Angle Conversion Calculator
Convert between degrees, radians, gradians, turns, and more
Angle Unit Converter
Conversion Result
Angle Type: Zero angle
Decimal Degrees: 0.000000°
DMS Format: 0° 0' 0.00"
Precision: Typically 6 decimal places
All Unit Conversions
Common Angle Conversions
| Degrees | Radians | π Radians | Gradians | Turns |
|---|---|---|---|---|
| 0° | 0 | 0 | 0g | 0 |
| 30° | 0.5236 | π/6 | 33.33g | 0.0833 |
| 45° | 0.7854 | π/4 | 50g | 0.125 |
| 60° | 1.0472 | π/3 | 66.67g | 0.1667 |
| 90° | 1.5708 | π/2 | 100g | 0.25 |
| 180° | 3.1416 | π | 200g | 0.5 |
| 270° | 4.7124 | 3π/2 | 300g | 0.75 |
| 360° | 6.2832 | 2π | 400g | 1 |
Conversion Formulas
Degrees ↔ Radians
radians = degrees × π/180
degrees = radians × 180/π
Degrees ↔ Gradians
gradians = degrees × 10/9
degrees = gradians × 9/10
Degrees ↔ Turns
turns = degrees / 360
degrees = turns × 360
Angle Types
Angle Tips
1 radian ≈ 57.2958 degrees
π radians = 180 degrees
Full circle = 2π radians = 360°
1 degree = 60 arcminutes = 3600 arcseconds
Gradians divide right angle into 100 parts
Understanding Angle Measurements
What is an Angle?
An angle is formed by two rays that share a starting point (vertex). Angles are fundamental in geometry, trigonometry, navigation, engineering, and many other fields. They help us measure rotation, direction, and spatial relationships.
Common Units Explained
- •Degrees (°): Most common unit, 360° in a full circle
- •Radians: Mathematical unit, 2π radians in a full circle
- •Gradians: Metric unit, 400 gradians in a full circle
- •Turns: 1 turn = full rotation
Degrees, Minutes, Seconds (DMS)
For high precision measurements (like GPS coordinates), degrees are subdivided:
• 1 degree = 60 arcminutes (60')
• 1 arcminute = 60 arcseconds (60")
• Example: 48°37'52" = 48.6311°
Applications
- Navigation: Compass bearings, GPS coordinates
- Engineering: Structural angles, mechanical rotations
- Astronomy: Celestial object positions
- Mathematics: Trigonometry, calculus
- Physics: Wave analysis, oscillations