There are regulations set down for legal requirements of a stair railing height, which must always be obeyed when constructing or remodeling a home. If a person intends to replace or renew a stair case they must follow these legal codes with regard to building regulations.
There is one date you need to remember: the standard railing height requirement was set March 15, 1991. If your current stair railing was installed prior to that date, you will probably (or should) have a hand railing of between 36 and 37 inches from highest surface of the stair treads. This refers to the tops edges of the handrail and not the lower edge. If a staircase has risers equal to or more than 30 inches in height a hand railing needs to be installed at 36 to 37 inches from the top of the tread. A hand railing must be installed of there are a series of steps rising more than 30 inches from ground point.
If your stairs were installed after 15th March, 1991, your hand railing cannot be shorter than 36 inches from the top of the tread on the stairs. Stair hand railings must also not have any protruding edges that can cause potential injury, either. Guard railings must also follow approved guidelines. There are also tread and riser laws too.
TIP: For best results, consult your area's building codes to verify these regulations and check for any unusual extra regulations you need to follow. You will also need to find out the regulations for stair width and related factors, especially if you think you'll have to rebuild the steps to accommodate disability equipment sometime in the future.