Convert Gradians to Milliradians
Convert Gradians (grad) to Milliradians (mrad) instantly and accurately.
Conversion Formula
mrad = grad × 15.70796327
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 Milliradians
A milliradian (mrad) is one thousandth of a radian (10⁻³ rad ≈ 0.05730°). The MIL-dot reticle system in precision rifle scopes uses milliradians for its elegant property: at range R metres, 1 mrad subtends exactly R mm - so at 300 m, 1 mrad = 300 mm; at 1,000 m, 1 mrad = 1,000 mm = 1 m. Semiconductor laser slow-axis divergence is typically 5-15 mrad. Note: 1 mrad ≠ 1 NATO mil (which is π/3,200 rad ≈ 0.9817 mrad). 1 mrad ≈ 0.05730° ≈ 3.438′ ≈ 206.3″.
Quick Reference Table
| Gradians (grad) | Milliradians (mrad) |
|---|---|
| 1 grad | 15.708 mrad |
| 2 grad | 31.4159 mrad |
| 5 grad | 78.5398 mrad |
| 10 grad | 157.08 mrad |
| 25 grad | 392.699 mrad |
| 50 grad | 785.398 mrad |
| 100 grad | 1570.8 mrad |