Gon (gon) - Unit Information & Conversion
🔄 Quick Convert Gon
What is a Gon?
Gon (also gradian or grad) is 1/400 of a full circle, designed for decimal calculations. 100 gons = right angle, 400 gons = full circle. Used in surveying, civil engineering, and some European countries.
History of the Gon
Introduced during French Revolution (1795) as part of metric system decimalization. Popular in continental Europe, especially France, Germany, and Scandinavia for surveying and construction.
Quick Answer
What is a Gon? A gon (or gradian) is 1/400th of a full circle, designed for easy decimal calculations. 100 gons = 90 degrees (right angle), 200 gons = 180 degrees, 400 gons = 360 degrees (full circle). Popular in European surveying and civil engineering. Use our angle converter for instant conversions.
Key Facts: Gon
| Property | Value |
|---|---|
| Symbol | gon |
| Quantity | Angle |
| System | Metric/SI Derived |
| Derived from | Radian |
| Category | Angle |
| Standard Body | NIST / ISO |
Definition
1 gon = 1/400 of a full circle = 0.9 degrees = 0.01571 radians
Key conversions:
- 100 gons = 90 degrees (right angle)
- 200 gons = 180 degrees (straight angle)
- 400 gons = 360 degrees (full circle)
- 1 gon = 0.9° = π/200 radians
Alternative names: Gradian, grad, grade (same unit, different names)
Common Uses
Surveying: Land surveys and topographic mapping in Europe, especially France, Germany, Switzerland - THE standard in continental Europe. Civil Engineering: Construction projects, road gradients, slope calculations - preferred by engineers trained in metric system. Military: Artillery targeting and ballistics in some European armies - standardized for ballistics calculations. Cartography: Map making and coordinate systems in countries using metric system - seamless with metric philosophy.
Real-World Examples
Gon vs Degree Comparison
Why gons make decimal calculations easier:
| Angle | Gons | Degrees | Radians | Notes |
|---|---|---|---|---|
| Zero | 0 | 0° | 0 | Reference |
| Right angle | 100 | 90° | π/2 | 100 is decimal-perfect |
| Straight | 200 | 180° | π | Exact decimal |
| Reflex | 300 | 270° | 3π/2 | Clean decimal |
| Full circle | 400 | 360° | 2π | Base unit |
| Quarter | 100 | 90° | π/2 | Repeating decimals in degrees |
| Eighth | 50 | 45° | π/4 | Easy decimal division |
| Sixteenth | 25 | 22.5° | π/8 | No fractions with gons |
Advantage: Dividing 400 by any power of 2 gives clean decimals (100, 50, 25, 12.5...)
Surveying Instrument Comparisons
How theodolites and transit levels display angles:
| Instrument Mode | Unit | For Right Angle | For Half | For Full Circle |
|---|---|---|---|---|
| Degree mode | Degrees | 90.0000° | 180.0000° | 360.0000° |
| Gon mode | Gons | 100.0000ᵍ | 200.0000ᵍ | 400.0000ᵍ |
| Radian mode | Radians | 1.5708 rad | 3.1416 rad | 6.2832 rad |
| Easiest mental math? | ✓ GON | ✓ GON | ✓ GON | ✓ GON |
Surveyor advantage: European surveyors often prefer gons for mental calculations (400 ÷ 4 = 100 instantly)
European Standardization by Country
Where gons are the official/preferred standard:
| Country | Surveying Standard | Civil Engineering | Notes |
|---|---|---|---|
| France | Gons primary | Gons preferred | Legal standard since 1800s |
| Germany | Gons standard | Gons common | DIN standards use gons |
| Switzerland | Gons official | Gons used | Cadastral surveys in gons |
| Belgium | Gons standard | Gons preferred | Official cadastral unit |
| Netherlands | Gons/degrees mix | Gons acceptable | Transitioning |
| Austria | Gons standard | Gons used | Professional surveying |
| Scandinavia | Mixed usage | Sometimes gons | Varies by country |
| Spain/Italy | Mixed | Degrees more common | Less standardized |
| USA/UK | Degrees dominant | Degrees only | Imperial tradition |
Mathematical Advantage: Decimal Calculations
Practical calculation benefits:
| Task | Gons Calculation | Degrees Calculation |
|---|---|---|
| Find quarter angle | 400 ÷ 4 = 100 gons | 360 ÷ 4 = 90° (easy) |
| Find eighth angle | 400 ÷ 8 = 50 gons | 360 ÷ 8 = 45° (easy) |
| Find sixteenth angle | 400 ÷ 16 = 25 gons | 360 ÷ 16 = 22.5° (needs decimal) |
| Find thirty-second | 400 ÷ 32 = 12.5 gons | 360 ÷ 32 = 11.25° |
| Find one-thousandth | 400 ÷ 1000 = 0.4 gons | 360 ÷ 1000 = 0.36° |
Winner: Gons for higher-precision decimal subdivisions!
Technology Support
Where you'll see gons in modern systems:
| Technology | Gon Support | Notes |
|---|---|---|
| Scientific calculators | Yes (GRAD mode) | Standard DEG/RAD/GRAD selector |
| Surveying software | Full support | Professional-grade equipment |
| Theodolites/transits | Most models | Standard on European instruments |
| GPS receivers | Some models | Primarily Degrees/Radians |
| CAD software | Version-dependent | AutoCAD, Revit support gons |
| Mobile apps | Few | Degree/radian dominant |
| Programming libraries | Limited | Not standard in most languages |
| Specialized surveying equipment | Full support | Industry standard in Europe |
Gon Conversion Formulas
To Degree:
To Radian:
To Gradian:
To Arcminute:
To Arcsecond:
To Turn:
To Revolution:
To Quadrant:
To Mil:
Frequently Asked Questions
Formula: Degrees = Gons × 0.9 (or Gons × 9/10) Examples:
- 100 gons = 90°
- 200 gons = 180°
- 400 gons = 360°
- 50 gons = 45°
- 1 gon = 0.9° Gons to Degrees converter →
Convert Gon
Need to convert Gon to other angle units? Use our conversion tool.