Every scope turret, every group size quoted on a range and every drop chart is written in angles rather than distances, and that is the one thing that makes the arithmetic confusing to newcomers. A minute of angle is a sixtieth of a degree. It does not have a size. It only acquires one when you name a distance, and then it grows in exact proportion to that distance. The MOA calculator above converts in both directions: an angle and a range give you inches and centimetres, and a measured figure off a target gives you the angle and the scope clicks it represents.
Arb Digital publishes free calculators that show their working rather than a single opaque figure, so this page also reports the same angle in milliradians, states the true-MOA and shooter's-MOA values side by side, and tells you how far apart those two conventions are at the range you entered. That last figure is small at short range and large at long range, and it is one of the most common quiet errors in the sport.
What This MOA Calculator Does
It implements the standard angular relations and nothing else. One minute of arc is one sixtieth of one degree, and the linear distance it covers at a range is found from the tangent of that angle. The Wikipedia article on the minute and second of arc gives the figure this page reproduces: one true MOA subtends 1.047 inches at 100 yards, which is where the familiar rounding to one inch comes from. The Wikipedia article on the milliradian gives the companion relation for mils, where a tenth of a mil is exactly one centimetre at a hundred metres and one mil is about 3.44 minutes of arc.
Alongside the headline subtension it converts your angle into all three conventions, converts a measured group or offset back into an angle, and divides that angle by the turret’s click value to give the number of clicks. The page publishes no velocity figures, no drop tables and no load data of any kind.
How to Use It
- Enter the range and its unit. Yards and metres both work and the page keeps them straight, but mixing a metre range with an inch measurement is the commonest way to get a wrong answer here, so check the two selectors agree with your data.
- Enter the angle you want converted. Choose true MOA, shooter's MOA or mils depending on which convention the figure came from. If you do not know which, the section below explains how to find out.
- Enter what you measured on the target. Extreme spread for a group, or centre-of-group to point-of-aim for a zeroing correction. Use the same unit as the rule you measured with.
- Enter the click value from the turret. Read it off the scope or the manual. A quarter MOA and a tenth of a mil are common but far from universal.
- Read the clicks figure as a whole number. Turrets move in discrete detents, so the tool gives the exact figure and the nearest whole click, and the difference between them is the residual you cannot dial out.
The Formula and How It Is Calculated
The exact relation is S = 2 × D × tan(θ ÷ 2), where S is the linear size, D is the distance and θ is the angle. For one true MOA the angle is one sixtieth of a degree, so at 100 yards, which is 3,600 inches, the subtension is 2 × 3600 × tan(1/120 of a degree) = 1.0472 inches. Everything else follows from that by proportion.
Work the default example through by hand. The range is 300 yards, which is 10,800 inches. One true MOA subtends 2 × 10800 × tan(0.0041667 degrees) = 3.1416 inches, or 7.98 centimetres. Shooter's MOA, defined as exactly one inch per hundred yards, would give 3.0000 inches at the same range, so the two conventions differ by 0.1416 inches there. The same angle expressed in mils is 1 ÷ 3.43775 = 0.2909 mils. The measured 1.5 inch figure at 300 yards works out at 1.5 ÷ 3.1416 = 0.4775 true MOA, and dividing that by a quarter-MOA click value gives 1.91 clicks, which rounds to two clicks on the turret with about 0.02 MOA left over in the other direction.
Converting the other way uses the inverse relation: θ = 2 × arctan(S ÷ (2 × D)). That is the calculation behind the measured-figure result. The page uses the exact tangent throughout rather than the small-angle approximation, which agrees to about one part in a hundred thousand at one MOA but drifts once you dial thirty or forty MOA of come-up.
True MOA Versus Shooter's MOA, and Why It Bites
This is the distinction the page exists to make explicit. True MOA is a real angle: one sixtieth of a degree, subtending 1.047 inches at 100 yards. Shooter's MOA, written SMOA or IPHY for inches per hundred yards, is a convenience convention in which one unit is defined as exactly one inch per hundred yards. The difference between them is 4.7 per cent, which is invisible at 100 yards and obvious at 1,000.
