I'm trying to calculate which percentage of Roman empire population was involved in the military. According to this article Imperial Roman Army, in 211 AD the size of the imperial Roman army was around 450,000 at its peak. is it known an estimate of which was the population of the Roman empire around 210 AD?
Giulio Castelli, scholar of late antiquity, wrote on his blog (in Italian) that the population of the Roman Empire oscillated between 80 million people in the first half of the second century and 40-50 million in the fourth and fifth century after pestilences and invasions.
Here is written that the Antonine Plague killed off as large a percentage of the population as the Black Death did in the Middle Ages. Since this is believed to have killed one third of all people in Europe at that time, the Roman population would have decreased to around 55 million people by 180 AD. I think the Wikipedia article has an overestimation, plus, it seems to consider only the 160s. In any case, you can assume a population of around 50 million people by 210 AD.