There are possibly 700 Starbases so 7 000-ship fleet is reasonable for Starfleet to maintain. Possibly even larger; however, we know that runabouts are included in NCC sequence and there is no way of knowing how large number of runabouts is when compared to capital ships, and I will do numbering for capital ships only. Given that by DS9 ship registries are in 70 000's, fleet of 30 - 50 000 ships with 7 000 to 30 000 being capital ships is reasonable.
In "The Dogs of War" Romulan commander is worried about losing "thousands of ships" in final assault on Dominion lines. But we have no clear figure.
Galaxy class: 120 (starting value)
EDIT: I ended my analysis, but Galaxy class appears too often, giving too low number of 682 ships in Starfleet. However, given that Galaxies will always be in middle of fight, just like Defiant, it is not very unreasonable to assume that actual percentage of GCS in fleet is lower. So I will assume that only 1/10 of fleet is shown, and only 12 Galaxy class ships within that part of fleet. So we have 6820 capital ships for Starfleet with 34 000 high limit.
I got these numbers from DS9 analysis:
120 Galaxy class starships
560 Excelsior class starships
610 Miranda class starships
90 Defiant class starships
180 Akira class starships
100 Saber class starships
90 Nebula class starships
However, other classes' appearances are less clear. Also, these numbers might be only ships that participated in Dominion war; given wierd warp speeds, Starfleet might or might not be able to get all ships to front lines. If entire fleet did participated in war, we have 6820 capital ships; if it did not, then number is around 34 000 ships.
I will now go with fleet sizes for all powers:
Lower value:
Starfleet: 6820 ships
Klingon fleet: 5456 to 6138 ships (2728 to 3069 BoP; 1705 to 1918 Vor'Cha; 682 to 767 K't'inga; 341 to 384 Negh'var).
Cardassian fleet: 1705 ships (1500 Galor and 205 Keldon class)
Romulan fleet: 974 D'deridex class warbirds
Breen fleet: 568 ships
Higher value:
Starfleet: 34 000 ships
Klingon fleet: 27 200 to 30 600 ships (13 600 to 15 300 BoP; 8500 to 9561 Vor'Cha; 3400 to 3824 K't'inga; 1700 to 1915 Negh'var)
Cardassian fleet: 8500 ships (7478 Galor and 1022 Keldon class)
Romulan fleet: 4856 D'deridex class warbirds
Breen fleet: 2832 ships
Additional analysis
There might be 1000 Excelsior and 300 Sabers in Starfleet. That means up to 2.5 times larger number, which gives 120 Galaxies, 1000 Excelsiors, 300 Sabers, 1200 Miranda, 180 Defiant, 405 Akira, 220 Nebula class starships, ending with 17 050 capital ships in Starfleet.
So:
Starfleet: 17 050 ships
KDF: 13 600 to 15 300 ships
Cardassian Guard: 4 250 ships
Romulan fleet: 2428 warbirds
Breen fleet: 1416 ships
UPDATE: It might be possible to get starship number by using number of starbases as basis. Here we have screenshot showing 16 ships (1 Defiant class, 2 Galaxy class, 5 Excelsior class, 4 Miranda class and 4 Centurion class ships) nearby. Highest starbase number we hear about is 718. If we use ratio of 20 ships for one starbase we get 14 360 ships (20 ships were what Captain Picard succeded in rallying for Klingon Civil War). If we use 16:1 ratio, we get 11 500 ships. However, not all starbases are space stations, so we can end up with 8 000 to 10 000 ships in Starfleet.
In "BoBW" we know that 39 ships will be replaced in "under a year". "Under a year" might be 6 months to 364 days. If we have 4 ships per month, with ships having lifespan of around 100 years, we get a fleet of almost 5000 ships for peacetime production. Given that Federation already fought several wars and probably boosted ship production during that time (possibly explaining large amount of Excelsiors) 8 000 ships is at least possible.
Starfleet size analysis on my site
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