Degrees ↔ Radians Converter
Convert between degrees and radians instantly
Enter angle in degrees to convert to radians
Enter angle in radians to convert to degrees
Conversion Result
180° = π radians
π ≈ 3.14159 radians • Full circle = 360° = 2π radians
📚 Degrees ↔ Radians Conversion Details
Degrees to Radians Formula
radians = degrees × (π ÷ 180)
To convert degrees to radians, multiply degrees by π/180.
Radians to Degrees Formula
degrees = radians × (180 ÷ π)
To convert radians to degrees, multiply radians by 180/π.
Bidirectional Conversion
This converter works both ways simultaneously:
- Type in degrees → radians updates automatically
- Type in radians → degrees updates automatically
- No buttons to click - works as you type
Key Relationships
- 360° = 2π radians
- 180° = π radians
- 90° = π/2 radians
- 1° ≈ 0.0174533 radians
📏 How This Converter Works
This is a bidirectional converter that works in real-time:
- Degrees → Radians: When you type in the degrees field, the radians field automatically updates
- Radians → Degrees: When you type in the radians field, the degrees field automatically updates
- No swapping needed: Both conversions happen simultaneously
- Real-time: Updates happen as you type, no button clicks required
// Bidirectional Conversion Logic:
radians = degrees × (π ÷ 180)
degrees = radians × (180 ÷ π)
// Example 1: Type "180" in degrees
radians = 180 × (π ÷ 180) = π ≈ 3.14159
// Example 2: Type "1.0472" in radians
degrees = 1.0472 × (180 ÷ π) ≈ 60°
radians = degrees × (π ÷ 180)
degrees = radians × (180 ÷ π)
// Example 1: Type "180" in degrees
radians = 180 × (π ÷ 180) = π ≈ 3.14159
// Example 2: Type "1.0472" in radians
degrees = 1.0472 × (180 ÷ π) ≈ 60°
📊 Common Angle Conversion Table
| Degrees | Radians | Radians (π) |
|---|---|---|
| 0° | 0 | 0 |
| 30° | 0.5236 | π/6 |
| 45° | 0.7854 | π/4 |
| 60° | 1.0472 | π/3 |
| 90° | 1.5708 | π/2 |
| 180° | 3.1416 | π |
| 270° | 4.7124 | 3π/2 |
| 360° | 6.2832 | 2π |
❓ Frequently Asked Questions
Q: What is the relationship between degrees and radians?
A: 180 degrees equals π (pi) radians. A full circle (360°) equals 2π radians.
Q: Why use radians instead of degrees?
A: Radians are the standard unit of angular measure in mathematics and physics because they simplify many mathematical formulas, especially in calculus and trigonometry.
Q: Do I need to click any button to convert?
A: No! The conversion happens automatically as you type in either field.
Q: How accurate is this converter?
A: This converter provides exact calculations up to 5 decimal places, using π ≈ 3.141592653589793.