How this calculator works
A minute of angle is one sixtieth of a degree. This tool treats the full group width as centred on the line of sight, with the extreme rays at half the full angle on each side. The tangent relation is exact for that geometry. For practical small angles it agrees closely with the common linear approximation. Distance and spread must refer to the same plane perpendicular to the sight line.
Formula
1 MOA=pi/10800 rad; spread=2 distance tan(angle/2); angle=2 atan(spread/(2 distance)).
Worked example
An angular width of 1 MOA spans approximately 1.047198 in at 100 yards. A full spread of 1 m at a distance of 1 m has angle 0.927295218 rad under the centred-width convention.
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Frequently asked questions
Is one MOA exactly one inch at 100 yards?
No. It is about 1.0472 inches. Treating it as exactly one inch introduces a small scaling error.
Can I enter milliradians?
Yes. Use the angle unit selector to enter mrad, degrees, radians or arcminutes.
Is this a ballistic drop calculator?
No. It converts an angular measurement and a linear width; it does not predict a projectile flight path.