Convert Turns to Microradians
Convert Turns (rev) to Microradians (µrad) instantly and accurately.
Conversion Formula
µrad = rev × 6283185.307
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 Microradians
A microradian (µrad) is one millionth of a radian (10⁻⁶ rad ≈ 0.206265 arcseconds). It is the standard unit for small angles in precision optics and structural monitoring. A 1 µm wavelength beam from a 1 mm aperture has a diffraction-limited half-angle divergence of ~1 µrad. Atmospheric seeing for ground-based telescopes is typically 2.4-9.7 µrad (0.5-2 arcseconds). Autocollimators resolve angular deviations to 0.05-1 µrad for machine tool alignment. Building tilt monitoring tracks µrad/day. 1 µrad ≈ 0.2063″ = 0.2063 arcseconds.
Quick Reference Table
| Turns (rev) | Microradians (µrad) |
|---|---|
| 1 rev | 6283190 µrad |
| 2 rev | 12566400 µrad |
| 5 rev | 31415900 µrad |
| 10 rev | 62831900 µrad |
| 25 rev | 157080000 µrad |
| 50 rev | 314159000 µrad |
| 100 rev | 628319000 µrad |