How to Convert Gradians to Degrees (gon to °)
Angle conversions show up in maths and physics lessons, surveying and navigation. This guide shows how to convert gradians into degrees by hand, with examples and a quick-reference table.
The conversion
To convert gradians to degrees, multiply the value by 0.9. To go the other way, divide by the same number (or multiply by 1.1111111111). For a quick estimate, multiply by about 0.9.
Degrees = gradians × 0.9
Worked examples
- 3 gon = 2.7 °
- 12.5 gon = 11.25 °
- 75 gon = 67.5 °
Gradians to Degrees table
| Gradians | Degrees |
|---|---|
| 1 gon | 0.9 ° |
| 2 gon | 1.8 ° |
| 5 gon | 4.5 ° |
| 10 gon | 9 ° |
| 20 gon | 18 ° |
| 25 gon | 22.5 ° |
| 50 gon | 45 ° |
| 100 gon | 90 ° |
| 250 gon | 225 ° |
| 500 gon | 450 ° |
| 1,000 gon | 900 ° |
Common questions
Is gon to ° exact?
The factors used here are the internationally defined values where they exist; results are rounded for display only.
How do I convert back?
Use the Degrees to Gradians converter.
Mistakes to avoid
Mixing similar-sounding units
US and imperial gallons, pints and tons are different sizes, and decimal kilobytes differ from binary kibibytes.
Rounding the factor too early
Using 3 instead of 3.28 for feet per metre introduces an error of almost 9% before you have started.
Forgetting squared and cubed units
Area and volume factors are the length factor squared or cubed, so 1 m² is about 10.76 sq ft, not 3.28.
Background
Many conversion factors are exact by definition. The inch has been defined as exactly 2.54 centimetres since 1959, and the pound as exactly 0.45359237 kilograms, so conversions involving them can be as precise as you need.
Unit conversion is simply multiplication by a fixed ratio. The ratio between two units of the same quantity never changes, so once you know it you can convert any value in either direction.
For everyday use, three or four significant figures are usually enough. Engineering, science and trade documents may need more, and rounding should happen only at the end of a calculation.
For any value, use the Gradians to Degrees Converter or browse all angle converters.
Run your own numbers: Gradians to Degrees Converter