Why scopes measure in angles, not inches
A scope turret moves the reticle by an angle, not a distance. That is the only sensible design, because the same turret has to work at every range: an angular correction automatically scales with distance, so one setting fixes the zero at 100 yards and at 600 yards alike. The inches you measure on a target are the consequence of that angle acting over a distance, and converting between the two is the whole job of this page.
A minute of angle is 1/60 of a degree, or 2.90888 × 10−4 radians. Multiply by the 3,600 inches in 100 yards and you get 1.04720 inches, which is what one MOA actually subtends at 100 yards. The rounding of that to a flat inch is so common that it has its own name, inch per hundred yards or shooter's MOA, and it is what most people mean when they say "a one-MOA rifle". The two differ by 4.72%, which is invisible at 100 yards and amounts to nearly half an inch at 1,000.
A milliradian is a thousandth of a radian, and it is cleaner in every respect. At 100 yards it subtends exactly 3.6 inches, because 3,600 inches divided by 1,000 is 3.6 by definition. At 100 metres it subtends exactly 10 centimetres. There is nothing to round and no competing convention. One mil equals 3.43775 MOA, which is the ratio 0.001 / 2.90888 × 10−4.
Neither unit is more precise than the other on the rifle. What matters is that your reticle and your turrets use the same unit, so that a correction you read off the reticle can be dialled without conversion. Mixing a mil reticle with MOA turrets is the classic setup error and produces corrections that are wrong by a factor of 3.44.
From a measured group to a number of clicks
Three steps, and only the first involves the target. Measure the offset from your point of aim to the centre of the group, separately in the vertical and horizontal axes, and record the sign: high and right are positive here, low and left are negative.
Convert to angle. Divide by the subtension at that distance. One MOA subtends 1.04720 × yards/100 inches, so at 300 yards it is 3.1416 inches, which is a coincidence worth remembering because it is very nearly π. A 6-inch offset at 300 yards is therefore 6 / 3.1416 = 1.910 MOA. For mils, divide by 3.6 × yards/100 instead.
Divide by the click value and round. With quarter-MOA turrets, 1.910 / 0.25 = 7.64 clicks, so you dial 8 and accept 0.09 MOA of residual, about a quarter of an inch at 300 yards. Tenth-mil turrets are finer at 0.36 inches per click at 100 yards against 0.262 inches for a quarter-MOA click, so mil dials give slightly coarser steps in linear terms, not finer.
The correction opposes the error. If the group is high you dial down; if it is right you dial left. Scope turrets are marked with the direction the impact moves, so a turret marked UP moves the group up, which is what you want when the group prints low. The calculator reports elevation as positive for up and windage as positive for right, and spells the direction out in words to remove the ambiguity.
The metric shortcut is worth knowing: at 100 metres, one mil is 10 centimetres and one tenth-mil click is one centimetre. A group 7 cm low at 100 m needs 7 clicks up on a 0.1 mil turret, with no arithmetic at all.
Worked example: zeroing a rifle at 100 yards
You fire a five-shot group at 100 yards. The centre of the group sits 3 inches above and 1.5 inches to the right of your aiming point, and the extreme spread of the group is 1 inch. The scope has quarter-MOA turrets.
- Subtension at 100 yards. One MOA = 1.04720 × 100/100 = 1.0472 in. One mil = 3.6 × 100/100 = 3.600 in.
- Elevation in MOA. The group is 3 in high, so the correction is downward: −3 / 1.0472 = −2.865 MOA. In mils that is −3 / 3.6 = −0.833 mil.
- Elevation clicks. −2.865 / 0.25 = −11.46, which rounds to 11 clicks DOWN. The residual is 0.46 of a click, about 0.12 in at this distance.
- Windage in MOA. The group is 1.5 in right, so the correction is leftward: −1.5 / 1.0472 = −1.432 MOA.
- Windage clicks. −1.432 / 0.25 = −5.73, which rounds to 6 clicks LEFT.
- Group size in angular terms. 1.0 in / 1.0472 = 0.955 MOA, so this is a sub-MOA group — but only just, and a single five-shot group is a weak estimate of a rifle's real dispersion.
Under the shooter's MOA convention the same 3-inch offset would be exactly 3.000 MOA and would call for 12 clicks rather than 11. On a scope whose turrets are actually graduated in true MOA, dialling those 12 clicks overcorrects by about 0.14 inches at 100 yards, which is harmless. At 800 yards the same convention error is over an inch, which is not.
