Convert Binary Degrees to Turns
Convert Binary Degrees (brad) to Turns (rev) instantly and accurately.
Conversion Formula
rev = brad × 0.00390625
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 Turns
A turn (revolution, cycle) equals one complete rotation - 2π rad = 360° = 400 grad. Rotational speed is naturally measured in turns per minute (rpm): a car engine idles at ~750 rpm; a hard disk spins at 7,200 rpm. The factor 2π in physics formulas (ω = 2πf, E = hf = ħω) arises from converting turns to radians. The turn is the natural unit for gear ratios, transformer winding counts, and thread pitch (turns per inch). The tau convention (τ = 2π ≈ 6.2832) proposes 1τ = 1 full turn. 1 rpm = 1/60 Hz = 2π/60 rad/s ≈ 0.10472 rad/s.
Quick Reference Table
| Binary Degrees (brad) | Turns (rev) |
|---|---|
| 1 brad | 0.00390625 rev |
| 2 brad | 0.0078125 rev |
| 5 brad | 0.0195313 rev |
| 10 brad | 0.0390625 rev |
| 25 brad | 0.0976563 rev |
| 50 brad | 0.195313 rev |
| 100 brad | 0.390625 rev |