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 ° | 0.0017453292519943 rad |
| 1 ° | 0.017453292519943 rad |
| 2 ° | 0.034906585039887 rad |
| 3 ° | 0.05235987755983 rad |
| 5 ° | 0.087266462599716 rad |
| 10 ° | 0.17453292519943 rad |
| 20 ° | 0.34906585039887 rad |
| 30 ° | 0.5235987755983 rad |
| 50 ° | 0.87266462599716 rad |
| 100 ° | 1.7453292519943 rad |
| 1000 ° | 17.453292519943 rad |
Convert Degrees (°) to other units of Angle
| ‣ Degrees (°) to radians (rad) |
| ‣ Degrees (°) to gradians (gon) |
| ‣ Degrees (°) to arcminutes (′) |
| ‣ Degrees (°) to arcseconds (″) |
| ‣ Degrees (°) to revolutions (rev) |