Reading group size in MOA, and when not to trust it
Dividing group size by subtension converts a linear measurement into an angular one, which is the only way to compare groups fired at different distances. A 2-inch group at 200 yards and a 1-inch group at 100 yards are both 0.955 MOA, and describe the same rifle performance.
Treat a single group's MOA figure with suspicion. Extreme spread — the distance between the two widest shots — is a biased estimator that grows with the number of shots fired, so a three-shot group will almost always measure smaller than a ten-shot group from the same rifle. Comparing a three-shot group against someone else's ten-shot group is meaningless. If you want a defensible number, fire several groups of the same shot count and average them, or use mean radius, which does not grow with sample size in the same way.
Turret tracking is worth verifying before you trust any click count. Shoot a tall-target test: aim at a mark, fire, dial a known number of MOA up, fire again, and measure. If 20 MOA of dialled elevation moves the group 19 inches at 100 yards rather than 20.9, your turret is tracking 9% low and every long-range correction you make will be short. Scopes with mis-scaled adjustments are not rare and the error compounds with distance.
Once the rifle is zeroed, the holdover you need at distance comes from the trajectory, not from the target. The bullet drop calculator produces the required correction in MOA and mils at any range, and this page converts that correction into clicks for your specific turret.
MOA and mil subtension at common distances
| Distance (yd) | 1 MOA (in) | 1 MOA (cm) | 1 mil (in) | 1 mil (cm) | 0.25 MOA click (in) | 0.1 mil click (in) |
|---|---|---|---|---|---|---|
| 100 | 1.047 | 2.66 | 3.600 | 9.14 | 0.262 | 0.360 |
| 200 | 2.094 | 5.32 | 7.200 | 18.29 | 0.524 | 0.720 |
| 300 | 3.142 | 7.98 | 10.800 | 27.43 | 0.785 | 1.080 |
| 400 | 4.189 | 10.64 | 14.400 | 36.58 | 1.047 | 1.440 |
| 500 | 5.236 | 13.30 | 18.000 | 45.72 | 1.309 | 1.800 |
| 600 | 6.283 | 15.96 | 21.600 | 54.86 | 1.571 | 2.160 |
| 800 | 8.378 | 21.28 | 28.800 | 73.15 | 2.094 | 2.880 |
| 1,000 | 10.472 | 26.60 | 36.000 | 91.44 | 2.618 | 3.600 |
At 100 metres one mil is exactly 10 cm and one 0.1 mil click is exactly 1 cm, which is why metric shooters rarely need a calculator at all.
Mistakes that leave a rifle unzeroed
- Dialling the wrong way. Turret markings describe where the impact moves, not where the reticle moves. Group high means dial DOWN.
- Mixing a mil reticle with MOA turrets. A hold read in mils and dialled in MOA is wrong by a factor of 3.44. Match the units on reticle and turret.
- Correcting off one three-shot group. If the offset is smaller than half the group size, you are chasing dispersion rather than a zero. Shoot more before you dial.
- Assuming quarter-MOA turrets are exactly quarter-MOA. Verify with a tall-target test. Tracking errors of several percent exist and multiply with distance.
- Guessing the range. Every conversion on this page is proportional to distance, so believing you are at 100 yards when you are at 110 puts every correction 10% out.
- Using shooter's MOA on a true-MOA scope. The 4.72% difference is invisible at 100 yards and matters past 500.
- Forgetting to reset the turret. After a zeroing session, re-index the turret to zero so field corrections start from a known reference.
MOA, mils and the rest of the shooting workflow
Angular measurement links every part of precision shooting. The reticle measures targets in the same units the turrets adjust in, which is what makes range estimation by reticle possible: an object of known height that subtends a known number of mils is at a computable distance. That relationship — distance = size / angle — is the same proportionality this calculator inverts.
Downstream, the correction you dial should come from a trajectory solution rather than trial and error past your zero. The bullet drop and trajectory calculator integrates the drag equation to give path and holdover at any range, in both MOA and mils, ready to divide by your click value here. Upstream, the terminal side of the same shot is quantified by the muzzle energy and momentum calculator, which converts retained velocity into energy, momentum and power factor.
A last word on conventions. Scope manufacturers overwhelmingly graduate in true MOA or in true mils, and the inch-per-hundred convention survives mainly in casual conversation about group size. Using it to describe a rifle's accuracy is harmless. Using it to compute a 900-yard elevation correction is not, and the option on this page exists so you can see exactly how much the two differ before you choose one.