Unit Conversions
Angle Converter
Convert angles between degrees (°), radians (rad), and gradians (grad) with formula explanations and a common angles table.
✓ Runs in your browser · Updated 2026-03-31Enter values and click Convert to see results
How Angle Conversion Works
The three common angle units are related through these 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
- Radians → Gradians: grad = rad × 200 / π
- Gradians → Radians: rad = grad × π / 200
A full circle = 360° = 2π rad = 400 grad.
Common Angles Reference
| Degrees | Radians | Gradians | Description |
|---|---|---|---|
| 0° | 0 | 0 | No rotation |
| 30° | π/6 ≈ 0.5236 | 33.33 | Common trig angle |
| 45° | π/4 ≈ 0.7854 | 50 | Half of right angle |
| 60° | π/3 ≈ 1.0472 | 66.67 | Equilateral triangle |
| 90° | π/2 ≈ 1.5708 | 100 | Right angle |
| 180° | π ≈ 3.1416 | 200 | Straight line |
| 270° | 3π/2 ≈ 4.7124 | 300 | Three-quarter turn |
| 360° | 2π ≈ 6.2832 | 400 | Full rotation |
When to Use Each Unit
- Degrees (°): Most common in daily life, geometry, navigation, and construction. Used in school maths in India (CBSE, ICSE, State Boards).
- Radians (rad): Standard in higher mathematics, physics, and programming. JavaScript's
Math.sin(),Math.cos()etc. all expect radians. - Gradians (grad): Used in surveying and some European engineering. A right angle = 100 gradians, making subdivision easier.
Related Converters
For physics calculations involving angles, see the Speed Converter. For mathematical utilities, check the Percentage Calculator.
Frequently Asked Questions
How do I convert degrees to radians?
Multiply the angle in degrees by π/180. For example, 90° = 90 × π/180 = π/2 radians (≈ 1.5708).
What is a gradian and how does it relate to degrees?
A gradian (also called gon) divides a right angle into 100 parts. So 360° = 400 gradians and 90° = 100 gradians.
How many radians are in a full circle?
A full circle (360°) equals 2π radians, which is approximately 6.2832 radians.