Radians to Degrees Converter
Convert between radians and degrees measurement units with our easy-to-use calculator. This tool helps students, engineers, and professionals quickly convert angle values between different measurement systems.
Common Angle Conversions
| Radians | Degrees |
|---|---|
| 0 rad | 0° |
| π/6 rad | 30° |
| π/4 rad | 45° |
| π/3 rad | 60° |
| π/2 rad | 90° |
| π rad | 180° |
| 2π rad | 360° |
Conversion Result: 57.2958 °
Conversion Formula
degrees = radians × (180° / π)
Where π (pi) is approximately 3.141592653589793
About Radians and Degrees
Radians and degrees are two units for measuring angles. A full circle is 360° or 2π radians. Radians are the standard unit of angular measure used in many areas of mathematics, while degrees are more commonly used in everyday applications.
What is a Radian?
A radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. One radian is approximately 57.2958 degrees. The radian is the SI derived unit for angle measurement.
What is a Degree?
A degree (symbol: °) is a measurement of plane angle, representing 1/360 of a full rotation. Degrees are more commonly used in practical applications like navigation, construction, and engineering drawings.
Conversion Formulas
The formulas to convert between these units are:
- From radians to degrees: degrees = radians × (180° / π)
- From degrees to radians: radians = degrees × (π / 180°)
Where π (pi) is approximately 3.141592653589793
When to Use Each Unit
Use Radians When:
- Working with trigonometric functions in calculus
- Calculating angular velocity in physics
- Performing mathematical analysis involving periodic functions
- Working with complex numbers and polar coordinates
Use Degrees When:
- Working with geographic coordinates (latitude/longitude)
- Measuring angles in construction or engineering drawings
- Using compass directions in navigation
- Working with most consumer-level applications
Example Calculations
| Description | Radians | Degrees |
|---|---|---|
| Right angle | π/2 rad | 90° |
| Straight angle | π rad | 180° |
| Full rotation | 2π rad | 360° |
| 1 radian | 1 rad | ≈57.2958° |
| 1 degree | ≈0.01745 rad | 1° |