The ideal height for a pull-up bar would be different depending on your height. It will have to be so high that you can't touch the ground with your feet when you are hanging freely. But in a home setup, you are limited by the height of your ceiling. Pull-up bars should be mounted in a way that will give you enough room for performance. You have to be able to at least touch the bar with your chest. Ideally, you have to be able to perform a full muscle up. In the highest position, you would need to stand on your fully extended arms. You will also want to be able to hang freely without touching the ground with your feet if possible. I have a ceiling-mounted bar, so I have little room above the bar - 12.5". This is just about enough to come close to a bar with my chest. I'm also with my feet on the ground when I hang freely from a bar. Not ideal, but you have to compromise if you don't have high ceilings in your home.