Gon (gon) - Unit Information & Conversion

Symbol:gon
Plural:gons
Category:Angle

🔄 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 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° 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:

1 gon = 0.9 °
Example: 5 gons = 4.5 degrees

To Radian:

1 gon = 0.015708 rad
Example: 5 gons = 0.07854 radians

To Gradian:

1 gon = 1 grad
Example: 5 gons = 5 gradians

To Arcminute:

1 gon = 54 ′
Example: 5 gons = 270 arcminutes

To Arcsecond:

1 gon = 3240 ″
Example: 5 gons = 16200 arcseconds

To Turn:

1 gon = 0.0025 turn
Example: 5 gons = 0.0125 turns

To Revolution:

1 gon = 0.0025 rev
Example: 5 gons = 0.0125 revolutions

To Quadrant:

1 gon = 0.01 quad
Example: 5 gons = 0.05 quadrants

To Mil:

1 gon = 16 mil
Example: 5 gons = 80 mils

Frequently Asked Questions

Formula: Degrees = Gons × 0.9 (or Gons × 9/10) Examples:

Convert Gon

Need to convert Gon to other angle units? Use our conversion tool.