Convert Gradians to Degrees
Convert Gradians (grad) to Degrees (°) instantly and accurately.
Conversion Formula
° = grad × 0.9
About Gradians
A gradian (grad), also called a gon (ISO 31/DIN), equals 1/400 of a full circle - π/200 rad = 0.9°. Its main advantage: a right angle = exactly 100 grad, simplifying complementary and supplementary angle arithmetic. Introduced during the French Revolution as part of decimal angle reform. Surveying in France, the Netherlands, Switzerland, and Scandinavia uses gradians; professional total stations display both degrees and gons. A 1% slope ≈ 0.6366 grad. 1 grad = 0.9° = 54′ = π/200 rad; 400 grad = 360° = one full circle.
About Degrees
The degree (°) is the most widely used angle unit in everyday life, tracing to Babylonian astronomy ~300 BCE - the ecliptic was divided into 360 parts because the sexagesimal base-60 system made 360 highly divisible (by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20). Each degree divides into 60 arcminutes and 3,600 arcseconds. The degree dominates practical work: compass bearings, geographic coordinates (latitude ±90°, longitude ±180°), wind direction, polygon angles, and engineering drawings. Calculus uses radians because sin(x) ≈ x only holds in radians. 1° = π/180 rad ≈ 17.453 mrad.
Quick Reference Table
| Gradians (grad) | Degrees (°) |
|---|---|
| 1 grad | 0.9 ° |
| 2 grad | 1.8 ° |
| 5 grad | 4.5 ° |
| 10 grad | 9 ° |
| 25 grad | 22.5 ° |
| 50 grad | 45 ° |
| 100 grad | 90 ° |