In an aquarium, people tend to consider that 20 gallons minimum and a total ratio of 1 goldfish (common) per 10 gallons is safe. That’s assuming 12 to 22 deep. For a pond, it really depends on the depth – deeper ponds will hold fewer fish, since surface area is crucial.

Furthermore, the climate and filtration are important. The warmer the climate (and less shade the pond gets), the fewer fish. In a windy area, more fish can be supported. The less aeration and water movement, the fewer fish. Filter capacity in ponds is also typically not very good unless the person is an enthusiast who built a massive custom oystershell/lava rock/trash can filter, for example.

However, ponds have the advantage of massive algae growth. Algae is somewhat beneficial, since it absorbs waste. Floating plants like water hyacinths are excellent for cleaning ponds (of waste compounds like nitrate, nitrite, and ammonia).

If conditions are ideal – strong filtration, shallow (20 or less), decent water movement (say, 4000 gph), and a cool, windy climate, with lots of floating plants… you could probably stock 50 goldfish with no problems. In a hot, windless area with little shade, no floating plants, no filtration, no bubblers, no forced water movement, and no water changes… I’m not sure. 4 koi and 8 comets might be close to the limit. For koi to goldfish equivalence, I would assume 1 inch of koi is similar to 4 or so of goldfish.