Convert Degrees to Radians
Please provide values below to convert Degrees [deg] to Radians [r].
How to Convert Degrees to Radians
1 deg = 0.017453292519943295 r
1 r = 57.29577951308232 deg
Example: convert 10 deg to r: 10 deg = 10 × 0.017453292519943295 deg = 0.17453292519943295 deg
Degrees
Definition: A degree (°) is a unit of angular measurement, with a full rotation equaling 360 degrees. Since one complete turn corresponds to 2π radians, a single degree is equal to π/180 radians. While not an SI (International System of Units) unit, the degree is officially recognized in the SI brochure.
History: The exact origin of the degree as a unit of rotation and angles remains uncertain. One theory suggests that 360 was chosen for its high divisibility, featuring 24 divisors and being divisible by every number from 1 to 10, except 7. This makes 360 a highly practical choice for measuring angles.
Radians
Definition: A radian (r) is the SI unit of angular measurement. One radian is the angle formed when the arc length of a circle equals the circle's radius, with a full rotation being equal to 2π radians.
History: The radian was first introduced in the 18th century by Roger Cotes but became widely accepted in the 19th century. It was officially defined as the standard unit of angular measurement in SI due to its natural mathematical properties, particularly in trigonometry and calculus.
Degrees to Radians Conversion Table
| Degrees | Radians |
|---|---|
| 0.01 deg | 0.00017453292519943296 r |
| 0.1 deg | 0.0017453292519943296 r |
| 1 deg | 0.017453292519943295 r |
| 2 deg | 0.03490658503988659 r |
| 3 deg | 0.05235987755982989 r |
| 5 deg | 0.08726646259971647 r |
| 10 deg | 0.17453292519943295 r |
| 20 deg | 0.3490658503988659 r |
| 50 deg | 0.8726646259971648 r |
| 100 deg | 1.7453292519943295 r |
| 1000 deg | 17.453292519943297 r |