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Convert angles between degrees and gradians (gon). Widely used in European surveying, navigation, and engineering.
gradians = degrees × (400 / 360)
gradians = degrees × 1.11111
Example: 90° = 90 × (400/360) = 100 gradians
| Degrees (°) | Gradians (gon) | Ratio |
|---|---|---|
| 0° | 0.00000 gon | |
| 30° | 33.33333 gon | |
| 45° | 50.00000 gon | |
| 60° | 66.66667 gon | |
| 90° | 100.00000 gon | 1/4 circle |
| 120° | 133.33333 gon | |
| 135° | 150.00000 gon | |
| 150° | 166.66667 gon | |
| 180° | 200.00000 gon | 1/2 circle |
| 270° | 300.00000 gon | 3/4 circle |
| 360° | 400.00000 gon | Full circle |
Gradians (also called gons or grades) are a unit of angular measurement where a full circle is divided into 400 gradians. This makes a right angle exactly 100 gradians, which simplifies many calculations. The system was designed to work well with decimal arithmetic, making it popular in continental Europe, particularly for surveying and civil engineering applications.
The gradian system divides a circle into 400 units because it creates convenient decimal relationships. A right angle becomes 100 gradians, making calculations easier in the metric system. Each gradian can be subdivided into 100 centigrad and 10,000 milligrad, maintaining decimal consistency throughout. This decimal nature was particularly valuable before electronic calculators became common.
Degrees divide a circle into 360 parts, a system dating back to ancient Babylon. Gradians divide a circle into 400 parts, a more recent decimal system. The conversion factor is simple: 1 degree = 1.11111 gradians, or 360° = 400 gon. While degrees are more common globally, gradians remain popular in surveying, construction, and engineering in many European countries.
Multiply the degree value by 400/360 (or 1.11111). For example, 90° = 90 × (400/360) = 100 gradians. This ratio comes from the fact that a full circle is 360 degrees or 400 gradians.
Gradians work well with the metric system because they're based on decimal subdivision. A right angle is exactly 100 gradians, making calculations simpler. Many European countries adopted gradians for surveying and civil engineering because they integrate seamlessly with metric measurements.
Yes, gradians remain in use, particularly in surveying and civil engineering in European countries like France, Germany, and Switzerland. Many surveying instruments and software packages support gradians. However, degrees are more common in most other fields and countries.
A full circle is 400 gradians or 2π radians. Therefore, 1 gradian = π/200 radians ≈ 0.0157 radians. To convert gradians to radians, multiply by π/200. To convert radians to gradians, multiply by 200/π.