How Many Degrees in a Radian?
Quick Answer
There are approximately 57.296 degrees in a radian.
1 radian = 180/π ≈ 57.296°
Understanding the Conversion
One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. Since a full circle has 360° and 2π radians, one radian equals 360/(2π) = 180/π ≈ 57.2958°. Radians are the natural unit for angles in mathematics and physics.
Formula
1 radian = 180/π ≈ 57.296°
Common Examples
| Description | Value |
|---|---|
| 1 radian | ≈57.3° (just under 60°) |
| π/4 radians | 45° |
| π/3 radians | 60° |
Quick Reference Table
Use this table for quick conversions between radian and degrees:
| radian | degrees |
|---|---|
| 1 | 57.296 |
| 2 | 114.59 |
| 5 | 286.48 |
| 10 | 572.96 |
| 25 | 1,432.4 |
| 50 | 2,864.79 |
| 100 | 5,729.58 |
Frequently Asked Questions
How Many Degrees in a Radian?
There are approximately 57.296 degrees in a radian. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. Since a full circle has 360° and 2π radians, one radian equals 360/(2π) = 180/π ≈ 57.2958°. Radians are the natural unit for angles in mathematics and physics.
What is the formula to convert radian to degrees?
The formula is: 1 radian = 180/π ≈ 57.296°. To convert, multiply the number of radians by 57.296 to get the equivalent in degrees.
How do I convert degrees to radian?
To convert degrees to radian, divide the number of degrees by 57.296. For example, 286.48 degrees equals 5 radians.