Angle Converter
Instantly convert measurements between Degrees (°), Radians (rad), and Gradians (grad). Simply type into any field.
Angle Converter
Common Angles Reference
| Degrees | Radians | Gradians |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 (≈ 0.524) | 33.33 |
| 45° | π/4 (≈ 0.785) | 50 |
| 60° | π/3 (≈ 1.047) | 66.67 |
| 90° | π/2 (≈ 1.571) | 100 |
| 180° | π (≈ 3.142) | 200 |
| 360° | 2π (≈ 6.283) | 400 |
Understanding Angle Units
Degrees (°)
Divides a full revolution into 360 equal slices. Originated in ancient Babylonian astronomy and is the most common unit for everyday navigation, construction, and geometry.
Radians (rad)
The standard SI scientific unit. One radian is the angle subtended at the center of a circle by an arc whose length equals the circle radius. A full circle is exactly 2π radians.
Gradians (grad / gon)
Divides a full revolution into 400 gradians, meaning a right angle is exactly 100 gradians. Widely favored in civil engineering and land surveying across Europe.
Mathematical Conversion Formulas
Degrees to Radians
Example: 90° × (π / 180) = π/2 ≈ 1.5708 rad
Radians to Degrees
Example: 1 rad × (180 / π) ≈ 57.2958°
Degrees to Gradians
Example: 90° × (10 / 9) = 100 grad
Gradians to Degrees
Example: 200 grad × (9 / 10) = 180°
Common Angles Reference Table
| Degrees (°) | Radians (π) | Radians (Decimal) | Gradians (grad) | Angle Type |
|---|---|---|---|---|
| 0° | 0 | 0.0000 | 0 grad | Zero |
| 30° | π/6 | 0.5236 | 33.33 grad | Acute |
| 45° | π/4 | 0.7854 | 50.00 grad | Acute |
| 60° | π/3 | 1.0472 | 66.67 grad | Acute |
| 90° | π/2 | 1.5708 | 100.00 grad | Right |
| 120° | 2π/3 | 2.0944 | 133.33 grad | Obtuse |
| 180° | π | 3.1416 | 200.00 grad | Straight |
| 270° | 3π/2 | 4.7124 | 300.00 grad | Reflex |
| 360° | 2π | 6.2832 | 400.00 grad | Full Turn |