Convert Signs to Microradians
Convert Signs (sign) to Microradians (µrad) instantly and accurately.
Conversion Formula
µrad = sign × 523598.7756
About Signs
An astrological sign equals 1/12 of a full circle - π/6 rad = exactly 30°. The zodiac divides the ecliptic into twelve 30° signs (Aries through Pisces), originating in Babylonian astronomy ~5th century BCE. Historical ecliptic longitude was expressed as sign + degrees: "Scorpio 12°" = 222°. The 30° spacing also appears in music theory: the circle of fifths has twelve equally spaced positions 30° apart, and the octave divides into 12 equal semitones. 1 sign = 30° = 1,800′ = π/6 rad = 533.3 NATO mils.
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
| Signs (sign) | Microradians (µrad) |
|---|---|
| 1 sign | 523599 µrad |
| 2 sign | 1047200 µrad |
| 5 sign | 2617990 µrad |
| 10 sign | 5235990 µrad |
| 25 sign | 13090000 µrad |
| 50 sign | 26179900 µrad |
| 100 sign | 52359900 µrad |