Convert Nanoradians to Degrees
Convert Nanoradians (nrad) to Degrees (°) instantly and accurately.
Conversion Formula
° = nrad × 5.729577951e-8
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 Degrees
The degree (°) is the most widely used angle unit in everyday life, tracing to Babylonian astronomy ~300 BCE - the ecliptic was divided into 360 parts because the sexagesimal base-60 system made 360 highly divisible (by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20). Each degree divides into 60 arcminutes and 3,600 arcseconds. The degree dominates practical work: compass bearings, geographic coordinates (latitude ±90°, longitude ±180°), wind direction, polygon angles, and engineering drawings. Calculus uses radians because sin(x) ≈ x only holds in radians. 1° = π/180 rad ≈ 17.453 mrad.
Quick Reference Table
| Nanoradians (nrad) | Degrees (°) |
|---|---|
| 1 nrad | 5.73 × 10-8 ° |
| 2 nrad | 1.146 × 10-7 ° |
| 5 nrad | 2.865 × 10-7 ° |
| 10 nrad | 5.73 × 10-7 ° |
| 25 nrad | 1.432 × 10-6 ° |
| 50 nrad | 2.865 × 10-6 ° |
| 100 nrad | 5.73 × 10-6 ° |