Convert Nanoradians to Binary Degrees
Convert Nanoradians (nrad) to Binary Degrees (brad) instantly and accurately.
Conversion Formula
brad = nrad × 4.074366543e-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 Binary Degrees
A binary degree (brad) divides the full circle into 256 equal parts - π/128 rad ≈ 0.024544 rad (= 1.40625°). The 256-part circle maps perfectly onto an 8-bit byte, making binary degrees ideal for memory-constrained embedded systems: headings stored in a single byte (0-255) need no floating-point arithmetic. Game engines, CNC machine controllers, and digital servo systems use this representation. 16-bit BAM (65,536 per circle) gives ~0.005° (≈ 89 µrad) per unit for precision heading systems. 1 brad = 1.40625° = 84.375′.
Quick Reference Table
| Nanoradians (nrad) | Binary Degrees (brad) |
|---|---|
| 1 nrad | 4.074 × 10-8 brad |
| 2 nrad | 8.149 × 10-8 brad |
| 5 nrad | 2.037 × 10-7 brad |
| 10 nrad | 4.074 × 10-7 brad |
| 25 nrad | 1.019 × 10-6 brad |
| 50 nrad | 2.037 × 10-6 brad |
| 100 nrad | 4.074 × 10-6 brad |