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Sort of, they are called "Cannons".

To determine the "gauge" of a barrel, you make a lead ball that is the same size as the hole in the barrel. Then you figure our how many of those lead balls it would take to weigh 1 pound. A 12 gauge would need 12 ~3/4 inch lead balls. to weigh 1 lb. A 1 gauge would need 1 1lb lead ball. If my math is right*, a 1 gauge shotgun would have a barrel that is just a little over 1.6 inches in diameter.

* Math

1 cubic foot of lead is 708 lbs. = 2.4 cubic inches = 1lb.

Formula of sphere volume..

V=4/3pir^3

Plug in and solve for d (d=2r)

(2.4/ (3.14 * 4 /3))^(1/3) *2 = 1.66 inches in diameter.

The UK does not have limits on the gauges of shotguns for hunting purposes. There was a guy making 1 gauge shotguns on order in the 1990's - I cannot find any reference to him on the web currently. He had completed his first and was working on the second when he did a video to show the 1 gauge being shot. It stood about 2 meters from butt to muzzle and had a little longer muzzle flash when fired. Many hunters opposed such large bore shotguns as it made hunting low flying geese more of a slaughter than a hunt - his operation may have been legislated out of operation. The point being that yes, there has been a 1 gauge shotgun but none ever manufactured on a production line and they are not legal in most countries.

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11y ago
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Q: Is there a 1 gauge shotgun?
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