Do women have less red blood cells per mm^3 of blood than men?

Yeah, it is! But for a slightly different reason than those quoted here. The other answers blame the different numbers of RBCs on the action of sex hormones or menstruation. But neither affects RBC count. read more

Now that we have out of the way, let's get down to why exactly the two sexes have different haematocrit levels (volume percentage of red blood cells). Short answer: Females have a higher level of tissue oxygenation than males for a given RBC mass, implying that females have a more efficient delivery of RBCs to body tissues. read more

Females are capable to elevate their haemoglobin / red blood cell levels to external stimuli, yet at same conditions (same altitude etc) the difference remains. Also: Men, premenopausal women and postmenopausal women have similar plasma erythropoietin levels, indicating that women do not attempt to compensate for their lower haemoglobin levels by increasing erythropoietic drive. read more

Probably because they have less mass per unit volume than men because most women have a significantly lower mass to men but most women aren't that much smaller than men in terms of overall size, this means that the amount of oxygen required in any one area is less at any one time compared to a man in the same conditions. read more