How to Convert Gradians to Radians (gon to rad)
Angle conversions show up in maths and physics lessons, surveying and navigation. This guide shows how to convert gradians into radians by hand, with examples and a quick-reference table.
The conversion
To convert gradians to radians, multiply the value by 0.0157079633. To go the other way, divide by the same number (or multiply by 63.6619772368). For a quick estimate, multiply by about 0.016.
Radians = gradians × 0.0157079633
Worked examples
- 3 gon = 0.047124 rad
- 12.5 gon = 0.19635 rad
- 75 gon = 1.1781 rad
Gradians to Radians table
| Gradians | Radians |
|---|---|
| 1 gon | 0.015708 rad |
| 2 gon | 0.031416 rad |
| 5 gon | 0.07854 rad |
| 10 gon | 0.15708 rad |
| 20 gon | 0.314159 rad |
| 25 gon | 0.392699 rad |
| 50 gon | 0.785398 rad |
| 100 gon | 1.5708 rad |
| 250 gon | 3.927 rad |
| 500 gon | 7.854 rad |
| 1,000 gon | 15.708 rad |
Common questions
Is gon to rad 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 Radians 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.
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.
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.
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.
A conversion table is handy for common values, but a calculator is faster and avoids interpolation errors for anything in between.
Singapore adopted the metric system in the 1970s, replacing imperial units and traditional Chinese measures in most official uses. Metric units are now standard in schools, trade and government, but older units survive in property, markets and imported goods.
For any value, use the Gradians to Radians Converter or browse all angle converters.
Run your own numbers: Gradians to Radians Converter