It's tough to say because the best thing that we can go off of is Herodotus who gives us specific numbers of soldiers that make up each unit. All in all, these add up to around 2.5 million people. This includes both soldiers, and sailors. However, with support personnel, such as cooks, and camp followers, this should be put at a higher number. However, modern scholars throw away this number because it is quite unrealistic. Some modern scholars say that it is closer to 300,000 which is much more realistic. I don't know exactly how they landed on this number, but there are many problems with a larger army such as Herodotus described. The largest of these is that the land of Greece would not be able to support that large an army for any sort of sustained period. Feeding an army that large would be near impossible. In addition, supply of water would pose a huge problem to such a large army. Again, Greece does not have that many large sources of fresh water.