Fish excrete ammonia (NH3), however below a certain pH (7.4, I believe), ammonia begins to get converted to ammonium (NH4). The amount increases as pH declines.
Ammonia is toxic to fish while ammonium is not (or if it is, it is enormously less toxic.) Additionally, ammonia is more toxic as temperature increases.
Assuming you're concerned with toxicity, you'd have to have a formula that takes all that into account. I've done the math to calculate the amount of ammonia, but not combined with pH or temp, since the latter 2 variables do not have a linear relationship to toxicity. (pH for example is a log function.)
There is no formula (or claim that I've ever seen) where a certain weight of fish (OP: "X pounds of fish") creates a certain amount of ammonia. The reason is that while fish always produce ammonia, the amount is highly correlated to the amount and type of food consumed along with the timing of the consumption. Weight of the fish has no direct impact on that other than the fact that larger fish can eat more, but of course, that is a spurious relationship. They produce more because they eat more, not because they are bigger.
The most direct relationship that I have found in my studies is the amount of nitrogen in the food consumed. More nitrogen means more ammonia. This unfortunately is a calculation that people can rarely do unless they can break down the protein in food into the proper components (amino acids, I believe) which each have a specific nitrogen content.
I use a generalized formula:
dry weight content of grams of food consumed x % protein content x 16% x 82%
1) all food has to be converted to dry weight equivalent, i.e., water or moisture content is excluded from gross weight
2) % of protein content in consumed food (dry weight equivalent) is used and assumes the protein in digested. Protein which bypasses digestion is problematic as it may be removed in filtration, cleaning, etc.
3) 16% represents the average nitrogen content in protein, however, there is a wide range of nitrogen in the protein components (~ 8-27%), so one should not take 16% as any more than a rough estimate. I.e., common foods that have the same protein content may cause very different amounts of ammonia because the amino acid components in the foods are very different.
4) 82% represents the ammonia content in nitrogen
That is a rough calculation based upon dry weight of grams of food consumed to grams of ammonia produced.
As to the timing, it varies by many factors which I would expect defy formulation such as species, temperature, type and amount of food consumed, etc.. Roughly speaking, ammonia output peaks 3-4 hours after consumption (at least based on some studies I've seen), but continues to a large some degree for many hours later (probably up to 24 hours) with some small amounts even afterwards.
