Convert Milliarcseconds to Binary Degrees
Convert Milliarcseconds (mas) to Binary Degrees (brad) instantly and accurately.
Conversion Formula
brad = mas × 1.975308642e-7
About Milliarcseconds
A milliarcsecond (mas) is one thousandth of an arcsecond - approximately 4.848 × 10⁻⁹ rad. It is the standard unit of precision astrometry. The ESA Hipparcos satellite measured stellar positions to ~1 mas; its successor Gaia achieves 7-100 µas for bright stars. A parallax of 1 mas corresponds to a distance of 1 kiloparsec (3,260 light-years). Very Long Baseline Interferometry (VLBI) resolves well below 1 mas, imaging structures around supermassive black holes. 1 mas = 10⁻³ arcseconds ≈ 4.848 × 10⁻⁹ rad.
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
| Milliarcseconds (mas) | Binary Degrees (brad) |
|---|---|
| 1 mas | 1.975 × 10-7 brad |
| 2 mas | 3.951 × 10-7 brad |
| 5 mas | 9.877 × 10-7 brad |
| 10 mas | 1.975 × 10-6 brad |
| 25 mas | 4.938 × 10-6 brad |
| 50 mas | 9.877 × 10-6 brad |
| 100 mas | 1.975 × 10-5 brad |