How to Convert Gradians to Arcminutes (gon to ′)
Angle conversions show up in maths and physics lessons, surveying and navigation. This guide shows how to convert gradians into arcminutes by hand, with examples and a quick-reference table.
The conversion
To convert gradians to arcminutes, multiply the value by 54. To go the other way, divide by the same number (or multiply by 0.0185185185). For a quick estimate, multiply by about 54.
Arcminutes = gradians × 54
Worked examples
- 3 gon = 162 ′
- 12.5 gon = 675 ′
- 75 gon = 4,050 ′
Gradians to Arcminutes table
| Gradians | Arcminutes |
|---|---|
| 1 gon | 54 ′ |
| 2 gon | 108 ′ |
| 5 gon | 270 ′ |
| 10 gon | 540 ′ |
| 20 gon | 1,080 ′ |
| 25 gon | 1,350 ′ |
| 50 gon | 2,700 ′ |
| 100 gon | 5,400 ′ |
| 250 gon | 13,500 ′ |
| 500 gon | 27,000 ′ |
| 1,000 gon | 54,000 ′ |
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 Arcminutes to Gradians converter.
Mistakes to avoid
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.
Multiplying when you should divide
Converting to a smaller unit gives a bigger number, and converting to a larger unit gives a smaller one. If your answer moves the wrong way, you have inverted the factor.
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
Writing the units next to every number while you work is the simplest way to avoid mistakes. If the units do not cancel to leave the one you want, the calculation is set up wrongly.
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.
A conversion table is handy for common values, but a calculator is faster and avoids interpolation errors for anything in between.
For any value, use the Gradians to Arcminutes Converter or browse all angle converters.
Run your own numbers: Gradians to Arcminutes Converter