CEP vs Group Size: A Better Way to Measure Shooting Accuracy

The short answer

CEP (Circular Error Probable) is the radius of a circle that would hold half of your shots. Group size is the width of the circle that contains all of them. Group size describes one string of shots well, but a single flyer can inflate it and it grows as you fire more shots. CEP holds up across shot counts and sessions, so it is the better number for tracking whether you are actually improving.

What group size measures, and where it falls short

Group size is the diameter of the smallest circle that contains every shot. It's easy to measure with a ruler and it's the number most shooters grew up with. It has three problems as a way to track progress:

• It is set by the outermost shots alone. The smallest circle around a group is fixed by just two or three of its outside holes, so every other shot can move without changing the number
• It is set by the two worst shots. Every other shot in the group can move without changing the number. One flyer can double it.
mdash; whether the group is five shots or a thousand. One flyer can double it.
• It grows with shot count. The more shots you fire, the more chances there are for a wide one, so a ten-shot group will usually measure larger than a three-shot group from the same shooter on the same day. A 3-inch group from three shots and a 3-inch group from fifteen tell very different stories, but they look identical on a scorecard.
• It ignores where you were aiming. A tight group two inches from the bullseye has the same group size as a tight group centered on it.

What CEP measures

CEP comes from ballistics, where it describes how reliably a projectile lands near its target. Applied to a paper target, CEP₅₀ is the radius of a circle, around a chosen center, that would hold half of your shots. Target Detect estimates it from the spread of every shot in the group, with a correction that keeps small groups from looking better than they are.

Because every shot contributes to it, a single wild shot moves it far less than it moves group size, which depends only on the two or three outermost shots. In a small group one flyer still shows, and the more shots in the group, the less any one of them moves the number. And because it describes a share of your shots rather than all of them, it stays comparable whether you fired three shots or thirty. That makes it possible to put a season of practice on one scale and see whether the number is moving.

Accuracy and precision: two CEPs, two questions

The center you measure from changes what CEP tells you. Target Detect reports it both ways:

• POA CEP (point of aim) is centered on where you were aiming. This is your accuracy — how close you got to where you meant to hit.
• POI CEP (point of impact) is centered on the actual center of your shots. This is your precision — how tightly your shots cluster, regardless of where they landed.

Reading the two together tells you what to work on:

• POI CEP much smaller than POA CEP: you're shooting tight, but something is consistently pulling every shot away from your aim point. It might be the sights, but it could just as easily be trigger pull, grip, stance, eye dominance, or another bias that moves every shot the same way.
• POI CEP and POA CEP close together: you're centered, and the size of the group itself is the limit. That comes from two places: your consistency, which technique can improve, and the mechanical precision of the firearm and ammunition, which sets a floor that even perfect technique can't beat.

A worked example

Here is a real 11-shot Slow Fire session on an NRA B-6 target at 7 yards, shot with a Webley Mk IV Service Revolver and scored in Target Detect:

• Score: 107 of 110
• Group size: 2.36 in, centered 1.31 in left and 0.48 in above the point of aim
• POA CEP: 1.30 in (17.69 MOA)
• POI CEP: 0.75 in (10.23 MOA)

Half of the shots landed within 0.75 in of their own center, but it took a 1.30 in circle around the aim point to hold the same half. The group is tighter than it is accurate: its mean position is 1.19 in left of where the shooter was aiming, and only 0.07 in above. That points to something pulling shots consistently left — worth checking the sights, then trigger and grip — rather than to a lack of precision. The group size alone, 2.36 in, says none of that.

CEP in MOA

Inches depend on distance, so a 1-inch CEP at 7 yards and a 1-inch CEP at 25 yards are very different performances. MOA (minute of angle) converts the measurement to an angle that is the same at any distance: 1 MOA is about 1.047 in at 100 yards, or about 0.073 in at 7 yards. That is how the 1.30 in POA CEP above works out to 17.69 MOA. Reporting CEP in MOA lets you compare a pistol session at 7 yards with one at 25. To convert your own groups, use the MOA group size calculator.

Measuring mechanical precision

Every firearm-and-ammunition pairing has a floor — the smallest CEP it can produce. The practical way to find it is from a proper bench rest, which removes as much shooter variability as possible. Technique still matters there: a wobbly setup or poor trigger control will inflate the measured floor. Comparing the same drill across different loads, or against a known-good firearm, is how you separate the shooter from the gear over time.

Flyers

A wild shot moves CEP less than it moves group size, but in a small group it still moves it

CEP isn't thrown off by a single wide shot, but flyers still matter: how often they happen is its own signal, often pointing to a lapse in technique or an equipment problem.mdash; and a tight group with one flyer can post the same CEP as a genuinely loose group. Those call for completely different work, so how often flyers happen is its own signal, often pointing to a lapse in technique or an ammunition problem. Target Detect reports flyers separately, using a robust statistical method (modified Z-score with median absolute deviation) so the baseline isn't skewed by the very outliers it's trying to find.

Tracking CEP with Target Detect

Measuring CEP by hand means locating every hole and doing the math for each target, which is why most shooters stick with a ruler and group size. Target Detect photographs the target, finds the shots with on-device machine learning, and reports POA and POI CEP, group size, mean radius and MOA for every session — then plots them over time. See Reading a Session Analysis for every statistic, or how Target Detect measures progress.

Target Detect on the App Store — $4.99, one-time purchase. iPhone, iPad, and Mac with Apple Silicon.