Degrees ↔ Gradians Converter
Convert between degrees and gradians instantly
📚 Degrees ↔ Gradians Conversion Details
Degrees to Gradians Formula
gradians = degrees × (10 / 9)
To convert degrees to gradians, multiply degrees by 10/9.
Gradians to Degrees Formula
degrees = gradians × (9 / 10)
To convert gradians to degrees, multiply gradians by 9/10.
Bidirectional Conversion
This converter works both ways simultaneously:
- Type in degrees → gradians updates automatically
- Type in gradians → degrees updates automatically
- No buttons to click - works as you type
Common Uses
- Surveying and land measurement
- Navigation systems
- Engineering calculations
- Mathematics education
📏 Angle Units Explained
Degrees (°) are the most common unit for measuring angles. A full circle is 360°.
Gradians (gon) are an alternative unit where a full circle is divided into 400 gradians.
1 full circle = 360° = 400 gon
1° = (400/360) gon = (10/9) gon ≈ 1.1111 gon
1 gon = (360/400)° = (9/10)° = 0.9°
// Example Conversions:
90° = 90 × (10/9) = 100 gon
100 gon = 100 × (9/10) = 90°
📊 Conversion Table
| Degrees (°) | Gradians (gon) | Description |
|---|---|---|
| 0° | 0 gon | Zero angle |
| 45° | 50 gon | Eighth of a circle |
| 90° | 100 gon | Right angle |
| 180° | 200 gon | Straight angle |
| 270° | 300 gon | Three-quarters circle |
| 360° | 400 gon | Full circle |
❓ Frequently Asked Questions
A: Gradians are primarily used in surveying, navigation, and some engineering fields where decimal divisions are preferred over fractional degrees.
A: There are exactly 400 gradians in a full circle, compared to 360 degrees.
A: Yes, the conversion is mathematically exact: 1° = 10/9 gon and 1 gon = 9/10°.
A: Gradians are commonly used in France and some other European countries, especially in surveying and military applications.