as the question states.
I am curious as to how common it was for a man to have served in the army during this time and how that compares to the modern day.
Any approximation would be appreciated and if you could also cite where you got the information from that would be great
I unfortunately cannot cite this as I write this from memory. I work for the chair of Roman classical history on a big German university as a scientific assistant. Please don't use uncited information in academic papers.
New estimates talk of a population of 50-55 million people in the whole Roman Empire in Augustus time. However this includes all provinces and colonies. Augustus was the first to introduce a standing army to the Empire, which consisted of approximately 300.000 soldiers. This army was again divided into different parts, mainly the legions and the auxiliary forces. Only Roman citizens could become a legionary whereas anyone could join the auxiliary forces. There were about 100.000-115.000 legionaries in Augustus army. For the percentage you have to do the math, but decide if you only want to include Roman citizens or all inhabitants of the Empire. I hope that helped a bit