A review of Simon Sebag-Montefiore , Heroes: History’s Greatest Men and Women at Mercator.net concludes thusly:
There was one glaring error: Alexander the Great’s height is given as 4’ 6”; but would make him the same height as the crippled poet Alexander Pope, and is never mentioned by the ancient authorities; surely the author means 5’ 6”, similar to Napoleon’s and quite a respectable stature?
I’m not sure we know what height Alexander was … over at Pothos.org there’s a reasonable guess of 5’6” or 5’7” …
rogueclassicism 
How on earth could anyone guess at such a thing? There is nothing to suggest Alexander’s height.