At 100 yards one of each differs by five hundredths of an inch, comfortably inside a bullet hole. At 1,000 yards the same one-unit difference is nearly half an inch, and since long-range elevation corrections routinely run to twenty or thirty units, the accumulated discrepancy reaches ten to fifteen inches. That is arithmetic, not the rifle.
The practical question is which convention your equipment uses. Almost all scopes with MOA turrets are calibrated in true MOA, and so are almost all published ballistic solvers; IPHY turrets exist and are usually labelled as such. The confusion rarely enters through the scope. It enters through mental arithmetic that treats one MOA as exactly one inch per hundred yards while reading a target, then feeds that number back into a true-MOA turret. Enter your figure under the right selector above and the page shows you both.
MOA and Mils Are Both Angles, and Neither Is More Accurate
Arguments about MOA against mils are usually arguments about arithmetic convenience rather than precision. One mil is 3.43775 MOA, so a tenth-mil click is a slightly coarser step than a quarter-MOA click — 0.344 MOA against 0.250. Neither system is inherently finer, and a scope's mechanical repeatability matters far more than the size of its detents ever will.
The one rule that matters is not to mix them. A spotter calling a correction in mils to a shooter dialling MOA produces an error of a factor of three and a half, which is a spectacular miss rather than a subtle one. If your reticle and your turrets use different units — a combination that used to be common on cheaper scopes — every hold you take off the reticle needs converting before it reaches the turret, and this page will do that conversion for you.
Turning a Measured Group Into Something Comparable
Group size in inches is only meaningful with a range attached, which is why groups are quoted in MOA. Converting is the easy part; measuring honestly is harder. Extreme spread is conventionally measured centre to centre between the two widest holes, and the usual shortcut is to measure outside to outside and subtract one bullet diameter.
The statistical caveat is real. A three-shot group is a very noisy estimate of a rifle’s dispersion, and extreme spread grows with the number of shots simply because more shots give more chances for an outlier. A five-shot and a ten-shot group from the same rifle and ammunition will not give the same MOA figure, and the ten-shot one will be larger. If you are comparing loads or rifles, keep the shot count constant and record it alongside the number.
The Part the Arithmetic Does Not Cover
This page is angular geometry, and geometry is a small part of what happens on a range. The standing safety framing applies and is worth stating once, plainly: every firearm is treated as loaded at all times, the muzzle stays pointed in a safe direction, the target and everything behind it are positively identified before the shot, and hearing and eye protection are worn. Ownership, transport and hunting are governed by law that varies enormously between jurisdictions, and that is a matter for the law where you are rather than for a calculator.
Nothing on this page can tell you that a rifle, a load or a zero is correct or safe. The Sporting Arms and Ammunition Manufacturers' Institute, which has published the industry's technical standards since 1926, and the manufacturer's own documentation are the authorities on chamber pressure, ammunition specification and what a given firearm is rated for. A gunsmith inspects a rifle. Current published manufacturer load data governs ammunition, and no website is a substitute for it. A web page converts angles.
Where This Sits Next to the Other Shooting Tools
The live angle converter handles unit-to-unit conversion between degrees, radians, gradians, arcminutes, arcseconds and milliradians. It does not convert an angle into a linear size at a distance, which is exactly the job this page owns — use that one for pure angular units and this one whenever a range is involved. For linear unit conversion on its own the length converter handles inches, centimetres, yards and metres.
On the ballistics side, the ballistic coefficient calculator covers the drag-model half of the problem and is explicit about the difference between G1 and G7 figures, and the barrel twist rate calculator works the Miller and Greenhill relations. The muzzle velocity calculator takes chronograph figures rather than publishing any, and the recoil energy calculator works free recoil from conservation of momentum.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Treating one MOA as exactly one inch at a hundred yards — it is 1.047 inches, and the 4.7 per cent difference compounds into a miss at long range.
