Convert Microradians to Semicircles
Convert Microradians (µrad) to Semicircles (sc) instantly and accurately.
Conversion Formula
sc = µrad × 3.183098862e-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 Semicircles
A semicircle equals 1/2 of a full circle - exactly π rad = 180°. GPS and GLONASS transmit satellite orbital elements with latitude and longitude in semicircles, maximising angular resolution within 32-bit signed integers: ±2³¹ units span ±π rad with ~1.46 × 10⁻⁹ rad resolution per unit. Euler's identity e^(iπ) + 1 = 0 encodes exactly 1 semicircle of rotation in the complex plane, mapping 1 to -1 - often called the most beautiful equation in mathematics. 1 semicircle = π rad = 180° = 200 grad = 3,200 NATO mils.
Quick Reference Table
| Microradians (µrad) | Semicircles (sc) |
|---|---|
| 1 µrad | 3.183 × 10-7 sc |
| 2 µrad | 6.366 × 10-7 sc |
| 5 µrad | 1.592 × 10-6 sc |
| 10 µrad | 3.183 × 10-6 sc |
| 25 µrad | 7.958 × 10-6 sc |
| 50 µrad | 1.592 × 10-5 sc |
| 100 µrad | 3.183 × 10-5 sc |