Convert Turns to Centesimal Seconds
Convert Turns (rev) to Centesimal Seconds (c″) instantly and accurately.
Conversion Formula
c″ = rev × 4000000
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.
About Centesimal Seconds
A centesimal second (c″) is 1/10,000 of a gradian - exactly π/2,000,000 rad ≈ 1.5708 × 10⁻⁶ rad. In the gradian hierarchy, 1 right angle = 100 grad = 10,000 c′ = 1,000,000 c″. High-precision total stations calibrated in gons report to 0.1-1 c″, equivalent to ~0.0324 arcseconds. Used in French, Dutch, Swiss, and Scandinavian cadastral surveys. DIN 1313 designates 10 c″ = 1 milligon (mgon). 1 c″ ≈ 0.324″ sexagesimal = π/2,000,000 rad.
Quick Reference Table
| Turns (rev) | Centesimal Seconds (c″) |
|---|---|
| 1 rev | 4000000 c″ |
| 2 rev | 8000000 c″ |
| 5 rev | 20000000 c″ |
| 10 rev | 40000000 c″ |
| 25 rev | 100000000 c″ |
| 50 rev | 200000000 c″ |
| 100 rev | 400000000 c″ |