- Mixing mils and MOA between reticle and turret — the two differ by a factor of about 3.44, so a mis-called correction lands nowhere near the target.
- Guessing the click value — quarter MOA is common, but eighth-MOA and half-MOA turrets both exist and the error is a straight doubling or halving.
- Quoting a group in MOA without the shot count — extreme spread grows with the number of shots, so three-shot and ten-shot figures are not comparable.
- Using a nominal range instead of a measured one — angular subtension scales directly with distance, so a range error passes straight through into every linear figure.
Related Free Tools From Arb Digital
For pure unit work use the angle converter and the length converter. For the ballistic side of the same shot, the ballistic coefficient calculator, the barrel twist rate calculator, the muzzle velocity calculator and the recoil energy calculator each handle one published relation and take your own measured figures as inputs. Everything Arb Digital publishes is listed on the free online tools hub, and if you want something built for your own audience you can talk to us.
Frequently Asked Questions
One true minute of angle subtends 1.047 inches at 100 yards, and that figure comes from the geometry rather than from convention: a minute is one sixtieth of a degree, and the tangent of that angle applied over 3,600 inches gives 1.0472. The rounding to a flat one inch is where shooter's MOA comes from, and at 100 yards the five-hundredths of an inch difference is smaller than a bullet hole. At 1,000 yards the same rounding is nearly half an inch per unit, which is why the distinction stops being academic.
True MOA is an actual angle, one sixtieth of one degree, subtending 1.047 inches per hundred yards. Shooter's MOA, also written SMOA or IPHY, is a convention that defines one unit as exactly one inch per hundred yards. The two differ by 4.7 per cent. Most scope turrets and most ballistic solvers use true MOA, so the error usually creeps in through mental arithmetic at the target rather than through the equipment, and it accumulates with every unit of correction dialled.
One milliradian is 3.43775 minutes of arc, and one minute of arc is 0.29089 milliradians. A milliradian is a thousandth of a radian, so it subtends one unit of size per thousand units of range in any consistent system: ten centimetres at a hundred metres, or about 3.6 inches at a hundred yards. Neither unit is inherently more precise than the other. The only thing that matters is not mixing them between a reticle and a turret, because the factor of three and a half produces a very large miss.
Measure the extreme spread of the group centre to centre, which in practice means measuring outside to outside and subtracting one bullet diameter, then divide by the linear size of one MOA at the range you shot. This page does that with the exact arctangent rather than the approximation. Record the shot count alongside the figure, because extreme spread grows with the number of shots and a three-shot group is not comparable to a ten-shot group from the same rifle.
Measure how far the centre of the group sits from the point of aim, convert that distance into an angle at the range you shot, and divide by the click value marked on the turret. This page does all three steps. Because the correction is angular it holds at every distance, which is the reason turrets are calibrated in angles rather than in inches. Turrets move in discrete detents, so the tool also gives the nearest whole click and the residual angle you cannot dial out.
Yes. The distance and the measured figure each have their own unit selector, and the headline result is given in both inches and centimetres regardless. The one thing to watch is that shooter's MOA is defined in inches per hundred yards and has no natural metric form, so if you are working entirely in metres the mil convention is the one that produces clean numbers: a tenth of a mil is exactly one centimetre at a hundred metres.
Because drop and wind depend on the projectile, the drag model, the atmosphere and the muzzle velocity, none of which are angular arithmetic and none of which can be published as a table that is right for your rifle. This page converts angles and distances. Muzzle velocity comes from your own chronograph or the ammunition manufacturer's published figure, and load data must come from a current manufacturer's manual rather than from any website.
This tool is provided for educational use. It performs published angular conversions from figures you enter and nothing more. It does not and cannot tell you that any firearm, load, zero or shot is safe or correct. A qualified gunsmith and the manufacturer's current published data govern; ownership, transport and hunting are subject to laws that vary by jurisdiction.
