I often think that it is hard to grasp the scale of the Imperium. I think a lot of 40k material consistently underestimates or misaligns scale. I like certainty and order in a setting; however, given the nature of 40k, a multi-author universe with hundreds of different interpretations, I'm unlikely to ever get it.
Nevertheless, I'm going to crunch some numbers. I'm going to attempt to set out my own interpretation of the scale of various facets of the Imperium, and you can tell me if these numbers ring true or not. I'm going here more on "gut feel" than canon sources, but if you are able to retort with evidence based on the canon that shows I'm wrong, by l means do so!
How many planets are there in the Imperium?
Multiple sources in the canon describe the Imperium as "an empire of a million worlds." The 1,000,000 number is one I never used to like, as I kind of want the Imperium to be bigger. After all, there are potentially several tens of billions of inhabitable worlds in the galaxy. However, the number is pretty ingrained.
Of course, it's obvious that no one in the Imperium knows exactly how many worlds it contains. it's like trying to say "how many people are currently riding on the London underground"? or "How many pigeons are currently flying over New York?" In the time it takes to ask the question, the number has changed, and it changes again in the time it takes to answer, and every second thereafter. New worlds are always being discovered, other worlds are being lost.
If we take it as read that the Imperium has "about" a million worlds, though, this does give us a starting point of sorts.
How many sectors are there in the Imperium?
My gut feel, based upon what we've seen of Imperial Sectors that are fairly well detailed in the Canon like the Scarus and Calixis sectors is that a "typical" Sector has about 200-250 inhabited Imperial worlds within it.
Of course, within the geographical boundary of the Calixis sector there will also be tens, possibly hundreds of thousands, of uninhabited and largely unexplored worlds.
If we assume (I know, I know, it's a big assumption, and I freely admit I could be wrong) that there are 200-250 worlds in each Sector, then just on numbers alone we're looking at somewhere between 4,000 to 5,000 Sectors.
These numbers feel about right to me. Figures in this region mean that there are 4 or 5 Sectors for every Space Marine Chapter, which gels well with their being a rarely seen force to the vast majority of citizens within the Imperium. Assuming most Chapters are based within Imperial space (I know,assumptions assumptions) this means that about 1 in 4 or 1 in 5 Sectors has a space marine chapter based somewhere within its boundaries.
How large is a Sector Battlefleet?
Again, this is a gut feel, there's no canon source for this, but I have always felt that the Imperial Navy has a 1:1 planet:ship ratio for its battlefleets. So a sector with 213 planets would be allocated 213 ships by the Imperial Navy.
I know I'l get criticised for plucking these numbers from thin air, but all I can say in my defence is that a 1:1 inhabited imperial world:imperial navy ship ratio feels right. It has a brutally simple logic to it, the sort o logic one can imagine an administratum scribe backing.
A Sector battlefleet might consist of a handful of battleships, 20-50 cruisers, and the remainder of the fleet would consist of escorts, frigates and light cruisers.
This sounds like a powerful force, but those 213 ships have to guard not only individual worlds, but the space lanes between them, and conduct patrol sweeps across the vast areas of wilderness space between the Sector's inhabited worlds.
How large is a Sector Merchant Fleet?
The Rogue Trader RPG describes the merchant fleets as amounting to around 90% of space traffic. Assuming that the space marine fleets, arbites fleets, black ships and the imperial navy between them make up the remaining 10%, then there's going to be a ratio of at least 9:1 for navy: civilian vessels. Meaning that in our theoretical 213 planet sector, there will be at least 1,917 civilian ships plying the space lanes, probably in practice more like 2,000.
Again, there is no canon source for this; but these numbers feel right. This number of ships would make the colossal crusades of the Imperial Guard feasible, and they would allow trade between worlds within and outside the Sector.
Anyway, what are your thoughts on these numbers so far?