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Angle
Degrees to Gradians
Convert degrees (°) to gradians (gon). Type a value below to see the result update instantly. Reference table and formula included.
Calculator
1 ° = 1.1111 gon
Degrees to Gradians Conversion Table
Common values, ready to copy:
| degrees | gradians |
|---|---|
| 1 ° | 1.1111 gon |
| 2 ° | 2.2222 gon |
| 5 ° | 5.5556 gon |
| 10 ° | 11.1111 gon |
| 25 ° | 27.7778 gon |
| 50 ° | 55.5556 gon |
| 100 ° | 111.11 gon |
| 1,000 ° | 1111.11 gon |
Formula
gradians = degrees × 1.11111111e+0
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 Degrees and Gradians
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.
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.
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 gradians = degrees × 1.11111111e+0, 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 degrees and gradians 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.