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I know that there isn’t any good information to base any numbers from but I wanted to attempt to work out the sizes of the navy’s in the galaxy. I just want to know if these numbers are believable.

Size of Hivefleet Kraken
I think there’s a minimum of 864 bio ships in Hivefleet Kraken, 96 Hiveships, 192 cruisers and 576 escort bioships.
Ive worked this out by using information from 7th edition Tyranid Codex pg23 that says splinter fleets can be between a few dozen to a few hundred bioships also on page 17 it says there can be as few as 12 hiveships or bioships in a splinter fleet.
Using the fleet information from the Battlefleet Gothic Armada supplement book that says for every hive Ship you can have up to 2 cruisers and between 6-12 escorts then a small splinter fleet with a dozen bioships will only have one hive ship and around 12 other ships and the larger splinter fleets will have up to 12 hiveships and a hundred or so other ships (108bioships), this keeps in line with the Codex so far.
Using information from the attack on Iyanden Craftworld, hivefleet Kraken attacked in around 7 waves plus one that attacked Ichar if I assume a wave equals to the size of a large splinter fleet then I can multiply 108 bioships by the number of waves 8 in total to get 864 bioships in total.
I know this math isn’t perfect and I’m assuming a lot. I’m not mentioning the millions of spores and other small Tyranid swarm ships.


Size of the Imperium of man’s fleet.
The numbers that I am going to state here are the minimalist amounts of ships in the Imperium of mans Imperial Navy, I have deliberately attempted to make the size of the whole fleet as small as reasonably possible. There are 250000 ships in the whole Imperial Navy 20161 are Battleships, 72580 Cruisers and 157258 Escorts.

There are many ways of looking at this but the most prominent way people tend to use is to work out the amount of Sectors in the IOM then multiply the known sizes of Sector Battlefleets.
So here goes, assuming there are only 1 million imperial worlds in the Imperium of Man, excluding Mechanicum worlds and Worlds without civilians on and so forth. If we go of the idea that there are on average 200 worlds in a sector based on a FFG book (Rogue Trader) that indicate’s the average sector caps off around 200 worlds.

1000000 worlds divided into sectors of on average 200 worlds equals 5000 Sectors in the Imperium of Man. According to the Battlefleet Gothic Rulebook pg.. each Sector has a fleet of between 50-75 ships on average. If we use the lower number of 50 ships in each fleet and multiply that by the amount of Sectors then we get a number of 250000 ships of the line in existence throughout the Imperium.

If we use Battlefleet Scarus as a basis for the Imperium’s fleets then according to the Book Eye of Terror Battlefleet Scarus has 5 Battleships, 9 cruiser squadrons and 13 escort squadrons. If we assume a cruiser squadron has 2 cruisers and a escort squadron has a minimum of 3 frigates or Cobra class destroyers then we get a total ship count of 62 ships. Interestingly this number is near the middle number of 50 and 75 ships.
The Battlefleet Scarus has then, 5 Battleships ,18 Cruisers and 39 Escorts. If we turn those numbers into percentages then 8•06% of the fleet are made up of Battleships, 29•03% are cruisers and 62•9% are Escort ships. Assuming Battlefleet Scarus is a typical example ,if we use those percentages to work out the amounts of Battleships/Cruisers/Escorts in the whole Imperium Navy then we get a grand total of 20161 Battleships, 72580 Cruisers and 157258 Escorts.

Sorry for the large amount of writing let me know what you think
Thanks

(Sisters of Battle rule!)

reading the first book in the siege of terra series at the moment and Horus's fleet had 10k ships, not sure if thats including others, is the whole force or whatever but that was just one part of the attack, going though the book so far it looks like just a portion of the traitor forces are attacking terra and were already at 40-50k ships and we havent seen all the traitor fleets I think