Angle Converter
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
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 to Radian Conversion Table
| Degree [deg] | Radian [rad] |
|---|---|
| 0.01 deg | 0.00017453 rad |
| 0.1 deg | 0.00174533 rad |
| 1 deg | 0.01745329 rad |
| 2 deg | 0.03490659 rad |
| 3 deg | 0.05235988 rad |
| 5 deg | 0.08726646 rad |
| 10 deg | 0.17453293 rad |
| 20 deg | 0.34906585 rad |
| 50 deg | 0.87266463 rad |
| 100 deg | 1.74532925 rad |
| 1000 deg | 17.45329252 rad |
How to Convert Degree to Radian
1 deg = 0.01745329 rad
1 rad = 57.2957795 deg
Example: convert 15 deg to rad:
15 deg = 15 × 0.01745329 rad = 0.26179939 rad
Did You Know?
- A full circle is divided into 360 degrees. This system likely originated from ancient Babylonians who used a base-60 number system.
- The radian is the standard unit of angular measure used in higher mathematics. One full rotation is exactly 2π radians.