Convert radian to degree
Please provide values below to convert radian [rad] to degree [°], or Convert degree to radian.
1 rad = 57.295779513 °. To convert radian to degree, multiply the value by 57.295779513; to go the other way, divide by it (1 ° = 0.01745329252 rad). Both units measure angle and appear in everyday as well as technical calculations, so switching between them quickly is often useful.
Quick Reference
- 1 rad = 57.295779513 °
- 1 ° = 0.01745329252 rad
- 10 rad = 572.95779513 °
- 100 rad = 5729.5779513 °
How to Convert Radian to Degree
1 rad = 57.295779513 °
Example: convert 15 rad to °:
15 rad = 15 × 57.295779513 ° = 859.436692695 °
Radian to Degree Conversion Table
| radian | degree |
|---|---|
| 1 rad | 57.295779513 ° |
| 2 rad | 114.591559026 ° |
| 3 rad | 171.887338539 ° |
| 5 rad | 286.478897565 ° |
| 10 rad | 572.95779513 ° |
| 20 rad | 1145.91559026 ° |
| 50 rad | 2864.78897565 ° |
| 100 rad | 5729.5779513 ° |
| 500 rad | 28647.8897565 ° |
| 1000 rad | 57295.779513 ° |
Radian
A radian is the standard unit of angular measure in mathematics, defined as the angle subtended at the center of a circle by an arc equal in length to the circle's radius.
History/Origin
The radian was introduced in the 19th century as a natural unit of angular measurement based on the properties of circles, providing a more mathematically convenient measure than degrees.
Current Use
Radians are widely used in mathematics, physics, and engineering for calculations involving angles, trigonometry, and periodic functions, serving as the standard angular unit in many scientific contexts.
Degree
A degree (symbol: °) is a unit of measurement for angles, representing 1/360th of a full circle.
History/Origin
The degree originated in ancient Babylonian astronomy, where the circle was divided into 360 parts, possibly due to the approximate number of days in a year. It has been used since antiquity for measuring angles and geographic coordinates.
Current Use
Degrees are widely used in geometry, navigation, engineering, and various sciences to measure angles, with applications in compass readings, trigonometry, and geographic positioning.
Frequently Asked Questions
What is 1 radian in degree?
1 radian (rad) = 57.295779513 degree (°).
How do you convert radian to degree?
Multiply the radian value by 57.295779513. For example, 25 rad × 57.295779513 = 1432.39448782 °.
What is 10 radian in degree?
10 rad = 572.95779513 °.
Which unit is larger, the radian or the degree?
The radian is the larger unit: 1 rad = 57.295779513 °.