Degrees (°) to Radians (rad) Conversion
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
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 (°) | Radians (rad) |
|---|---|
| 0.1 ° | 0.00175 rad |
| 1 ° | 0.0175 rad |
| 2 ° | 0.0349 rad |
| 3 ° | 0.0524 rad |
| 5 ° | 0.0873 rad |
| 10 ° | 0.1745 rad |
| 20 ° | 0.3491 rad |
| 30 ° | 0.5236 rad |
| 50 ° | 0.8727 rad |
| 100 ° | 1.7453 rad |
| 1000 ° | 17.4533 rad |
Frequently Asked Questions (FAQ)
How many radians are in 1 degrees?
1 degrees (°) is exactly 0.017453 radians (rad).
How do I convert degrees to radians?
Multiply the value in degrees by 0.017453 to get the result in radians. Or use the converter above — type any number and see the result instantly.