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My towel bar is about 4-1/8-inch in height. I've no problem reaching my towel from where it is hanging.
Oh my!
There is no specific height mentioned anywhere. It depends on the accessiblity and ease of individuals. I have it at 50 inches. Its your bathroom and you need to figure out at what height do u need it...
I would suggest you to keep it neither too high nor too low. It should be easy to reach for you.
There is no real standard for towel bar installation, however, a common height is about 2" to 3" above counter surface height. Some bathrooms may call for the towel bar to be installed under the window because of a lack of wall space. In this case the height may vary according to the window height.
Where possible, choose a long rod (24" at least). This way you will be able to hang one bath sheet or 2 hand towels.