A shotgun's gauge is based on the gauge of a smoothbore musket. This was defined on the number of lead balls fitting the barrel that would weigh 1 pound.
The density of lead is 11.35 g per cubic cm.
1 pound of shot weighs 453.6 grams.
radius of spherical shot fitting the barrel =
= (diameter of the barrel in cm) / 2
volume of the shot in cubic cm =
= 4 * PI() / 3 * ((radius in cm)^3)
weight of the shot =
= (volume in cubic cm) * 11.35
shotgun gauge =
= ROUND(453.6/(weight of shot in grams)
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