Convert Nanoradians to Arcminutes
Convert Nanoradians (nrad) to Arcminutes (′) instantly and accurately.
Conversion Formula
′ = nrad × 3.437746771e-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 Arcminutes
An arcminute (′) is 1/60 of a degree - π/10,800 rad ≈ 2.909 × 10⁻⁴ rad. One arcminute of latitude equals exactly one nautical mile (1,852 m), which is the origin of the nautical mile unit. The Moon and Sun both subtend ~30 arcminutes in apparent diameter - the coincidence exploited in total solar eclipses. Human 20/20 visual acuity resolves letters 5 arcminutes tall at 6 m. Binocular and telescope apparent fields of view are quoted in arcminutes. 1′ = π/10,800 rad ≈ 0.01667° ≈ 290.9 µrad.
Quick Reference Table
| Nanoradians (nrad) | Arcminutes (′) |
|---|---|
| 1 nrad | 3.438 × 10-6 ′ |
| 2 nrad | 6.875 × 10-6 ′ |
| 5 nrad | 1.719 × 10-5 ′ |
| 10 nrad | 3.438 × 10-5 ′ |
| 25 nrad | 8.594 × 10-5 ′ |
| 50 nrad | 0.000171887 ′ |
| 100 nrad | 0.000343775 ′ |