Convert Binary Degrees to Gradians
Convert Binary Degrees (brad) to Gradians (grad) instantly and accurately.
Conversion Formula
grad = brad × 1.5625
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 Gradians
A gradian (grad), also called a gon (ISO 31/DIN), equals 1/400 of a full circle - π/200 rad = 0.9°. Its main advantage: a right angle = exactly 100 grad, simplifying complementary and supplementary angle arithmetic. Introduced during the French Revolution as part of decimal angle reform. Surveying in France, the Netherlands, Switzerland, and Scandinavia uses gradians; professional total stations display both degrees and gons. A 1% slope ≈ 0.6366 grad. 1 grad = 0.9° = 54′ = π/200 rad; 400 grad = 360° = one full circle.
Quick Reference Table
| Binary Degrees (brad) | Gradians (grad) |
|---|---|
| 1 brad | 1.5625 grad |
| 2 brad | 3.125 grad |
| 5 brad | 7.8125 grad |
| 10 brad | 15.625 grad |
| 25 brad | 39.0625 grad |
| 50 brad | 78.125 grad |
| 100 brad | 156.25 grad |