How big are Star trek fleets?

Assuming a UFP population of around 1,000,000,000,000 (a 'trillion') then 0.001% of the population would be approximately 10 million personnel, which might be in the ballpark for the 'peacetime' component, but is only about the same as the active component (not including reserves or paramilitary forces) of the eleven largest militaries on Earth (just over 10.1 million) serving a population of over 3.76 billion people. Which gives us an average of about 0.26% or about ten times more than my proposed figure for Starfleet. Which given that Starfleet appears to handle a lot of non-military 'civil service' jobs as well would seem to suggest that I might be lowballing.