Angle Units Guide
Degrees vs radians explained — understand angles for math, navigation, and engineering
Overview
An angle measures the rotation between two lines or planes that meet at a point. The most common units are degrees (°) for everyday use and radians (rad) for mathematics and science.
Understanding angle units is essential for geometry, trigonometry, navigation, engineering, and computer graphics.
Common Angle Units
Degree
Most common unit
Full circle = 360°
Radian
SI derived unit
Full circle = 2π rad
Gradian
Surveying, Europe
Full circle = 400 grad
Turn / Revolution
Rotations
Full circle = 1 turn
Angle Unit Comparison
| Angle | Degrees | Radians | Gradians | Turns |
|---|---|---|---|---|
| Full circle | 360° | 2π (6.283) | 400 | 1 |
| Straight angle | 180° | π (3.142) | 200 | 0.5 |
| Right angle | 90° | π/2 (1.571) | 100 | 0.25 |
| 60 degrees | 60° | π/3 (1.047) | 66.67 | 0.167 |
| 45 degrees | 45° | π/4 (0.785) | 50 | 0.125 |
| 30 degrees | 30° | π/6 (0.524) | 33.33 | 0.083 |
| 1 degree | 1° | 0.01745 | 1.111 | 0.00278 |
| 1 radian | 57.3° | 1 | 63.66 | 0.159 |
Degrees vs Radians
Origin: Ancient Babylon (base-60 system)
Full circle: 360°
Used in:
- Navigation and maps
- Architecture and construction
- Everyday measurements
- GPS coordinates
Origin: Mathematical definition (arc length / radius)
Full circle: 2π radians
Used in:
- Mathematics and calculus
- Physics equations
- Computer programming
- Engineering calculations
Real-World Angle References
Quick Conversion Tips
Multiply by π/180
90° × π/180 = π/2
Multiply by 180/π
π × 180/π = 180°
1 radian ≈ 57.3°
1° ≈ 0.0175 rad
90° = π/2 rad
180° = π rad