Angle Converter
Common Angles Reference
| Degrees | Radians | Gradians |
|---|---|---|
| 0° | 0 | 0 gon |
| 30° | π/6 | 33.3333 gon |
| 45° | π/4 | 50 gon |
| 60° | π/3 | 66.6667 gon |
| 90° | π/2 | 100 gon |
| 180° | π | 200 gon |
| 270° | 3π/2 | 300 gon |
| 360° | 2π | 400 gon |
Angle Converter: Degrees, Radians & Gradians
Angles are a fundamental concept in mathematics, physics, and engineering. Different fields prefer different units: degrees are used in everyday contexts, radians are the standard in calculus and trigonometry, and gradians (also called gons) are common in surveying and some European engineering fields. This free angle converter lets you instantly translate between all three systems.
How to Use
- Enter a value in any of the three fields (Degrees, Radians, or Gradians).
- The other two fields update automatically in real time.
- The visual arc diagram shows the angle you entered.
- Use the reference table below for quick lookups of common angles.
FAQ
- What is the formula to convert degrees to radians?
- Multiply the degree value by π/180. For example, 90° × π/180 = π/2 radians (≈ 1.5708).
- What are gradians used for?
- Gradians divide a right angle into 100 equal parts, making them convenient for surveying and civil engineering calculations. A full circle is 400 gradians.
- How do I convert radians to gradians?
- First convert radians to degrees (multiply by 180/π), then convert degrees to gradians (multiply by 10/9). Or directly: gradians = radians × 200/π.
- Why do calculators use radians?
- Radians are the natural unit for measuring angles in calculus because the derivatives of trigonometric functions have their simplest form when angles are in radians. For instance, the derivative of sin(x) is cos(x) only when x is in radians.
- Is there a difference between a gradian and a gon?
- No. "Gradian" and "gon" are two names for the same unit. A full circle is 400 gradians or 400 gon.