Angle Units Explained
| Unit | Symbol | Full Circle | Common Use |
|---|---|---|---|
| Degree | ° | 360 | Everyday geometry, navigation |
| Radian | rad | 2π ≈ 6.2832 | Mathematics, physics, calculus |
| Gradian | grad | 400 | Surveying, civil engineering |
| Arcminute | ′ | 21,600 | Navigation, astronomy |
| Arcsecond | ″ | 1,296,000 | Precision astronomy, GPS |
| Turn | tr | 1 | Rotations, robotics |
Key Conversion Formulas
Degrees → Radians
rad = deg × π / 180
Radians → Degrees
deg = rad × 180 / π
Degrees → Gradians
grad = deg × 10 / 9
Gradians → Degrees
deg = grad × 9 / 10
Degrees → Arcminutes
arcmin = deg × 60
Arcminutes → Arcseconds
arcsec = arcmin × 60
Common Angle Reference
| Degrees | Radians | Gradians | Description |
|---|---|---|---|
| 0° | 0 | 0 | Zero angle |
| 30° | π/6 ≈ 0.5236 | 33.33 | Acute angle |
| 45° | π/4 ≈ 0.7854 | 50 | Half of right angle |
| 60° | π/3 ≈ 1.0472 | 66.67 | Equilateral triangle angle |
| 90° | π/2 ≈ 1.5708 | 100 | Right angle |
| 180° | π ≈ 3.1416 | 200 | Straight angle |
| 270° | 3π/2 ≈ 4.7124 | 300 | Three-quarter turn |
| 360° | 2π ≈ 6.2832 | 400 | Full circle |
Frequently Asked Questions
How do I convert degrees to radians?â–¼
Multiply degrees by π/180. For example, 90° = 90 × π/180 = π/2 ≈ 1.5708 radians.
What is a gradian?â–¼
A gradian (also called gon) divides a full circle into 400 equal parts. A right angle is exactly 100 gradians. It is used in surveying and civil engineering.
Why are radians used in mathematics?â–¼
Radians are the natural unit for angles in calculus and physics because they make formulas simpler — for example, the derivative of sin(x) is cos(x) only when x is in radians.
What is the difference between arcminute and arcsecond?â–¼
1 degree = 60 arcminutes. 1 arcminute = 60 arcseconds. These tiny units are used in astronomy and precision navigation where fractions of a degree matter.