Two ways to describe a group
"How big is the group?" has more than one answer, and mixing them up is behind a lot of arguments about accuracy. The two measures you'll see most are:
- Extreme spread (ES), the distance between the centers of the two shots that are furthest apart. It's the traditional number, the one in most rifle reviews and the one people mean by "it shoots half-MOA".
- Mean radius (MR), the average distance of every shot from the center of the group. It uses every shot instead of just the two worst, so it's a steadier measure of precision, and it's harder to do by hand.
Neither one is wrong, but they aren't interchangeable. Mean radius is always much smaller than extreme spread for the same group, so a "0.3 MOA" mean radius and a "0.3 MOA" group are very different claims. Always say which you mean.
Measuring extreme spread by hand
You can't easily find the center of a bullet hole with calipers, but you can measure edges. The standard method:
- Find the two holes furthest apart.
- Measure from the outside edge of one to the outside edge of the other.
- Subtract one bullet diameter. Taking off half a diameter at each end leaves the center-to-center distance.
Use the bullet's actual diameter, not the cartridge name: .308 Winchester bullets are 0.308", 6.5 mm bullets are 0.264", .223 Remington bullets are 0.224", and 9mm bullets are about 0.355". Paper tears and target material can make holes look slightly smaller or larger than the bullet, which is one reason edge-to-edge measurements carry a little error.
Worked example: 100 yards
A five-shot group from a .308 measures 1.064" outside to outside.
1.064 − 0.308 = 0.756" center to center.
Converting inches to MOA
A minute of angle (MOA) is 1/60 of a degree. Because it's an angle, the size it covers grows with distance. At 100 yards, 1 MOA is 1.047 inches, and it scales in a straight line:
| Distance | 1 MOA | 1 mil |
|---|---|---|
| 100 yd | 1.047" | 3.6" |
| 200 yd | 2.094" | 7.2" |
| 300 yd | 3.142" | 10.8" |
| 500 yd | 5.236" | 18.0" |
| 1,000 yd | 10.47" | 36.0" |
| 100 m | 29.1 mm | 100 mm (10 cm) |
The formula is simply:
MOA = group size (inches) ÷ (1.047 × distance in yards ÷ 100)
For the 100-yard example: 0.756 ÷ 1.047 = 0.72 MOA.
You'll also see "shooter's MOA" or IPHY (inches per hundred yards), which rounds 1 MOA to exactly 1.000" at 100 yards. The difference is about 4.7%, which is small for groups but adds up when dialing elevation at long range. Most scopes marked in MOA use true MOA, but check your scope's manual.
Worked example: 300 yards
A five-shot group from a 6.5 Creedmoor measures 2.400" outside to outside.
- Center to center: 2.400 − 0.264 = 2.136"
- 1 MOA at 300 yards: 1.047 × 3 = 3.141"
- Group size: 2.136 ÷ 3.141 = 0.68 MOA
Notice the group is almost three times bigger in inches than the 100-yard one but slightly smaller in MOA. That's why angular units are the fair way to compare groups shot at different distances.
Converting to mils
A milliradian (mil or MRAD) is 1/1000 of a radian. It's a bigger unit than MOA: 1 mil is about 3.438 MOA. The handy part is how cleanly it works in metric: 1 mil is 1 cm at 100 meters, or 1 mm per meter of distance. In yards, it's 3.6" at 100 yards.
- 100-yard example: 0.756 ÷ 3.6 = 0.21 mil
- 300-yard example: 2.136 ÷ 10.8 = 0.20 mil
- Metric: a 25 mm center-to-center group at 100 m is 25 ÷ 100 = 0.25 mil, or 25 ÷ 29.1 = 0.86 MOA
Use the unit that matches your scope. If your turrets click in 0.1 mil, thinking about groups in mils tells you directly how many clicks of uncertainty you're working with.
Mean radius, worked through
Mean radius needs the position of every shot, so it's normally done from a photo or a target scanner rather than calipers. Here's the arithmetic so you can see what a tool is doing. Five shots at 100 yards, with positions measured in inches from the lower-left shot:
| Shot | x (in) | y (in) | Distance from center (in) |
|---|---|---|---|
| 1 | 0.0 | 0.0 | 0.397 |
| 2 | 0.6 | 0.1 | 0.340 |
| 3 | 0.3 | 0.5 | 0.240 |
| 4 | 0.1 | 0.3 | 0.204 |
| 5 | 0.5 | 0.4 | 0.244 |
- Find the group center by averaging the coordinates: x = (0 + 0.6 + 0.3 + 0.1 + 0.5) ÷ 5 = 0.30, y = (0 + 0.1 + 0.5 + 0.3 + 0.4) ÷ 5 = 0.26.
- Measure each shot's distance from that center with Pythagoras. For shot 1: √(0.30² + 0.26²) = 0.397".
- Average the distances: (0.397 + 0.340 + 0.240 + 0.204 + 0.244) ÷ 5 = 1.425 ÷ 5 = 0.285", or 0.285 ÷ 1.047 = 0.27 MOA.
The extreme spread of the same group is between shots 1 and 5: √(0.5² + 0.4²) = 0.64", or 0.61 MOA. Same five holes, two very different-sounding numbers.
Getting numbers you can trust
- Shoot more shots per group. Extreme spread grows as you add shots, because each extra shot is another chance to land outside the others. A three-shot group almost always looks better than a ten-shot group from the same rifle. Compare groups with the same number of shots.
- Shoot more than one group. A single group is a small sample. The average of several groups, or the mean radius over 10 to 20 shots, says much more about a rifle or a load.
- Measure from the actual distance. A "100-yard" range that's really 95 yards inflates your MOA numbers by about 5%. If you're not sure, measure the distance.
- Keep a record. Distance, load, shot count, conditions, ES and MR. That's how you'll tell a real improvement from a lucky group.
Measuring groups in GunCollector
GunCollector measures groups from a photo of your target. You calibrate it by tapping two points a known distance apart, mark the holes, and it reports extreme spread and mean radius in inches, MOA and mils, center to center, for the distance you shot. Each group is saved against the firearm and ammo lot in your range trip, so over time you can see which loads your rifle prefers. The walkthrough is in how to log a range trip and measure your group.
Quick answers
How many inches is 1 MOA at 100 yards?
1.047 inches. It scales with distance: about 2.094 inches at 200 yards, 3.142 at 300 and 10.47 at 1,000.
How do you measure group size center to center?
Measure from the outside edge of the two furthest-apart holes, then subtract one bullet diameter.