Well, the calculation is actually pretty simple. The volume of a 1" cylinder is Pi times the pot diamter squared, divided by 4. (Remember Pi R Squared is the area of a circle and the diameter is twice the radius, R.) This equation gives the result in cubic inches and each gallon is 231 of them. Here's a table of the results.
|Pot Diameter in Inches||Volume in Cubic Inches||Quarts, Rounded to 1/2|
The surprising thing to me is that other than our really big pots, most would do just fine with a half gallon of water.