How many firearms were owned by civilian population between 1836 and 1912 in USA?

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There is a great paper (63 pages) where they go through how some of these numbers that you see, and how they are obtained. Basic conclusion is that there are no direct numbers for how many guns were in circulation. In fact due to laws in some cases it was illegal to list them in estates (common record to obtain this data). The toughest part about this is that it wasn't until 1934 that manufactures were required by the National Firearms act to serialize their firearms.

The estimates range from 14.7% to upwards of 70.6% of households had firearms at the time, but that still doesn't give you a count of how many firearms were out there it just "helps" narrow down how many households had them. I would suggest reading the paper to help get a better understanding here is an exert of the conclusion:

50% of male and female wealthholders owned guns in 1774 colonial America are the first carefully weighted national probate-based estimates for gun ownership in eighteenth-century America. If we exclude estates that have nosignificant itemization of personal property, 54% of male wealthholders have guns, as do 19% of female wealthholders. We also provide the first weighted regional estimates of colonial gun ownership: 69% in the South, 50% in New England, and 41% in the Middle colonies. Given that these counts are based on incomplete probate inventories, unless nudity was also widely practiced,1 56 these gun counts are likely to be substantial underestimates.

Source: http://scholarship.law.wm.edu/cgi/viewcontent.cgi?article=1489&context=wmlr

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