From this thread on pros and cons of various shotgun gauges.
10 gauge 0.775″
12 gauge 0.729″
16 gauge 0.662″
20 gauge 0.615″
28 gauge 0.550″
410 bore 0.410″
In shotguns, gauge is equivalent to the number of lead balls of the given diameter necessary to equal one pound. So the bigger the shotgun barrel, the smaller the gauge.
.410 isn’t a gauge, it’s a caliber. So people typically (and correctly) say, e.g., 12 gauge and .410 bore. More from Chuck Hawks:
If the .410 had been named in the traditional fashion, by the number of lead balls .41 inch in diameter needed to make one pound, it would be about a 67-68 gauge. Many years ago it was also called the 36 gauge, and I have seen a picture of an old box of Remington shells marked “(36 GA.) .410-2 1/2 IN. (12 MM).” However, the “36 Gauge” designation was very inaccurate, as a true 36 gauge gun would actually have a .506 inch bore diameter.