Convert Turns to Centesimal Minutes
Convert Turns (rev) to Centesimal Minutes (c′) instantly and accurately.
Conversion Formula
c′ = rev × 40000
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 Minutes
A centesimal minute (c′) is 1/100 of a gradian - exactly π/20,000 rad ≈ 1.5708 × 10⁻⁴ rad (= 0.9 sexagesimal arcminutes). Also designated cgon (centigon) in ISO/DIN standards. Total stations in the grad system display readings to 1 c′ or 0.1 c′; a right angle = 100 grad = 10,000 c′. A 1% slope ≈ 0.6366 grad ≈ 63.66 c′ - a simple calculation that makes the centesimal minute popular in road and railway alignment. 1 c′ = 0.9′ = 54″ = π/20,000 rad.
Quick Reference Table
| Turns (rev) | Centesimal Minutes (c′) |
|---|---|
| 1 rev | 40000 c′ |
| 2 rev | 80000 c′ |
| 5 rev | 200000 c′ |
| 10 rev | 400000 c′ |
| 25 rev | 1000000 c′ |
| 50 rev | 2000000 c′ |
| 100 rev | 4000000 c′ |