system
Given the following post, respond as if you're commenting on Reddit:
human
[40k] How big is the Imperial Navy?
gpt
There are no concrete numbers. We know how it's organized, and the aproximate size of various fleet-missions, but we have no idea how many fleets exist, or how many ships are in reserve at any given time. 

The Imperial Fleets are divided into Sigmentum Commands, one for each of the Imperiums 5 Sigmentums. These overall commands are then subdivided by Sector commands, under which the command of the entire Sector Fleet is assigned. The Sector Fleet is then further divided into individual task forces, ranging from patrol and escort, to seek and destroy. The size of a fleet depends on further conditions, such as the danger of the area, the value of cargo, expected threats etc.

Typical escorts in most areas consist of between a single Destroyer, to as many as a dozen. On rare occasions, a Crusier may be assigned to the escort as well. 

Patrolls typically consist of half a dozen Destroyers and a Crusier, though can range as high as several cruisers, a battleship and more thana dozen Destroyers in dangerous areas of space. 

Colony flotillas typically consist of a cruiser and up to 6 Destroyers, along with several personelle transports. 

Major battlefleets can consist of more than a score of Cruisers, several battleships and dozens of destroyers.

Some pivotal battles in the Imprriums history have seen massive fleets, numbering thousands of ships. And they've only really counted the fleets in the emediate vacinity. Armageddon, for instance, hasn't even had an entire Sector committed (yet, the front is constantly expanding) and it's committed more thana thousand vessels.

Put on top of this Mechanicus Fleets, Astartes fleets, Rogue Trader fleets and PDF fleets, which are not under the umbrella of the Sigmentum command... It's impossible to know.