Convert Turns to Arcminutes
Convert Turns (rev) to Arcminutes (′) instantly and accurately.
Conversion Formula
′ = rev × 21600
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 Arcminutes
An arcminute (′) is 1/60 of a degree - π/10,800 rad ≈ 2.909 × 10⁻⁴ rad. One arcminute of latitude equals exactly one nautical mile (1,852 m), which is the origin of the nautical mile unit. The Moon and Sun both subtend ~30 arcminutes in apparent diameter - the coincidence exploited in total solar eclipses. Human 20/20 visual acuity resolves letters 5 arcminutes tall at 6 m. Binocular and telescope apparent fields of view are quoted in arcminutes. 1′ = π/10,800 rad ≈ 0.01667° ≈ 290.9 µrad.
Quick Reference Table
| Turns (rev) | Arcminutes (′) |
|---|---|
| 1 rev | 21600 ′ |
| 2 rev | 43200 ′ |
| 5 rev | 108000 ′ |
| 10 rev | 216000 ′ |
| 25 rev | 540000 ′ |
| 50 rev | 1080000 ′ |
| 100 rev | 2160000 ′ |