When planning and building a pond, you need to stock it properly. Too many fish can cause all manner of problems for the pond and its inhabitants. You can stock the pond based on volume or surface area.
Stocking guidelines based on volume generally follow rules based on the number of gallons per fish. Sources vary, but one rule holds that you should stock a pond at a level of one goldfish per 30 gallons of pond volume. For koi, keep them at twice this volume, since they grow much larger than goldfish. Guidelines based on volume are typically intended to address the space needed for beneficial bacteria that break down fish waste.
By Surface Area
Most of the oxygen exchange in ponds happens at the surface of the water. So some guidelines work around the surface area of the pond to take into account the amount of oxygen the fish may need. A good guideline is to stock a pond with 12 inches of koi or goldfish for every 100 square feet of surface area. Keep in mind that goldfish in a pond can grow to a foot in length, and koi may reach 3 feet.
Keep in mind that all of these guidelines assume some degree of filtration. Without sufficient filtration and water movement, the ability of a pond to sustain fish is limited. Not only do fish need oxygen, but the bacteria that break down fish waste also depend on oxygen. Without sufficient water movement and oxygen exchange, the fish will suffer not only from hypoxia, but also from ammonia poisoning as the pond loses the ability to break down fish waste.
Dangers of Overstocking
If you overcrowd your pond, you can have several problems. Like ponds with insufficient water movement, oxygen problems begin quickly in overcrowded aquariums. This also leads to high levels of ammonia. Ammonia is toxic to fish, and can kill both goldfish and koi. Additionally, ammonia and related chemicals promote the growth of unsightly green water algae. This algae can wreck further havoc on the pond and its inhabitants.