Theoretically
As for the possible number of fish in the tank, the answer cannot be certain. Still, for 40-50 l tank with no aeration it can be recommended to seat so many fish that each specimen no longer than 5 cm receives not less than 2 l of water, 3-4 in. long - 3-4 l, over 4.7 in. - 8-10 l. Apparently, both the volume of the tank and the kind of fish and its size are important.
The primary limiting factor for small fish is concentration of oxygen. In order to prevent oxygen insufficiency in a non-aerated aquariums sized 20 l or so each fish, which is about 5 cm long, should receive 1.5-3 l of water, but for small-sized livebearers 1-2 l is enough.
The bigger is the tank, the more fish can live there. Thus, with a 40 l tank you can admit 25-30 fish, with 100 l - about 80, and with 150 - 150 fish. When the fish length is about 3.1-3.9 in. the density reduces twice.
If the tank is supplied with an air-pump that works round-the-clock or at least 8-10 hrs (at night), the density of settling can be increased two or two-and-a-half times.
Practically
However the described quota is very rough and undergoes very many exceptions. You can settle more fish in a low and wide tank than in a "tall" tank even if it has the same volume, since water takes up oxygen by its surface.
For the two fish, which have the same size but belong to different species, the volume needed can differ drastically. Thus, the labyrinth fish requires volume 2 to 3 times less than described above, while various goldfishes require 2 to 3 times bigger volumes. With the cichlids of African Great Lakes that are accustomed to a good oxygen regimen 5 to 20 l is needed per each fish (the rate depends on the fish size). Many fish used to still water are not active swimmers and require lesser volume than the species that naturally occupy streaming water and are quite mobile.
* Modern aquarium devices help increase density, but remember that too many fish doesn't meet the aesthetic norms and natural requirements of animals
The logic implies that the number of fish and aquatic plants should be calculated on the basis of the volume of water in the tank, not the tank itself. At this the volume of substrate, pebbles, decorations must be counted too!
The idea that a fish sized less than 2 in. needs less than 2 l of water is out of date. It is not just absurd but it borders tormenting of living creatures. Fit this example to a human scale: this means that we'd have to spend all our life inside a small pantry!
Most often the beginning hobbyists make the mistakes of such kind as early as during visiting the pet-shop. Novice aquarists do not consider that they deal with the young, non-mature fish (and, by the way, plants). With the good care these fish will soon overgrow many times their initial size.
Therefore at the moment when you acquire a fish or a plant, ask the shop assistant about the final size of your potential pets. This will be good for everybody - both for the fish and plants and for you as well.
I think that the following suggestion is more becoming than the "rule" mentioned above. Each fish needs as many water as 6.6 l per each square inch of the fish body projection.
E.g.: tank volume - 120 l. Subtract at the least 20 l accounted for sand/gravel, pebbles and decorations. Hence, you have 100 l at your disposal. We suppose, you are going to settle mainly large-sized fish. Let their body length be 2.3 in. approximately and body heights are 0.6 and 0.8 in. Thus, each fish needs 6.6 ? 2.3 ? 0.6 = 9 l or 6.6 ? 2.3 ? 0.8 = 12 l of water (if the fish's height is 1 inch and more, count their height as 1 inch). Thus, you can place 8-10 fish in the tank. Beside this, the future growth and the degree of the fish activity must be regarded.
Translated by Tatiana Karpova (Moscow)
(MSU, Biology faculture, Dep. zoology and ecology).