Hit probability
Enter a measured mean radius (or MOA equivalent) at the distance you shot, and see extrapolated hit probability across ranges and target sizes. Uses a 2D Gaussian (Rayleigh) dispersion model and assumes σ scales linearly with range. Doesn't model wind, MV SD, or BC uncertainty, so real long-range hit rates typically come in lower than shown, especially past ~600yd.
Measured group
= 0.500″ MR · 0.50 MOA
Hit probability Manual entry · 0.500″ MR at 100yd (0.50 MOA)
Assumes shooter dispersion is the dominant error source and scales linearly with range. Doesn't model wind, MV SD, or BC uncertainty — those matter more as distance grows, so real-world hit rates at long range will typically be lower than shown.
Swipe the table sideways for larger targets →
| Range | 0.5 MOA | 1 MOA | 2 MOA | 8" | 10" | IPSC A |
|---|---|---|---|---|---|---|
| 100 yd (measured) | 18% | 54% | 96% | ≥99% | ≥99% | ≥99% |
| 200 yd | 18% | 54% | 96% | ≥99% | ≥99% | ≥99% |
| 300 yd | 18% | 54% | 96% | ≥99% | ≥99% | 99% |
| 400 yd | 18% | 54% | 96% | 96% | 99% | 94% |
| 500 yd | 18% | 54% | 96% | 87% | 96% | 86% |
| 600 yd | 18% | 54% | 96% | 75% | 89% | 77% |
| 700 yd | 18% | 54% | 96% | 64% | 80% | 68% |
| 800 yd | 18% | 54% | 96% | 54% | 71% | 60% |
| 900 yd | 18% | 54% | 96% | 46% | 62% | 52% |
| 1000 yd | 18% | 54% | 96% | 40% | 54% | 46% |
| 1100 yd | 18% | 54% | 96% | 34% | 48% | 40% |
| 1200 yd | 18% | 54% | 96% | 29% | 42% | 35% |
Comparison
Tick the box to enter a second mean radius at the same observation distance and see its table below.
How the math works
- Mean radius to Rayleigh sigma
- σ = MR / √(π/2)
- Linear scaling with range
- σ(target range) = σ × (target / observation range)
- Circular target
- P(hit) = 1 − exp(−r² / (2σ²))
- Rectangular target
- P(hit) = erf(w/(σ√2)) × erf(h/(σ√2))
- MOA convention
- 1 MOA = 1″ per 100 yd (matches the rest of DOPE Book)
The "measured" row (highlighted) is the distance you actually shot at. Everything else is extrapolated: trust nearby rows more than distant ones.