During a viewing of the Nutcracker, sometime around the battle between the soldiers and the mice, my thoughts turned to warhammer 40K and I was thinking about the setting for the Jericho reach in Deathwatch. I wondered just how to represent the size of the Imperial army and came up with a recruiting concept to put things in perspective.
What if the goal of the Imperial army was to muster a fresh Billion ( or 1,000,000,000) soldiers for the Imperial army per day. That would be 1,000 on average per world in the Imperium. Assuming the average population of a given world was about a billion, averaging out barely populated mining and frontier worlds, with ultra populated hive worlds with populations in the tens of billions. 1 billion per world might even be conservative. That would mean that the imperial tithe for a given world would be approximately 360,000 a year for a planet with a population the size of India or China. Assuming a growth of 1% a year, which might be low given that Earth has been growing about 2% a year until recently, there would be another 10 Million people added per year on said planet. The Imperial Tithe would represent 3.6% of population growth ( or, the populace would need to grow 1.03% per year to maintain a 1% growth rate including seepage).
The Achilus Campaign has about 6 Billion soldiers devoted to it which means it would have taken about a week to raise (in the entirety of the Imperium). Since the Imperium has countless crusades going on and countless soldiers being thrown into the meatgrinder, this is only 1 of many campaigns going on.
Bear in mind though, that a billion soldiers sounds like a lot, but spread over the galaxy, it dillutes to insignificance. The Imperial Guard is like the Russian army, lots of soldiers thrown into the fires of war for little gain and with alot of losses expected because, well, there are lots of other people you can recruit to replace them.
In addition, getting these soldiers to the right place is difficult,due to logistics, administrative errors, bureaucracy, warp storms, the limits of how many troops the fleet can carry (a main limiting factor), warp storms, planetary rebellions, corrupt planetary governments. etc. etc.
Compare this with the Tau. Many people would wonder why the Imperium has not crushed the Tau which is a tiny empire compared to the Imperium. If the Imperium is like Russia, The Tau empire is like Israel. On paper Israel should have been crushed by the arabs ages ago given the sheer size and population of the Arab world compared to the Israel, however, history has shown the opposite. Israel won because it is a tiny country with superior weapons and doctrine (like the Tau) against an army of conscripts with poor logistics (like the Imperium). The tiny size of the Tau empire allow them to have compact and efficient supply lines to get re-enforcements into the battle quick while the Imperium must send troops vast distances to keep the war going (the book Savage Scars, highlighted this quite well).

