As I grew up, I was taught that a goldfish will only grow to a certain point dependent upon the size of their container and how many fish are in the container; all the fish within the same container would be limited by this rule.
Is it true that the growth of a goldfish is limited by its container size?
Toxotoes answer references an article on trout studies. There's no basis for equating a study on trout with that of goldfish. Moreover, the study referenced doesn't even support the researchers hypothesis.
Unlike other aquarium fish, goldfish excrete a hormones such as aminobutyric acid (GABA) and somatostain, that acts as signal of how many other fish and what sized body of water they are in.
In the wild, this will regulate their size and the size of others and help keep them from running out of resources. While the GABA / somatostain regulation is an example of a "crowding effect", it shouldn't be confused with the stress based responses common to all fish in which epinephrine and norepinephrine increase due to poor living conditions (bad water and overcrowding).
Refs:
http://jeb.biologists.org/content/203/9/1477.full.pdf
http://thefishvet.com/2012/02/28/do-goldfish-grow-to-the-size-of-their-tank/
My understanding is that this is a myth with a sort-of truth to it: Fish in undersized tanks are more likely to be stressed due to a lack of swimming space (if the species is an active swimmer), overcrowding, and poor water quality, which leads to health and feeding problems. So the growth may be stunted, but it's not something you can really consider as a healthy approach to housing them.
One reference I found to support this is Effect of tank size on food intake and growth in individually held juvenile rainbow trout Oncorhynchus mykiss (Walbaum), by Tomi Ranta & Juhani Pirhonen in Aquaculture Research. They note a surprising lack of research in this area.
It's true-ish. Goldfish don't naturally stop growing, but if their environment is poor (which is usually the case in a smaller tank), they won't be healthy and that will stop/slow their growth.
There is an element of truth to this, but it is not as innocent as it sounds and is related more to water quality than tank size. When properly cared for, goldfish will not stop growing. Most fishes are in fact what are known as indeterminate growers. This means that, unlike humans, they grow until they die. What really stunts a fish’s growth is poor water quality and improper care. In smaller aquariums or bowls, water quality is typically very poor. With little or no filtration and infrequent water changes, goldfish suffer. The stunting that results is not a good thing. Rather, it is a sign of ill health, and, frequently, stunted fish take on a deformed appearance and die at a young age. As already stated, some goldfish grow very large, so it is important to know what size your fish will attain before purchase and to make sure you can provide it with the proper care it requires.
Goldfish are limited in size by the hormones they release. They do this for instances in the wild where they are trapped in small pools or to inhibit the size of their competitors. But this does not mean keep a goldfish in a small tank or overstock a tank. This is because the hormones that inhibit growth are first released into the water before being absorbed, since they want to try to inhibit competitors over themselves. So unless you never do water changes or do them super infrequently, you remove the hormones from the water. The stunting that most people see means they either somehow found the perfect balance between water changes and hormone level, or they are killing their fish by not doing enough water changes or keeping them stressed out enough to release large amounts of the hormones which can not get affected by water changes, both of which will impact the health of the fish. Goldfish release this hormones in small or crowded tanks because if they were any bigger they would die.
Directly Sources used: https://www.fishkeeper.co.uk/faq/will-my-fish-only-grow-to-the-size-of-the-tank/ https://petkeen.com/do-goldfish-grow-to-the-size-of-their-tank/ Sources referenced: https://cosmosmagazine.com/nature/do-goldfish-really-grow-to-the-size-of-their-tank/?amp=1 https://www.inverse.com/science/why-are-these-fish-so-big/amp
