The studies I have seen indicate that on average, 1 square foot of bio film can convert .05 grams of ammonia per day. (It varies based upon temperature, ph, water flow, availability of food, nitrite levels, etc., so this is just an average. The actual range is quite wide and likely varies as water parameters vary.)
The conversion I have seen from food to ammonia looks like this: 4 ounces of 50% protein food = 28.35 grams x 4 x 50% = protein content. Protein is 16% nitrogen and nitrogen is 82% ammonia. So, 4 oz of 50% protein food = 7.44 grams of ammonia.
7.44/.05 = 148.8, therefore, you'll want 148.8 square feet of bio film per 4 ounces of 50% protein food. (Higher protein content requires more bio film.) Bioballs are around 160 square feet for 1 gallon of 1" bio balls, 100 square feet for 1 gallon of 1.5".
If you are feeding fish, their intake varies with size and temperature, but full grown fish are roughly 2% of body weight. (Lower amounts might be for colder water specimens, and this does not take into account spawning. Younger specimens typically are much higher %, but are of course, much smaller. I've seen studies of rates below 1%, but it's not a practical number to use if you are feeding a large fish and trying to reach maximum growth.) 4 ounces daily rations at 2% body weight would equal 12.5 lbs of fish.
This is very rough estimate and is probably the optimal result. You could easily aim higher by a factor of 2 or 3 to 1 just to be on the safe side as not all the media will be completely covered at any point in time due to water flow, dirt, etc. (Maximum capacity is probably never reached.)
Note that ammonia is not produced at a flat rate per hour all day, nor is it produced instantly after feeding. For example in one trout study I saw, ammonia was excreted after eating each hour like this: first hour 8%, second hour 22%, 3rd hour 14%, then 9%, 7%, 6%, 5%, etc. You'll want the media to convert the ammonia quickly, so added over capacity is a good thing to handle the flood of ammonia in hours 1-4 after feeding.
It's better to have more capacity than less, so I'd err on the side of enough to cover a 24 hour period, even if feeding is spaced apart.
Ultimately, these are rough guidelines. Each tank, species, owner, water, and food are different and it's best to have enough media and then test parameters and add more if the readings warrant.