Radians to Degrees Converter
Convert radians to degrees and other angular measurements
Convert Radians and Degrees
1 radian ≈ 57.2958°
Range: -3600° to 3600°
Conversion Results
Conversion Formulas
Radians to Degrees: degrees = radians × (180°/π)
Degrees to Radians: radians = degrees × (π/180°)
*π ≈ 3.14159265359 | 1 radian ≈ 57.2958°
Example Calculations
Example 1: π/2 Radians
(π/2) × (180°/π) = 90°
This represents a right angle or quarter circle
Example 2: π Radians
π × (180°/π) = 180°
This represents a straight line or half circle
Example 3: 2π Radians
2π × (180°/π) = 360°
This represents a complete rotation around a circle
Common Radians to Degrees Conversions
| Radians (exact) | Radians (decimal) | Degrees | Description |
|---|---|---|---|
| 0 rad | 0.000000 rad | 0° | No rotation |
| π/6 rad | 0.523599 rad | 30° | 30 degrees |
| π/4 rad | 0.785398 rad | 45° | 45 degrees |
| π/3 rad | 1.047198 rad | 60° | 60 degrees |
| π/2 rad | 1.570796 rad | 90° | Right angle |
| 2π/3 rad | 2.094395 rad | 120° | 120 degrees |
| 3π/4 rad | 2.356194 rad | 135° | 135 degrees |
| 5π/6 rad | 2.617994 rad | 150° | 150 degrees |
| π rad | 3.141593 rad | 180° | Straight angle |
| 3π/2 rad | 4.712389 rad | 270° | 3/4 circle |
| 2π rad | 6.283185 rad | 360° | Full circle |
Angular Units
Radian (rad)
Arc length = radius
Degree (°)
1/360 of a full circle
Gradian (gon)
1/400 of a full circle
Key Relationship
1 radian ≈ 57.2958°
Quick Facts
2π radians = 360°
π radians = 180°
π/2 radians = 90°
1 radian ≈ 57.2958°
Used in advanced mathematics
Understanding Radians to Degrees Conversion
What is a Radian?
A radian is the standard unit of angular measurement in mathematics. One radian is the angle subtended at the center of a circle by an arc whose length equals the radius of the circle. This natural definition makes radians ideal for mathematical calculations.
Conversion Formula
- •Radians to Degrees: multiply by 180°/π
- •Degrees to Radians: multiply by π/180°
Example Calculation
Convert π radians to degrees:
π × (180°/π) = 180°
Practical Applications
- 1Pure mathematics: natural unit for calculus and analysis
- 2Physics: angular motion and wave functions
- 3Engineering: signal processing and control systems
- 4Computer science: algorithms and graphics programming
Common Conversions
π/2 rad: 90° (right angle)
π rad: 180° (straight angle)
3π/2 rad: 270° (three-quarters circle)
2π rad: 360° (full circle)