Convert Radians to Degrees
Use our free online converter to easily convert from Radians to Degrees. Get accurate conversions instantly.
Converting Radians to Degrees
Converting radians to degrees is important in mathematics, physics, engineering, and computer graphics, particularly when translating the results of calculations into more intuitive angle measurements for practical applications.
Mathematical Relationship
The mathematical relation between radians and degrees is: π radians = 180 degrees. To convert an angle in radians to degrees, multiply the radian value by 180/π.
Common Conversion Values
| Radians | Degrees |
|---|---|
| 0 | 0 |
| 0.5236 | 30 |
| 0.7854 | 45 |
| 1.5708 | 90 |
| 3.1416 | 180 |
Unit Definitions
Radians
The radian (symbol: rad) is the SI unit of angle measurement, defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. One full rotation equals 2π radians.
Degrees
The degree (symbol: °) is a unit of angle measurement defined as 1/360 of a full rotation. It is widely used in many fields including navigation, surveying, mathematics, and everyday contexts.
Historical Context
The radian was first recognized as a unit of measurement in the mid-18th century and was adopted as the SI unit of angle measurement in 1960. The degree has ancient origins, possibly derived from the Babylonian sexagesimal (base-60) system and the approximation of a year as 360 days. Both units remain important in different contexts, with degrees being more intuitive for everyday use and radians being more mathematically convenient for calculations.