Convert Gradians to Turns
Convert Gradians (grad) to Turns (rev) instantly and accurately.
Conversion Formula
rev = grad × 0.0025
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 Turns
A turn (revolution, cycle) equals one complete rotation - 2π rad = 360° = 400 grad. Rotational speed is naturally measured in turns per minute (rpm): a car engine idles at ~750 rpm; a hard disk spins at 7,200 rpm. The factor 2π in physics formulas (ω = 2πf, E = hf = ħω) arises from converting turns to radians. The turn is the natural unit for gear ratios, transformer winding counts, and thread pitch (turns per inch). The tau convention (τ = 2π ≈ 6.2832) proposes 1τ = 1 full turn. 1 rpm = 1/60 Hz = 2π/60 rad/s ≈ 0.10472 rad/s.
Quick Reference Table
| Gradians (grad) | Turns (rev) |
|---|---|
| 1 grad | 0.0025 rev |
| 2 grad | 0.005 rev |
| 5 grad | 0.0125 rev |
| 10 grad | 0.025 rev |
| 25 grad | 0.0625 rev |
| 50 grad | 0.125 rev |
| 100 grad | 0.25 rev |