Convert degree to radian
Please provide values below to convert degree [°] to radian [rad], or Convert radian to degree.
1 ° = 0.01745329252 rad. To convert degree to radian, multiply the value by 0.01745329252; to go the other way, divide by it (1 rad = 57.295779513 °). Both units measure angle and appear in everyday as well as technical calculations, so switching between them quickly is often useful.
Quick Reference
- 1 ° = 0.01745329252 rad
- 1 rad = 57.295779513 °
- 10 ° = 0.1745329252 rad
- 100 ° = 1.745329252 rad
How to Convert Degree to Radian
1 ° = 0.0174532925199684 rad
Example: convert 15 ° to rad:
15 ° = 15 × 0.0174532925199684 rad = 0.261799387799526 rad
Degree to Radian Conversion Table
| degree | radian |
|---|---|
| 1 ° | 0.01745329252 rad |
| 2 ° | 0.0349065850399 rad |
| 3 ° | 0.0523598775599 rad |
| 5 ° | 0.0872664625998 rad |
| 10 ° | 0.1745329252 rad |
| 20 ° | 0.349065850399 rad |
| 50 ° | 0.872664625998 rad |
| 100 ° | 1.745329252 rad |
| 500 ° | 8.72664625998 rad |
| 1000 ° | 17.45329252 rad |
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.
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.
Frequently Asked Questions
What is 1 degree in radian?
1 degree (°) = 0.01745329252 radian (rad).
How do you convert degree to radian?
Multiply the degree value by 0.01745329252. For example, 25 ° × 0.01745329252 = 0.436332312999 rad.
What is 10 degree in radian?
10 ° = 0.1745329252 rad.
Which unit is larger, the degree or the radian?
The radian is the larger unit: 1 ° equals only 0.01745329252 rad.