Is one MOA one inch at 100 yards?

Where the number comes from

A minute is an angle, not a length.

One minute of angle is one sixtieth of a degree. An angle covers more ground the further it travels, so a MOA is not a fixed number of inches: it is 0.262 inches at 25 yards and 10.47 inches at a thousand.

At a hundred yards the arithmetic is 3600 inches of distance times the tangent of half a minute, doubled, which comes to 1.04720 inches. There is a pleasant accident hiding in that figure: it is π/3 to seven decimal places, because 3600 inches multiplied by π/10800 radians is exactly one third of π. Nothing follows from it. It is just easier to remember as a third of pi than as 1.047.

Rounded to three decimals. A true MOA at any distance is 1.04720 inches times the range in hundreds of yards.

The part that gets written down backwards

The rounded inch makes your rifle look worse.

This is the half everyone gets the wrong way round, including us until recently. The instinct is that a target drawn too small flatters you. It does the opposite.

Your group's size is set by the rifle and the range, not by the paper. It is whatever it is before the sheet gets a say. So picture a grid whose squares are labeled "1 MOA" but drawn at the rounded inch, meaning each square is 4.5% smaller than a true minute. A rifle that genuinely shoots one MOA puts 1.047 inches on the paper. Counted in those undersized squares, that spans 1.05 of them, and you write down "1.05 MOA" for a rifle that shot 1.00.

Smaller squares mean more of them fit across the group, so the number comes out 4.7% larger than the truth, every time, in the same direction. A true 0.75 MOA group is recorded as 0.78. Check it against an absurd case if the sign still feels wrong: squares drawn at half an inch but labeled one MOA would report that same group as 2.09 MOA.

Two numbers live next to each other here and it is easy to attach the wrong one. The inch is 4.5% smaller than a minute. A group measured against it reads 4.7% larger than it is. Both are true; they are not the same statement.

Dialing inherits the same error with the same sign. Read a correction off an inch grid labeled in MOA and you will dial 4.7% more than the sight needs.

In fairness to the shortcut

When one inch is near enough.

Most of the time, honestly. Sighting in at 100 yards with a 4-inch gong, zeroing a hunting rifle, any correction under about three MOA: the rounding disappears inside the group and inside the click. Nobody has ever missed a deer because of 0.047 of an inch.

It starts to matter in three places. Past about 400 yards, where the error clears half an inch per MOA and keeps going. On any correction big enough that 4.7% of it exceeds one click of your turret. And in load development, where you write a number in a book and compare it against another number six months later, so a consistent bias never averages out and quietly ranks your loads in the wrong order.

The error nobody checks

Your printer is doing this too, and by more.

"Fit to page" is the default on most printers and it shrinks a letter sheet by about four percent without telling you. That is the same size of error as the MOA rounding, in the same direction, stacked on top of it, and you cannot see it by looking at the page.

It is also trivially detectable, which is why every sheet we draw carries a five-inch bar along the bottom. Lay a ruler on it once, before the first print of the day. If it reads 5.00 inches, every dimension on that page is real. If it does not, change one setting and print it again. A target that cannot be checked is an assertion; one with a ruler on it is a measurement.

Everything we make is drawn to true MOA — 89 sheets across seventeen disciplines, each one carrying the bar.