Convert Microradians to Turns

Convert Microradians (µrad) to Turns (rev) instantly and accurately.

Microradians (µrad)
Turns (rev)

Conversion Formula

rev = µrad × 1.591549431e-7

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.

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

Microradians (µrad)Turns (rev)
1 µrad1.592 × 10-7 rev
2 µrad3.183 × 10-7 rev
5 µrad7.958 × 10-7 rev
10 µrad1.592 × 10-6 rev
25 µrad3.979 × 10-6 rev
50 µrad7.958 × 10-6 rev
100 µrad1.592 × 10-5 rev

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