The absolute minimum depth for a koi pond is generally accepted to be at least four feet deep over most of it’s floor area.
If possible, five or six feet deep would be much better. Koi use different muscles to swim at a constant depth to the muscles that they use when they also swim up and down through greatly differing depths. By providing them with the opportunity to regularly exercise all the muscles in their bodies, they will develop much better body shape. In an unheated pond in winter they will fare better if they can retreat from the cold water near the surface to the relatively warmer water at the bottom of a deep pond.
A well designed Koi pond should not have any sharp edges, either in the pond or hanging immediately over the water surface. Koi are not, by nature, skittish fish but will occasionally dart away from an unexpected movement. At feeding times, hungry fish will try to climb over each other to get to the food. Sometimes Koi will dart forward to flush water through their gills to clean them. If there are objects in the pond or if there are overhanging rocks, then the Koi may injure themselves. At best, these injuries may leave a scar that would spoil the look of the fish. Worse still, the wounds may become infected, and, if untreated, the infection could lead to the death of the fish.
While it is arguable that a few small Koi could be kept in a large pond which has no form of filtration, it is, without doubt, impossible to keep a pond full of Koi without proper filtration. A Koi pond should have a filtration system suitable for the number of fish and the size of the fish that it will eventually have to support. A point that is usually well understood is that the biological section of a filter system deals primarily with the waste products of fish. Less well understood, however, is that these waste products depend more on the amount of food (and type of food) that the fish eat than the size of the pond. So, do not buy filter systems solely on the size of the pond. It is wise to ensure that your filtration will cope with the expected ammonia load that the fish will produce.