BallistaRanging with a Reticle: The Mil-Relation Formula and What a Misread Costs
The mil-relation formula in MIL and MOA, how far off a 0.1 mil misread or a wrong target size puts your range at 300 to 800 yards, and how many inches that error moves the impact on an 18-inch plate.
An 18-inch plate at 800 yards is 0.625 mil tall in the reticle. Misread it by one tenth of a mil and the mil-relation formula puts the plate at 690 or 952 yards. Dial the 6.5 Creedmoor for either number and the bullet misses the plate by 37 or 58 inches. The formula is exact. The reading is what breaks, and it breaks faster than linearly with distance.
The mil-relation formula
A milliradian is one thousandth of the distance. One mil is 36 inches at 1,000 yards, 3.6 inches at 100. Turn that around and you have range from size and angle:
range in yards = target size in inches × 27.78 ÷ size in mils
The 27.78 is 1,000 ÷ 36. With an MOA reticle the same idea uses 1.047 inches per MOA at 100 yards:
range in yards = target size in inches × 95.5 ÷ size in MOA
The 95.5 is 100 ÷ 1.047. If your reticle is graduated in inches per hundred yards (shooter’s MOA), use 100. In metric, a size in meters × 1,000 ÷ mils gives meters directly.
Example: the 18-inch plate reads 0.83 mil. 18 × 27.78 ÷ 0.83 = 602 yd. On an MOA reticle the same plate at 600 yd reads 2.87 MOA, and a quarter-MOA misread gives 552 or 657 yd. A quarter MOA is 0.073 mil, so it behaves a little better than a 0.1 mil misread, nothing more.
A tenth of a mil at every range
The reading shrinks in proportion to range, but your ability to read it doesn’t. A 0.1 mil misread is 6% of the reading at 300 yd and 16% at 800 yd. The range error grows roughly with the square of the distance.
| True range, yd | Reading, mil | Read 0.1 high: range, yd | Elevation error, mil | Miss, in | Read 0.1 low: range, yd | Elevation error, mil | Miss, in |
|---|---|---|---|---|---|---|---|
| 300 | 1.67 | 283 | -0.13 | -1 | 319 | 0.15 | 2 |
| 400 | 1.25 | 370 | -0.25 | -4 | 435 | 0.30 | 4 |
| 500 | 1.00 | 455 | -0.42 | -8 | 556 | 0.53 | 10 |
| 600 | 0.83 | 536 | -0.64 | -14 | 682 | 0.87 | 19 |
| 700 | 0.71 | 614 | -0.93 | -23 | 814 | 1.34 | 34 |
| 800 | 0.63 | 690 | -1.29 | -37 | 952 | 2.00 | 58 |
Two things stand out.
The error is lopsided. Reading the plate too small (low) pushes the estimate farther than reading it too large pulls it closer. At 800 yd the low reading costs 152 yd and the high reading 110 yd. Dividing by a smaller number does that.
Past about 460 to 490 yd a single tenth misses the plate. The chart shows the miss from a 0.1 mil error for both rifles against the edge of the plate, 9 in from center.
The .308 suffers sooner because its trajectory is more curved. The same range error needs more elevation change, so it turns into more inches at the target. The 6.5’s flatter path forgives a bit more, but not enough to make reticle ranging reliable at 800.
The target’s size is the other half of the formula
A perfect reading of the wrong size gives the wrong range by the same percentage. Call a 20-inch plate 18 inches and every estimate is 10% short. Call a 16-inch plate 18 and every estimate is 12.5% long.
| True range, yd | Plate is 20 in: range, yd | 6.5 miss, in | .308 miss, in | Plate is 16 in: range, yd | 6.5 miss, in | .308 miss, in |
|---|---|---|---|---|---|---|
| 300 | 270 | -2 | -3 | 338 | 3 | 4 |
| 400 | 360 | -5 | -6 | 450 | 6 | 8 |
| 500 | 450 | -8 | -10 | 562 | 11 | 14 |
| 600 | 540 | -13 | -17 | 675 | 17 | 23 |
| 700 | 630 | -19 | -26 | 788 | 26 | 36 |
| 800 | 720 | -27 | -38 | 900 | 37 | 54 |
That error grows with range in the same way, and it doesn’t depend on how steady your reticle reading is. Known-size steel helps. Game animals and natural objects vary in size, so ranging them with a reticle carries a size error you can’t measure in the field.
Making the reading better
The cure for a small angle is a bigger target. Read the same 800 yd distance off a 36-inch object and the reading is 1.25 mil; a 0.1 mil low reading then gives 870 yd instead of 952. Halving the fraction you can misread roughly halves the range error.
The rest is technique:
- Measure the largest known dimension. A bigger object is a bigger reading, so the same misread is a smaller fraction of it.
- Use the highest power and the finest marks. On a second focal plane scope, read only at the power the marks are true at; any other power changes the reading. The reticle holds article shows how much.
- Read several times and average. Brace the rifle, read top to bottom, then bottom to top. If the readings disagree by more than 0.1 mil, the range estimate isn’t good to better than the table above shows.
- Bracket instead of trusting one number. Work out the range for your reading ±0.1 mil. If the elevation for those two ranges differs by more than your target allows, use a laser rangefinder or expect to correct off the first impact.
A short routine
- Know the target size in inches. If you’re guessing it, the range is a guess too.
- Read the target in mils at the reticle’s true power. Write the reading down.
- Range = size × 27.78 ÷ mils (or × 95.5 ÷ MOA).
- Also work the range for the reading ±0.1 mil. Past about 460 yd on an 18-inch target, expect the bracket to be wider than the plate allows.
- Dial for the center estimate, watch the impact, and correct from it.
Sources
- Pure geometry: 1 mil = 3.6 in at 100 yd and 36 in at 1,000 yd; 1 MOA = 1.047 in at 100 yd. The mil-relation constants 27.78 and 95.5 follow from these.
- Every elevation and miss in this article: Ballista engine (BallistaCore point-mass solver), inputs in the box above. Misses are the difference between the elevation for the estimated range and for the true range, applied at the true range. See how we compute.