There's no direct ratio established. Just to give you an idea though, the one study I'm aware of puts the amount of nicotine in a puff of a full flavored cigarette at 0.1mg. An equal puff of a 16mg e-cig was 0.01mg. The absorption rate of the cigarette is estimated at >95%. The absorption rate of nicotine in ecig vapor is estimated at 30-70%, depending on the technique of the vapr. Also, a typical vaper takes a longer, larger drag from an e-cig than he does a cigarette, so that has to be accounted for as well.
Doing all the math and taking all the variables of hit size, vaping technique, strength of juice and absorption rate into account, the answer is, nobody really knows.