do I convert radians to degrees?
Multiply the value in radians by 57.296 to get the result in degrees. Or use the converter above — type any number and see the result instantly.