There is no standard size, but for professional standard, it had better be 16.5"(419mm), some also have 16"(406mm).
I am 1.9m tall and I play a 16.5", I have a 17" also but I won't play it, for the matter of timbre.
If I were you, a 16.5", can't cope with it? a 16", still can't? then must be a 15.5", or you may learn violin instead.
Some researches state that a 16.25" is the best but there is no such cases, so consider yourself.