Convert Semicircles to Binary Degrees

Convert Semicircles (sc) to Binary Degrees (brad) instantly and accurately.

Conversion Formula

brad = sc × 128

About Semicircles

A semicircle equals 1/2 of a full circle - exactly π rad = 180°. GPS and GLONASS transmit satellite orbital elements with latitude and longitude in semicircles, maximising angular resolution within 32-bit signed integers: ±2³¹ units span ±π rad with ~1.46 × 10⁻⁹ rad resolution per unit. Euler's identity e^(iπ) + 1 = 0 encodes exactly 1 semicircle of rotation in the complex plane, mapping 1 to -1 - often called the most beautiful equation in mathematics. 1 semicircle = π rad = 180° = 200 grad = 3,200 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

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