How to Calculate MOAFormula & Examples
Calculating MOA from your group size takes one simple formula. Below you will find the formula, step-by-step instructions, worked examples at different distances, and common mistakes to avoid.
The MOA Formula (Metric)
1 MOA (Minute of Angle) is approximately 1/60th of a degree.
This is the simplified formula — accurate to within 0.3%. More than enough for any practical shooting application.
The formula works because 1 MOA ≈ 2.91 cm at 100 m (exact: 2.908 cm). Dividing your group size by the distance and multiplying by 100 converts centimeters into the angular unit.
An alternative way to think about it: MOA = (group size in cm × 3.438) / distance in meters. Both forms give the same result — use whichever is easier to remember.
Exact formula (advanced) →
The difference from the simplified formula is below 0.3% — negligible in practice.
Step by Step
Measure your group
Find the distance between the two farthest shot holes (outside edge to outside edge), then subtract one bullet diameter to get the center-to-center measurement.
Record the distance in meters
Use the shooting distance in meters. If your range uses yards, multiply by 0.9144 to convert, or use the imperial version of the formula.
Apply the formula
Divide the group size in cm by the distance in meters, then multiply by 100. Round to one decimal place.
Interpret the result
Lower MOA = tighter group = better accuracy. Compare against your previous sessions to track improvement.
Worked Examples
Example 1: Pistol at 25 m
You fire 5 rounds from your 9mm at 25 meters. You measure the group center-to-center: 3 cm.
For a pistol at 25 m, 12 MOA is a typical recreational result. With practice, bringing this under 8 MOA is a realistic goal.
Example 2: Rifle at 50 m
You shoot a 5-round group from a bench rest at 50 meters. The group measures 5 cm.
At 10 MOA from a rest, there is room for improvement. Check your ammo, ensure the scope is properly mounted, and try again with a different load.
Example 3: Precision rifle at 100 m
You fire 5 rounds of match-grade .308 at 100 meters. The group measures 7 cm.
A 7 MOA group at 100 m with a precision rifle suggests something is off — check fundamentals, ammo consistency, and barrel condition. A well-tuned setup should be under 2 MOA.
Quick Reference Table
| Distance | Group | Result |
|---|---|---|
| 25 m | 3 cm | 12.0 MOA |
| 50 m | 5 cm | 10.0 MOA |
| 100 m | 7 cm | 7.0 MOA |
| 25 m | 0.73 cm | 2.9 MOA |
| 100 m | 2.9 cm | 2.9 MOA |
Common Mistakes
Measuring edge-to-edge instead of center-to-center
Always subtract one bullet diameter from your outside-to-outside measurement. Skipping this inflates your group size by the width of one bullet hole.
Mixing units
Make sure your group size and distance use the same system. The metric formula expects cm and meters. If you use mm, divide by 10 first.
Too few shots
A 3-shot group can look great by luck. Use at least 5 shots per group. For proper ammo testing, shoot three or more 5-shot groups and average them.
Ignoring flyers
Some shooters exclude obvious flyers to get a better number. Be honest with your data — if a flyer happens consistently, it is part of your real accuracy.
Comparing different conditions
Wind, temperature, fatigue, and rest type all affect group size. When comparing sessions, note the conditions so you are comparing like with like.
When to Use MOA
MOA is most useful when you need to compare accuracy across different distances or over time. Here are the situations where MOA matters most:
- -Zeroing your optic — knowing how many MOA clicks to move lets you zero efficiently without wasting ammunition.
- -Testing ammunition — compare different brands and loads on a level playing field.
- -Tracking your progress — a session at 25 m and a session at 100 m can be directly compared in MOA.
- -Setting realistic goals — "get under 4 MOA with my carry pistol" is a measurable, distance-independent target.
Frequently Asked Questions
What is the MOA formula in metric?
MOA = (group size in cm / distance in meters) × 100. This is a simplified formula accurate to within 0.3% — more than sufficient for practical shooting.
Do I measure group size center-to-center or edge-to-edge?
The standard method is center-to-center (CTC): measure the distance between the two farthest shot holes, then subtract one bullet diameter. This gives the true spread of your shots, removing the bullet's width from the measurement.
Can I use this formula for yards and inches?
For imperial units, use: MOA = (group size in inches / distance in yards) × 100. At 100 yards, 1 MOA ≈ 1.047 inches. The metric and imperial formulas are equivalent — just use consistent units.
How many shots should I fire for a reliable MOA measurement?
A minimum of 5 shots per group is the common standard. Three-shot groups can look flattering due to luck. For serious testing, shoot multiple 5-shot groups and average the results.
Why does my MOA vary between sessions?
MOA describes the combined system: shooter, firearm, ammunition, and environmental conditions. Fatigue, different ammo lots, temperature, and even how you hold the gun all affect the result. Track your MOA over time to see meaningful trends rather than focusing on a single session.
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