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Angle
Gradians to Degrees
Convert gradians (gon) to degrees (°). Type a value below to see the result update instantly. Reference table and formula included.
Calculator
1 gon = 0.9 °
Gradians to Degrees Conversion Table
Common values, ready to copy:
| gradians | degrees |
|---|---|
| 1 gon | 0.9 ° |
| 2 gon | 1.8 ° |
| 5 gon | 4.5 ° |
| 10 gon | 9 ° |
| 25 gon | 22.5 ° |
| 50 gon | 45 ° |
| 100 gon | 90 ° |
| 1,000 gon | 900 ° |
Formula
degrees = gradians × 0.9
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
About Gradians and Degrees
Gradians (gon): 1/400 of a full turn; introduced in revolutionary France as a metric-style angle unit (100 gradians = right angle). Common uses: Surveying in some European countries, some scientific calculators have a 'GRAD' mode, mostly historical interest elsewhere.
Degrees (°): 1/360 of a full turn; the 360-degree division comes from ancient Babylonian astronomy and the convenience of 360 being divisible by many small integers. Common uses: Navigation (compass headings), construction (angle cuts), geometry, geography (latitude and longitude), and almost any practical angle measurement.
How the conversion works
Angles are ratios, not absolute quantities, so the conversion factors are exact. 1 full turn = 360° = 2π rad ≈ 6.2832 rad = 400 gon. 1° = 60 arcminutes = 3,600 arcseconds.
The exact relationship is degrees = gradians × 0.9, which the calculator at the top of this page applies in both directions. Type into either field and the other updates immediately.
When this conversion matters
Converting between gradians and degrees comes up wherever angle measurements move between systems — from one country's conventions to another's, from a scientific reference to a practical specification, or from one industry's working unit to another's. The calculator and reference table above cover the everyday range; for unusual values you can type any number into either field.