Radians ↔ Degrees Converter
Convert between radians and degrees instantly
📋 Common Radian Values
📚 Radians ↔ Degrees Conversion Details
Radians to Degrees Formula
To convert radians to degrees, multiply by 180 and divide by π (approximately 57.2958).
Degrees to Radians Formula
To convert degrees to radians, multiply by π and divide by 180 (approximately 0.0174533).
Bidirectional Conversion
This converter works both ways simultaneously:
- Type in radians → degrees updates automatically
- Type in degrees → radians updates automatically
- No buttons to click - works as you type
Common Uses
- Trigonometry calculations
- Geometry problems
- Physics and engineering
- Computer graphics
- Navigation systems
📏 Understanding Radians and Degrees
Both radians and degrees are units for measuring angles:
Degrees (°)
- Based on dividing a circle into 360 equal parts
- Common in everyday use
- Used in navigation, geography
- Easier for human comprehension
Radians (rad)
- Based on radius of the circle
- Used in mathematics, physics
- One radian = angle where arc length equals radius
- More natural for calculus
degrees = radians × (180 / π)
radians = degrees × (π / 180)
// Where π ≈ 3.141592653589793
// Example 1: Convert π radians to degrees
degrees = π × (180 / π) = 180°
// Example 2: Convert 90° to radians
radians = 90 × (π / 180) = π/2 rad
📊 Conversion Table
| Radians | Degrees | Fraction of π |
|---|---|---|
| 0 | 0° | 0 |
| π/6 ≈ 0.5236 | 30° | π/6 |
| π/4 ≈ 0.7854 | 45° | π/4 |
| π/3 ≈ 1.0472 | 60° | π/3 |
| π/2 ≈ 1.5708 | 90° | π/2 |
| π ≈ 3.1416 | 180° | π |
| 3π/2 ≈ 4.7124 | 270° | 3π/2 |
| 2π ≈ 6.2832 | 360° | 2π |
❓ Frequently Asked Questions
A: One radian is approximately 57.2958 degrees.
A: 180 degrees equals π radians (approximately 3.14159 radians).
A: Radians are more natural for mathematical calculations, especially in calculus and trigonometry, because they relate directly to the radius of a circle.
A: No! The conversion happens automatically as you type in either field.
A: This converter uses π ≈ 3.141592653589793 for high precision calculations.