A simple formula to tell you how much fish you can keep comfortably in a given sized pond.
The number gives a reasonable stocking density and should be revised as any material increases in length occur. (At least annually in young Koi.) These numbers are not liberal and of course, larger is better. To the person keeping 135 inches of fish in two hundred gallons, "Watch for slower growth and don't be surprised if the fish are consistently sicker than your neighbors."
Measure all fish in inches.
Total all the inches up.
Multiply that sum by itself. (Essentially, squaring it.)
Multiply the product of this by two.
Divide the product by 231
Multiply that dividend by 10 for a comfortable minimum amount of water needed.
Multiply that dividend by 20 for an ideal, growth-comprehensive number.
These derivations are the gallons needed by the fish to feel comfortable with reasonable filtration. This is not a number to use if there is no filtration, or if you are a retailer who will need to crowd the fish to remain profitable. For home care of fish, wherein the hobbyist wants to know how many fish to keep in a pond and expect reasonable health and growth, this is the formula.
Let's work a specific example.
A person is just starting out, and they have two dozen (twenty four) small fish of a seven to eight inch length.
Sum it = Roughly 180 inches of fish.
Square it = 32,400
Double it = 64,800
Divide by 231 = 280 is the dividend.
Multiply dividend by ten = 2,800 gallons is the ideal product.
Multiply dividend by twenty = 5,600 gallons is a lofty, luxurious number.
Another person has obtained some gigantic fish, five of them, from Alabama and they are all thirty-six inches in length. The sum of the inches is also 180 and the final minimum analysis yields a 2,800 gallon pond for these five lunkers. Ideally, a 5,600 gallon facility would be provided.