Degrees to Gradians Converter
Convert angle measurements from degrees to gradians (also known as gons or grades). Gradians divide a right angle into 100 equal parts, making calculations with perpendicular lines simpler.
Common Degrees to Gradians Conversions
| Degrees (°) | Gradians (grad) |
|---|---|
| 0° | 0 grad |
| 15° | 16.6667 grad |
| 30° | 33.3333 grad |
| 45° | 50 grad |
| 60° | 66.6667 grad |
| 90° | 100 grad |
| 120° | 133.3333 grad |
| 180° | 200 grad |
| 270° | 300 grad |
| 360° | 400 grad |
How to Convert Degrees to Gradians
Converting degrees to gradians is straightforward using a simple multiplication factor. The gradian system divides a full circle into 400 equal parts instead of 360, making it particularly useful in surveying and some European engineering applications.
The Conversion Formula
Or equivalently:
Example: Converting 45 Degrees to Gradians
gradians = 45° × (10/9) = 45° × 1.111111 = 50 grad
Example: Converting 90 Degrees to Gradians
gradians = 90° × (10/9) = 90° × 1.111111 = 100 grad
What Is a Gradian?
A gradian (also called gon, grad, or grade) is a unit of angle measurement where a full circle equals 400 gradians. This system was introduced in France during the late 18th century as part of the metric system, aiming to decimalize angle measurement.
Key relationships:
- 1 right angle = 100 gradians = 90 degrees
- 1 full circle = 400 gradians = 360 degrees
- 1 gradian = 0.9 degrees
- 1 degree = 1.111... gradians
Why Use Gradians?
Surveying: Gradians are popular in surveying because perpendicular angles are exactly 100 gradians, making field calculations easier.
European Engineering: Some European countries use gradians in engineering and construction drawings.
Metric Consistency: Gradians provide a decimal-based angle system that aligns with the metric philosophy of base-10 measurements.
Historical Background
The gradian was introduced in France in 1793 as part of the decimal metric system. The French revolutionaries sought to decimalize all measurements, including time and angles. While decimal time was quickly abandoned, gradians found lasting use in certain professional fields, particularly land surveying in France, Germany, and other European nations.