Angle Unit Converter
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Angle Units Explained
Angles can be expressed in many units. The most familiar is degrees, but radians are essential in mathematics and physics, and other units have specialised applications.
| Unit | Full Circle | Used In |
|---|---|---|
| Degrees (°) | 360° | Everyday geometry, navigation, maps |
| Radians (rad) | 2π ≈ 6.2832 | Mathematics, physics, programming |
| Gradians (grad) | 400 grad | Surveying, European engineering |
| Turns | 1 turn | Rotation mechanics, CSS animations |
| Arcminutes (') | 21,600' | Astronomy, GPS coordinates |
| Arcseconds (") | 1,296,000" | Astronomy, high-precision navigation |
Common Angle Reference
| Degrees | Radians (exact) | Radians (decimal) |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.5236 |
| 45° | π/4 | 0.7854 |
| 60° | π/3 | 1.0472 |
| 90° | π/2 | 1.5708 |
| 180° | π | 3.1416 |
| 270° | 3π/2 | 4.7124 |
| 360° | 2π | 6.2832 |
Frequently Asked Questions
Why are radians used instead of degrees in mathematics?
Radians make calculus and trigonometry formulas simpler. For example, the derivative of sin(x) is cos(x) only when x is in radians. With degrees, an extra conversion factor appears.
What is a gradian?
A gradian (or gon) divides a right angle into 100 equal parts, making a full circle 400 gradians. It's used in surveying and civil engineering in some European countries.
How precise are arcminutes and arcseconds?
One arcsecond is 1/3600 of a degree. At Earth's surface, one arcsecond of latitude ≈ 31 metres — showing how fine-grained these units are for astronomy and geodesy.