Convert Milliradians to Turns
Convert Milliradians (mrad) to Turns (rev) instantly and accurately.
Conversion Formula
rev = mrad × 0.0001591549431
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″.
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
| Milliradians (mrad) | Turns (rev) |
|---|---|
| 1 mrad | 0.000159155 rev |
| 2 mrad | 0.00031831 rev |
| 5 mrad | 0.000795775 rev |
| 10 mrad | 0.00159155 rev |
| 25 mrad | 0.00397887 rev |
| 50 mrad | 0.00795775 rev |
| 100 mrad | 0.0159155 rev |