I get asked this question every day. There is a common thought that the number of gallons is in direct relation to the number of Koi you can have. And while this is true to a point, the fact of the matter is the number of gallons is only one of MANY factors that determine the number of Koi you can keep. Feeding, filtration, circulation, and aeration all come into play. You also have to ask yourself, what do you want from your Koi? Are they show Koi? A high end collection? Or just some pretty pets in the pond? Also, how much time do you want to spend maintaining the water quality? High stocking densities are usually a LOT more work. My point is, it’s a system and the number of gallons per fish is only one part of the equation.
Filtration is going to be the most important factor in determining the number of Koi you can have. It is more important then the number of gallons. Many store bought filters will tell you they can filter 1000 gallon ponds or 2000 gallon ponds. These ratings are not usually accurate. They base these on the assumption that you will have very few fish, usually only two or three goldfish. Just because you have a 1000 gallon pond and you bought a filter for 1000 gallon doesn't mean you can put 20 Koi in there and expect great water quality. As a general rule, cut the number of gallons the filter says it can filter in half, and even then keep the stocking density low. But you can have 15-20 Koi in 1000 gallons IF the filter is large enough to handle the waste produced...both solid and ammonia. (Basically a filter designed for a 5-6000 gallon pond) The key to deciding if you are over stocked is water testing. If you have ammonia that simply won't go away, or waste and debris in the water, then you are over stocked for the size of the filter. To correct this you need to either cut back on feeding, reduce the number of fish or increase the size of the filter.
Another major consideration is circulation. A Koi pond with poor circulation will have a lot of trouble at higher stocking densities. The reason is the filter cannot treat waste it doesn't come in contact with. You need to circulate the ponds entire volume every hour. And that does not just mean a 1000 gallon pump for a 1000 gallon pond. You need to make sure there are no "dead spots" in the pond where water does not flow properly. If you notice certain areas of the pond have more debris settling then others, then you need to correct the circulation. A bottom drain is the best way to prevent poor circulation. Skimmer only ponds will be plagued with poor circulation and stocking density should be kept very low. You can also add small underwater jets or air stones to help circulate the water towards the filter
The type of food and the amount you feed also play a major role in the stocking density. Low quality foods have fillers and low digestibility. This means more waste for the filter to handle. Also, the more you feed them the more waste the Koi produce. So feeding heavily with cheap food means you need to keep a very low stocking density. This isn't to say you should not feed the Koi. But rather if you want to feed heavily to get maximum growth and development you need to use only high quality foods and keep a low stocking density with a large enough filter to handle the waste from such a heavy feeding routine. Again it comes back to what you want from your Koi.
Aeration is also major factor in stocking density. The bacterium in the bio filter is highly oxygen dependent. If you do not have enough O2 saturation in the water then the bio filter will not be as effective and in turn you must keep a lower stocking density. Another thing to keep in mind is during the warmer months the water will not hold as much oxygen and this is also the time the fish are eating the most so your bio filter needs to be at its peak. That means it needs as much O2 as it can get. Luckily aeration is one of the easiest things to correct. An air pump with a few air stones can correct this problem very quickly. It will also help with your circulation by bringing the water from the bottom of the pond back to the top...remember its a system and all the parts work together.
The last thing to consider is how much time do you want to spend cleaning and back washing filters, testing the water, doing water changes, etc ,etc. If the maintenance becomes too much of a chore then after awhile it won't get done and the water quality will suffer. Heavy stocking densities require more time and effort. If you want to spend less time working on the pond and more time enjoying it, keep the stocking density low and the filtration big.