What is the regulation height for a wall mounted hand rail, and where is it measured between?
If you mean the hand rail that you hold onto as you walk down stairs then it is a minimum of 30″ and a maximum of 38″ above the nose of the tread. This is the regulation for the State of Wisconsin (Section 21.04 # 3 b). It should be pretty uniform for the rest of the USA but I can’t guarantee that. It need to run the length of the stairs for any stairway more than 3 steps. There are also regulations in regard to the size and shape as well as the strength of the mounting. But i you use a standard railing and normal hardware you will be in compliance.
