Angle Converter
Radian
Definition: The radian (symbol: rad) is the SI derived unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends.
History/origin: The concept of radian measure, as opposed to the degree of an angle, is normally credited to Roger Cotes in 1714. However, the actual term "radian" first appeared in print much later, in 1873, by James Thomson.
Current use: The radian is strictly used in physics, calculus, and advanced mathematics because it greatly simplifies formulas, particularly those involving trigonometric functions and derivatives.
Degree
Definition: A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle in which one full rotation is 360 degrees.
History/origin: The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun advanced roughly one degree in the sky each day.
Current use: Degrees are widely used in geometry, trigonometry, geography (latitude and longitude), astronomy, and everyday engineering applications.
Radian to Degree Conversion Table
| Radian [rad] | Degree [deg] |
|---|---|
| 0.01 rad | 0.57295779 deg |
| 0.1 rad | 5.72957795 deg |
| 1 rad | 57.2957795 deg |
| 2 rad | 114.591559 deg |
| 3 rad | 171.8873385 deg |
| 5 rad | 286.4788975 deg |
| 10 rad | 572.957795 deg |
| 20 rad | 1145.91559 deg |
| 50 rad | 2864.788975 deg |
| 100 rad | 5729.57795 deg |
| 1000 rad | 57295.7795 deg |
How to Convert Radian to Degree
1 rad = 57.2957795 deg
1 deg = 0.01745329 rad
Example: convert 15 rad to deg:
15 rad = 15 × 57.2957795 deg = 859.4366925 deg
Did You Know?
- The radian is the standard unit of angular measure used in higher mathematics. One full rotation is exactly 2π radians.
- A full circle is divided into 360 degrees. This system likely originated from ancient Babylonians who used a base-60 number system.