Shotgun Gauge Diameter Formula
The standard definition of shotgun gauge assumes that a pure lead ball is used. With this assumption, since the room temperature density for lead is 11.34 g/cm3, and with there being 7,000 grains to a pound, the following formula results:
This formula accurately estimates the diameter (dn) in inches of any shotgun gauge size (n). For example, a 67.62-gauge equates to a lead ball diameter of 0.410-inch by this formula, hence the .410 shotgun shell nomenclature.
Another source for a gauge diameter formula can be found in gauge (bore diameter).
Read more about this topic: Shotgun Shell
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