Convert Microradians to Binary Degrees
Convert Microradians (µrad) to Binary Degrees (brad) instantly and accurately.
Conversion Formula
brad = µrad × 4.074366543e-5
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.
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
| Microradians (µrad) | Binary Degrees (brad) |
|---|---|
| 1 µrad | 4.074 × 10-5 brad |
| 2 µrad | 8.149 × 10-5 brad |
| 5 µrad | 0.000203718 brad |
| 10 µrad | 0.000407437 brad |
| 25 µrad | 0.00101859 brad |
| 50 µrad | 0.00203718 brad |
| 100 µrad | 0.00407437 brad |