Some other games and books have come up with figures:
Federation Reference Series:
36 Saladin
13 Achernar
12 Federation
22 Renner
26 Knox Class
22 Avenger Class
3 Menhaga
7 Mitannic
28 Belknap
8 Enterprise
10 Asencion
9 Federation(uprated)
514 Independence Class Transports
306 Sherman Class Transports
15 Ptolemy Class
In addition, the related SPO book "Starship Design" suggests
362 ships of ALL types are constructed over a 5 year period, Of which 46 are cruisers and above. The total here is
1031. This doesn't include all possible ships, but major classes. I suspect they felt it was the bulk of the fleet.
Starfleet Dynamics puts the fleet size at
3137, of which only
937 are major combatants.
The STNG FASA manual:
38 Excelsiors
50 Enterprise
26 Constellation
240 Decker Class
12 Royal Sovereign Class
13 M'Benga Hospital Ships
17 Sagan Class Science Vessels
33 Wellington Class
25 Paine Class
22 Moscow Class
15 Ambassadors
2 Galaxy Class
3945 Shuttles
1500 Long Range Shuttles
That's
593 major ships.
In the "canon" universe there is no set number, yet if we assume as many fleets as numbers (I believe 9 is still the highest?), then we multiply it by the 600+ of Sisko's fleet, we have at least
5400, though the composition is uncertain. Are they all warships? To sustain a war with the Dominion, a power which summoned over 2000 ships for an invasion, Starfleet must come somewhere near them in total numbers, though not over(add to that allied fleets of course).
For what it's worth to the discussion, over in the Star Fleet Battles universe, the game Federation & Empire (F&E) is considered to be a massive game. The General War starts in Year 168 (after contact with the Vulcans) between the Klingons and Lyrans vs. Kzintis and Hydrans (Lyrans and Hydrans are on the far side of the Klingon Empire). The Federation has at that time 125 ships (including 30 Constitution-class Heavy Cruisers & Command Cruisers), plus 47 older ships in mothball status. They build another 34 ships befor getting pulled into the War in Year 171. The General War runs for another fourteen years, to Year 185, during which time the Federation builds roughly another 773 ships, of which 332 are Light Cruiser size and 354 are War Destroyer / Frigate size. In the game, they lose tons of ships of course, but assuming they don't lose a single ship they would have a fleet of 979 main-line ships.So, when you're talking fleets of 6,000 to 19,000 combat ships, it boggles the mind. I would not want to game that out.
Automation should have reduced the need for personnel, much like on ships of the current navy. Even at half your total and .002% the Federation could have a lot of beings in Starfleet.
Using the US as an example again, just for the sake of it
Active duty personnel armed forces 1,281,900
This is .004% even with that ratio using the Federation population, Starfleet should have at least 395 million members on active duty.
Or using the UK active armed forces 196,840 including reserves, population 64.1 million
Ratio 0.003% or 302 million members. Lets assume a third are human since it is a Terran based organisation thats 100 million humans in Starfleet.
A plausible in universe scenario?