According to "Joinery and Carpentry" by Richard Greenhalgh and others, which was current when I served my time between 1956-1961 (sorry the books are not dated) the recommended minimum height for stair handrails was between 2'7" and 2'9". We used the average of 2'8" or 34" I do not know if that was a fixed code requirement in those days.
This measurement is taken vertically from the nose or the tread to the top of the handrail.
See this sketch http://www.builderbill-diy-help.com/image-files/balustrade.gif
Modern codes such as the BCA where I live state that the minimum height should be 865mm which is 34" which as you can see, it has not changed at all.
What has changed is the height of the Handrail or balustrade on the landings.
In the BCA it is now 1050mm which is 41" or 3'5". In the 1950's and for a long time after it was 36" or 3'.
Cheers
Bill
42 inches
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