How Many Fish Can I Put in My Pond?
The USDA (United States Department of Agriculture) offers this "consensus"regarding fish stocking:
Unaerated ponds: up to 1, 12" fish per 10 square feet of surface area. (To calculate surface area multiply the length x width of your pond).
Aerated ponds: up to 1, 12" fish per 2-3 square feet of surface area... and says that conservative hobbyist should stay well below these guidelines.
To apply this to smaller fish, note that while their weight goes up almost with length cubed, their metabolic rate goes down with length. So feeding rate, oxygen demand, and stocking rate go with length squared, as a rough guide. What this actually means is that stocking 4 times as many fish of half the length (4 fish of 6" long) is about equivalent as the the 1, 12" fish in the above formula....but that is, until they grow!
Pushing these guidelines and allowing the fish the room and requirements for growth, requires good aeration, biofiltration, keeping the temperature from getting to high, not overfeeding, and increases the risk of losses during spring cycling. So there isn't a fixed stocking formula, but a range of difficulty.
In jist, follow the guidelines above but PLAN on the fish growing when you select pumps and filters, etc. to begin with or you may have to add more later to keep your fish healthy and your pumps and filters working properly.