MOA Calculator (minute of angle ↔ inches, cm & mils at any distance)

Understanding the MOA calculator — concept and principle

Shooters describe group sizes and sight adjustments as angles, in minutes of angle (MOA) or milliradians (mrad, often called mils). This calculator converts an angle into a size at any distance, or a measured size back into an angle, and shows how many scope clicks it corresponds to.

One sixtieth of a degree spans 1.047 in at 100 yards, close to the shooter’s 1 inch.

How it is calculated

1 MOA = 1/60 degree; 1 mrad = 1/1000 radian ≈ 3.438 MOA

Size = distance × tan(angle)

Angle = arctan(size ÷ distance)

Shooter's MOA (IPHY) = inches ÷ (distance ÷ 100 yd)

Clicks = MOA × 4 for ¼-MOA turrets; mrad × 10 for 0.1-mrad turrets

1 yd = 0.9144 m and 1 in = 2.54 cm exactly.

The principle

An angle opens wider the further it goes. At 100 yards, one minute of angle spans about 1.047 inches; at 200 yards, twice that. Expressing group size or correction as an angle makes it independent of distance, so a rifle that shoots 1 MOA groups does so at any range, at least in principle. Sight turrets are marked in angular units for the same reason: each click moves the point of impact by a fixed angle. Many shooters round 1 MOA to exactly 1 inch at 100 yards (inches per hundred yards), which is about 4.7% smaller than the true MOA.

Worked example

Default inputs: angle 1 MOA, distance 100 yards.

Distance = 100 × 0.9144 = 91.44 m.
1 MOA = π ÷ 10,800 rad = 0.000291 rad = 0.291 mrad = 0.0167°.
Size = 91.44 × tan(0.000291) = 0.0266 m = 1.05 in (1.047) = 2.66 cm.
Shooter's MOA at this distance = 1.047 inches per 100 yd.
Clicks: 1 × 4 = 4 at ¼ MOA; 0.291 × 10 = 2.9 at 0.1 mrad.

Each point is the calculator re-run with only “Angle” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Angle	Angle (MOA)
0.25	0.25
0.5	0.5
0.75	0.75
1	1
1.25	1.25
1.5	1.5
2	2

How to read the result

Use the size to understand what an angle means on paper at your distance, or enter a measured group to express accuracy as an angle. For corrections, convert the miss into clicks for your turret. Check which unit your scope uses: mixing MOA turrets with mil reticles leads to errors. Some scopes are calibrated in true MOA, others in IPHY.

Common mistakes

Assuming 1 MOA is exactly 1 inch at 100 yards for long-range corrections.
Mixing MOA and mrad between turret and reticle.
Using metres with yards-based rules of thumb.
Forgetting that clicks change with turret value.

Keep in mind: Real point-of-impact shifts depend on ballistics, wind and sight calibration. Confirm adjustments on target, and follow range safety rules.

Frequently asked questions

How many inches is 1 MOA at 100 yards?

About 1.047 inches, often rounded to 1 inch.

What is a mil?

A milliradian, 1/1000 of a radian; 1 mil is 10 cm at 100 m.

Which is better, MOA or mrad?

Neither is more accurate; choose one and match turret and reticle.

How do I convert MOA to mrad?

Divide by about 3.438.

Sources: Standard angle definitions (1° = 60′, 1 mrad = 0.001 rad, SI radian); 1 yd = 0.9144 m and 1 in = 2.54 cm exactly (NIST SP 811)

Checked 9 Nov 2026. Angle definitions: 1° = 60′ (minutes of angle), 1 mrad = 0.001 rad (SI derived unit radian, standard values); 1 yd = 0.9144 m and 1 in = 2.54 cm exactly. Size = distance × tan θ (standard trigonometry).

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