How tall a horse can grow depends on several factors. The most important factor is genetics. While there are horses recorded in history that stood over 20 hands high, The average horse is around 15 or 16 hands. How tall a horse can grow depends on their breed and lineage. To calculate how tall a young horse could potentially grow, you should look at its parents, Sire and Dam.
How tall a horse's parents are is a good indication of how tall a young horse will grow. But genetics is always a gamble, so there is no guarantee that a horse will be the same size as its parents. But as a general rule, on average, a horse will mature the height its parents were. A horse generally will not grow taller than its tallest parent, although we have exceptions to this rule on our own farm. (Though the offspring is taller than either parent, however, he is shorter than his tallest grandparent). The offspring will rarely grow taller than it's tallest parent, and almost never grow taller than its tallest grand-parent. If you want your young horse to grow as tall as it possibly can, genetically , you should make sure that your horse is on a good well-balanced diet, has plenty of turn out, proper veterinary care, and is not started under saddle too soon or too heavily. These factors all affect how tall a horse can grow.