Having just read this thread, something stands out. Nothing has yet been mentioned about what really does decide whether a tank is or is not overstocked. It is not the filter size, or even the bioload (number of fish per volume of water)--important as these certainly are. It is the species of fish and their individual numbers and the tank's aquascape that most impact the tank's biological system in terms of the effect on the fish's well-being. And this is why calculator sites cannot really provide reliable numbers. It is not easy, if it is even possible, to programme all of this data into a calculatory site.
Filters for example move water around and provide filtration, mechanical and biological in all cases, and sometimes chemical depending upon the filter media. Obviously the size of the filter will have some impact on mechanical, but it might surprise some how small a sponge you need to have clear water which is what mechanical filtration is--just water clarity,
not water cleanness. Bilogical filtration will occur in any operating filter whatever the media, on the sponge/pad, carbon, sides of the filter, and elsewhere like throughout the aquarium's substrate especially.
This goes on with or without any filter. And live plants are important in this area too. The degree of biological filtration depends entirely upon the production of ammonia, then nitrite, then nitrate, then denitrification. This level of biological activity will be in proportion to the bioload, always, because that is how the natural processes operate. Adding larger filters or more filters does
not increase biological filtration beyond what the system
needs.
@AbbeysDad has written of this frequently, he may have more to add here, I have been as brief as I can to get the point across. Mike has looked into this more than I have, and I'm sure other members have too.
The number of fish (and their size) in relation to the water volume is certainly important. But not all fish of "x" size will have the same impact on the system. If the species is shoaling and needs say 10 to be "settled," the impact on the bioload of those ten will generally be less than will fewer. This may seem odd, but it involves what the fish species needs or expects in its habitat, and when these species' expectations are not being met the fish can be stressed, and stress impacts the fish detrimentally, weakening it, and ultimately creating more stress--all of which further impacts the system because it impacts all the other fish too. Environmental factors like providing the right habitat conditions that every species in the tank must share; the same water parameters that each species requires; providing the numbers of each shoaling species that will improve its life; ensuring other species are compatible, not combatable, to every other species in the tank.
So a given tank might for example support 25 cardinal tetras. But the same tank will not support 25 Zebra Danio in good health because the space is too small, even though the fish adult size of both species is roughly the same. Swimming activity here determines tank length, just one factor. Numbers are not the key, but the behaviours of the individual species. Having the danios in with sedate fish is going to detrimentally impact the system more, because the active fish are stressors to sedate fish.
Having likely aggressive-behaviour species like the Tiger Barbs mentioned earlier in with sedate fish is never going to work long-term, unless things are bad enough to cause behavioural changes in the TB, which can occur, but that in itself is detrimental to the fish and the system. Or if the group of TB is sufficient in number, and the tank considerably larger in area, to allow multiple species--which is not the case here. And there is more to this aspect, but I've probably given enough examples to illustrate my original point that the fish species themselves are really the key to stocking levels and healthy fish. I'll try to further clarify anything if asked.