How this instrument works
A minute of angle (MOA) is a unit of angular measure: one-sixtieth of a degree, or about 0.0002909 radians. A rifle scope's turret does not move the barrel — it tilts the sight picture by a set angle, and that fixed angle opens into a wider physical gap the farther downrange you look, the same way a laser dot spreads as it travels from a steady hand. This calculator turns that fixed angle into a linear distance in inches for whatever range you choose.
The constant 1.047 is not a rounding convenience; it falls out of the trigonometry. One MOA in radians, times 36 inches per yard, times a 100-yard reference distance, works out to 1.0472 inches — the true circular subtension the geometry demands. Optics makers who instead calibrate turrets and reticles to move exactly 1.000 inch per 100 yards are selling a different, simplified unit, sometimes called Shooter's MOA or IPHY (inches per hundred yards): close enough at short range to get confused with true MOA constantly, and different enough at long range that mixing the two throws holdovers off by more than a click.
Because the relationship is linear in range, the same MOA value opens to a larger physical gap every hundred yards: 1.047 inches at 100 yards becomes 5.235 inches at 500 and 10.47 inches at 1000. The formula assumes a flat, static line of sight — it says nothing about bullet drop, wind drift, or the curved path a fired round actually follows. It converts an angle to a length at a distance; working out how much elevation a shot needs against gravity and wind is a separate ballistic problem this instrument does not attempt.
- Enter the angular correction in MOA adjustment — the number of minutes you want to convert, such as a scope's total elevation correction.
- Enter the range to the target in Distance, yards — the distance at which you want to know the physical size of that adjustment.
- Read Adjustment size, inches — the linear gap that many minutes of angle opens at the chosen distance.
- To check a different range, change only Distance, yards; the MOA value stays fixed while the inch reading scales with it.
Worked example — one MOA at 100 yards
Set MOA adjustment to 1 and Distance, yards to 100 — the reference point scope makers build their click values around. The formula gives 1 × 1.047 × (100 ⁄ 100) = 1.047, so Adjustment size, inches reads 1.047 inches: the true, trigonometrically exact size of one minute of angle at the range most riflescopes are zeroed and tested at.
The figure matters because turrets are usually marked in quarter-minute clicks, four per full minute. At 100 yards, four clicks move point of impact 4 × 0.25 × 1.047 = 1.047 inches, matching the example above exactly. Shooters often round this to 'one click, one quarter inch, per hundred yards' — a shortcut about 4.5 percent smaller than the true figure, a gap that stays trivial at close range but grows into real inches once distance or click count climbs.
Questions
Why is one MOA equal to 1.047 inches instead of exactly one inch at 100 yards?
Because MOA is a true angular unit — one-sixtieth of a degree — and the inch figure comes from trigonometry, not a round number. Converting one arcminute (π⁄10800 radians) into a linear distance at 100 yards (3600 inches) gives 1.0472 inches, which this calculator rounds to 1.047. Turrets sold as a flat 1.000 inch per 100 yards use a different, simplified unit, not true MOA.
What is the difference between true MOA and Shooter's MOA (SMOA)?
True MOA is the trigonometric angle, 1.047 inches per 100 yards; Shooter's MOA, also called SMOA or IPHY, is rounded down to exactly 1.000 inch per 100 yards to simplify field math. The gap between them grows with range — about a quarter inch by 500 yards and just under half an inch by 1000 — enough to matter when a true-MOA scope is read with SMOA arithmetic at distance.
How many inches does 1 MOA cover at 500 and 1000 yards?
1.047 inches scales linearly with distance: multiply by the range in hundreds of yards. At 500 yards, 1 MOA spans 5.235 inches; at 1000 yards it spans 10.47 inches. Enter either range with an MOA value of 1 in this calculator to see the same figures directly, or scale any other MOA value the same way.
How far does a quarter-MOA scope click move the point of impact at 100 yards?
About 0.262 inch — a quarter of the 1.047-inch true-MOA figure, not a flat quarter inch. Four such clicks move impact 1.047 inches, a full minute of angle. Most turrets are marked in these quarter-minute increments, so this calculator's inch output divided by four gives what a single click is worth at that distance.
Does this formula work for metric distances in meters?
No — the 1.047 constant is tied to yards and inches by its derivation (36 inches per yard, a 100-yard reference). For metric ranges, a mil-based figure fits better: one milliradian subtends roughly 1 centimeter at 100 meters, a metric-native angular unit that needs no rounded conversion constant.
Why do rifle scopes use minutes of angle instead of whole degrees?
A degree is too coarse for aiming corrections — one degree at 100 yards spans nearly 63 inches, far wider than any practical adjustment. A minute of angle, one-sixtieth of a degree, scales down to about an inch at 100 yards, a size that matches typical group sizes and turret mechanics, which is why MOA became a standard angular unit in shooting long before milliradians gained ground.