The appropriate dimensions for horse corrals is important for the health and safety of both the horse and handler. The number of horses and size of horses will help determine what size corral is going to be needed.
For a single horse, a corral of 10 feet by 12 feet and 5 feet high will be sufficient. This is considered small, but is plenty of room for a short stay. Most public corrals will be this size.
The standard rule of thumb is a corral should be at minimum 10 feet X 20 feet. This size will accommodate two horses that get along. You should expand the corral by half of that for each additional horse. Larger horses or aggressive horses may need larger corrals, and should be corralled either alone, or only with other horses which they are familiar with. It's a good idea to have the height at least 5 feet to prevent jumping.
Many cities have ordinances in place that specify how large a corral should be. If you are building a new corral and are unsure of what the regulations are, you can check with your local equestrian society for more information. They will be able to provide you with any regulations that may affect your building process.