Scope adjustment is angular. The turret does not move your point of impact by a distance; it moves the line of sight by an angle, and the distance that angle covers grows with range. Two units are in common use.
The exact definitions
Milliradian (mrad, “mil”). One thousandth of a radian, exactly. There are 2π × 1000 ≈ 6283.19 mrad in a circle.
Minute of angle (MOA). One sixtieth of a degree, i.e. π / 10800 radian exactly. There are 21600 MOA in a circle.
From those:
| at 100 m | at 100 yd | |
|---|---|---|
| 1 mrad | 10.0 cm | 10.94 cm (3.6 in) |
| 1 MOA | 2.909 cm | 2.66 cm (1.047 in) |
And the conversion between them: 1 mrad = 3.4377 MOA, 1 MOA = 0.29089 mrad.
The two shortcuts that are wrong
- “1 MOA = 1 inch at 100 yards.” It is 1.047 inch — 4.7 % low. At 1000 yards, dialling 10 MOA moves you 104.7 inches, not 100. Nearly five inches of unaccounted error. The industry sometimes calls the rounded version “IPHY” or “shooter’s MOA” and some scopes are actually built to it; if yours is, that is a different unit, not a rounding of this one.
- “1 mrad = 3.6 inch at 100 yards, so 1 MOA = 3 cm at 100 m.” The mrad figure is right (it is exact by the definition of the yard); the MOA one is not. 1 MOA is 2.909 cm at 100 m, and the 3 % error is why people find their “MOA in centimetres” arithmetic drifting at distance.
The milliradian’s appeal in a metric system is that it needs no conversion at all: 1 mrad = 10 cm at 100 m, 20 cm at 200 m, 65 cm at 650 m. The “0.1 mrad = 1 cm at 100 m” click is a decimal system that composes cleanly with metric range estimation. This is why it is standard across European and military optics.
Clicks, and the residual
Turrets move in discrete steps. Common values:
| Click | In its own unit | At 100 m | At 300 m |
|---|---|---|---|
| 1/8 MOA | 0.125 MOA | 3.6 mm | 10.9 mm |
| 1/4 MOA | 0.25 MOA | 7.3 mm | 21.8 mm |
| 1/2 MOA | 0.5 MOA | 14.5 mm | 43.6 mm |
| 0.05 mrad | 0.05 mrad | 5 mm | 15 mm |
| 0.1 mrad | 0.1 mrad | 10 mm | 30 mm |
Because you can only dial whole clicks, the correct correction is almost never exactly dialable. Suppose you need 2.63 mrad at 300 m on a 0.1 mrad turret. Twenty-six clicks give 2.60 mrad — 0.03 mrad short, which at 300 m is 0.9 cm of impact low.
This is not an error in the solution; it is a property of the hardware, and it is worth knowing because it tells you when a finer turret would actually change anything. The rounding must be done in click space — round the number of clicks, then convert back — and never by rounding centimetres and hoping. The calculator does exactly this and prints the leftover as a linear distance at the target, which is the form you can compare against your group size.
Notice from the table that at 300 m a 1/2 MOA click is already coarser than 4 cm. If your groups are 5 cm at that distance, half of your adjustment resolution is being spent on the turret. Conversely, a 0.05 mrad or 1/8 MOA turret has resolution far below any practical field group at 100 m — its value is at 800 m and beyond, and in the patience it demands of you when you count 60 clicks.
Which should you pick?
There is no ballistic advantage to either. Pick the one your reticle is in, so that a hold you measure in the glass converts to a dial with no arithmetic — a mrad reticle with an MOA turret is a needless conversion under time pressure. Then pick the one your shooting partners use, so calls can be shouted rather than translated.