Convert Signs to Binary Degrees
Convert Signs (sign) to Binary Degrees (brad) instantly and accurately.
Conversion Formula
brad = sign × 21.33333333
About Signs
An astrological sign equals 1/12 of a full circle - π/6 rad = exactly 30°. The zodiac divides the ecliptic into twelve 30° signs (Aries through Pisces), originating in Babylonian astronomy ~5th century BCE. Historical ecliptic longitude was expressed as sign + degrees: "Scorpio 12°" = 222°. The 30° spacing also appears in music theory: the circle of fifths has twelve equally spaced positions 30° apart, and the octave divides into 12 equal semitones. 1 sign = 30° = 1,800′ = π/6 rad = 533.3 NATO mils.
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
| Signs (sign) | Binary Degrees (brad) |
|---|---|
| 1 sign | 21.3333 brad |
| 2 sign | 42.6667 brad |
| 5 sign | 106.667 brad |
| 10 sign | 213.333 brad |
| 25 sign | 533.333 brad |
| 50 sign | 1066.67 brad |
| 100 sign | 2133.33 brad |