Adding fish to your pond not only brings color and movement to the water feature but also adds to the ecological stability of the pond. The size of your pond and the type of fish you add to it are important to achieve that ecological balance. If your fish are too big for the pond, or you add too many, they may not thrive.
Koi
Koi fish can grow up to 2 feet long, so they need plenty of room in the pond. For koi, you need 10 gallons of water for every 1 inch of fish. To demonstrate, one two-foot long koi would need 240 gallons of pond water (24 inches x 10 gallons of water = 240 gallons of water).
The koi you add to your pond are more likely to grow to be approximately 6 inches in length, so if you wanted to have four koi in your pond, your pond would need to hold at least 240 gallons.
Goldfish
Goldfish do well in ponds because they can tolerate a wide range of temperature variations. For goldfish, allow 5 gallons of water for every inch of fish. If you wanted four 10-inch-goldfish, you would need a pond that holds at least 200 gallons (40 inches x 5 gallons of water = 200 gallons of water).
Goldfish tend to grow only to the relative size of their environment, whereas koi can outgrow a backyard pond. That's why you need twice as much water for each inch of koi.
Considerations
Before adding fish to your pond, consider not only how many gallons of water are in your pond, but the depth of the pond. For koi, you want a depth of 6 feet. For goldfish, a 4- to 4 1/2- foot depth is sufficient.
Also consider how many plants you intend to add to your pond. Allow extra room for your aquatic greenery. For example, if you have four goldfish, consider a pond that holds up to 250 gallons of water, allowing an extra 50 gallons to account for the greenery.
Babies
Extra room in the pond also allows for reproduction. Should your fish reproduce, you do not want them crowded out of their home. The extra room guards against immediate problems, but have a plan for relocating offspring. Too many fish will cause the water to become cloudy from excessive waste. Your plants may also suffer from the excess carbon dioxide produced by the overabundance of fish.
Types
Goldfish and koi are common fish for ponds, but you may want to consider other types as well. The red comet fish can withstand water temperatures up to 95 degrees. The calico fantail is also used for ponds, but may be too sensitive for climates with extreme highs and lows. The calico fantail prefers a temperature range of between 55 degrees and 75 degrees.
Both the red comet and the calico fantail need to have at least 5 gallons for every inch of their length. They each grow to approximately 10 inches long, like the goldfish.

Nice info, xoenrt209. To add to your data, my koi/goldfish do fine in a 2 1/2 to 3 ft. deep 1,000 gallon pond. Also, I have calico fantails and they also do fine in my zone 7 pond, which ends up frozen over in winter with ice. I use a small de-icer to keep a hole open, and I keep my waterfall running all year, so the pump contributes a bit of warmth. All of these 'hibernate' during the winter. I also have some rosy minnows, which are active throughout the winter.

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I run mine through the winter too but I by-pass the waterfall during the winter. I have koi and they basically slow down to a slumber.