So your wondering how many fish you can put into a tank.
First let me say that this depends on such a huge and varied bunch of variables such as substrate, substrate heating, aquarium temperature, plants, filtration capacity and water buffering that no equation can accurately tell how many fish you can put into a tank. But for a rule of thumb we can combine two equations ti give us a rough idea which is better then nothing.
The Inch Per Gallon Rule
Pretty basic stuff one inch of fish of fish for each gallon of water. Remember two things when using this rule.
1 Use the full grown size of the fish. A one inch catfish can grow to be half a foot long.
2 The equation assumes that they are fairly slender fish. Stocking a ten gallon tank with ten slender Minnows is different that stocking it with ten full bodied goldfish. Full bodied fish produce more waste and thus need more water capacity.
The Surface Area Rule
This rule has one main advantage in that it takes into account the shape of the tank. This is important because contact with the air is the main way that oxygen is introduced into the water. Thus a tall narrow tank can support less fish then a standard, flatter tank. For this rule there should be 12 inches of surface area for each fish. There are once again two things to consider.
1 Plants, air rocks, and some filters add extra oxygen to the water, making this equation less accurate.
2 Once again the equation assumes that they are fairly slender fish. Stocking a ten gallon tank with ten slender Minnows is different that stocking it with ten full bodied goldfish. Full bodied fish produce more waste and thus need more water capacity.
These are very rough rules that should only be used as a guide. I wouldn't stock a tank above 75 to 80 percent to stay on the safe side, especially if your a day or two late in your water change it provides a bit of a buffer zone.
Hopefully this is helpful but remember that in each aquarium you have unique conditions, so do your home work before adding more fish.