Convert Nanoradians to Centesimal Minutes
Convert Nanoradians (nrad) to Centesimal Minutes (c′) instantly and accurately.
Conversion Formula
c′ = nrad × 6.366197724e-6
About Nanoradians
A nanoradian (nrad) is one billionth of a radian (10⁻⁹ rad), the smallest angle unit in regular scientific use. LIGO and Virgo gravitational-wave observatories maintain mirror tilts to sub-nanoradian stability - a 1 nrad tilt on a 4 km mirror shifts the reflected beam by 4 nm. Earth-tidal deformation deflects the local plumb line by roughly 50 nrad over a full tidal cycle, measurable with superconducting gravimeters and ring-laser gyroscopes. Synchrotron X-ray beamline mirrors are steered to single-digit nanoradians by piezo actuators. 1 nrad = 10⁻⁹ rad ≈ 0.206 µas.
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.
Quick Reference Table
| Nanoradians (nrad) | Centesimal Minutes (c′) |
|---|---|
| 1 nrad | 6.366 × 10-6 c′ |
| 2 nrad | 1.273 × 10-5 c′ |
| 5 nrad | 3.183 × 10-5 c′ |
| 10 nrad | 6.366 × 10-5 c′ |
| 25 nrad | 0.000159155 c′ |
| 50 nrad | 0.00031831 c′ |
| 100 nrad | 0.00063662 c′ |