Convert Gradians to Binary Degrees
Convert Gradians (grad) to Binary Degrees (brad) instantly and accurately.
Conversion Formula
brad = grad × 0.64
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.
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
| Gradians (grad) | Binary Degrees (brad) |
|---|---|
| 1 grad | 0.64 brad |
| 2 grad | 1.28 brad |
| 5 grad | 3.2 brad |
| 10 grad | 6.4 brad |
| 25 grad | 16 brad |
| 50 grad | 32 brad |
| 100 grad | 64 brad |