Convert Centesimal Minutes to Microradians

Convert Centesimal Minutes (c′) to Microradians (µrad) instantly and accurately.

Conversion Formula

µrad = c′ × 157.0796327

About Centesimal Minutes

A centesimal minute (c′) is 1/100 of a gradian - exactly π/20,000 rad ≈ 1.5708 × 10⁻⁴ rad (= 0.9 sexagesimal arcminutes). Also designated cgon (centigon) in ISO/DIN standards. Total stations in the grad system display readings to 1 c′ or 0.1 c′; a right angle = 100 grad = 10,000 c′. A 1% slope ≈ 0.6366 grad ≈ 63.66 c′ - a simple calculation that makes the centesimal minute popular in road and railway alignment. 1 c′ = 0.9′ = 54″ = π/20,000 rad.

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

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