Convert Binary Degrees to Arcseconds

Convert Binary Degrees (brad) to Arcseconds (″) instantly and accurately.

Conversion Formula

″ = brad × 5062.5

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′.

About Arcseconds

An arcsecond (″) is 1/3,600 of a degree - π/648,000 rad ≈ 4.848 × 10⁻⁶ rad. It is the fundamental resolution unit of classical astronomy and geodetic surveying. The Hubble Space Telescope delivers ~0.05″ resolution; atmospheric seeing at excellent sites gives 0.4-0.6″. Stellar parallax of Proxima Centauri is 0.7687″, defining its distance of 1.3009 parsecs. The parsec is defined as the distance at which 1 AU subtends exactly 1 arcsecond - giving 1 pc = 3.0857 × 10¹⁶ m. 1″ = π/648,000 rad ≈ 4.848 µrad.

Quick Reference Table

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