Given how old the galaxy is and how many stars are in it, Federation space and the surrounding star systems are remarkably mundane. We know that by the late 2300s the Federation spans around 8,000 light years in 2 dimensions, but space is 3 dimensional, and it stands to reason that since the thickness of the Milky Way is 1,000 to 2,000 light years, the thickness has been completely explored.

Now, before we get into actual calculations, Federation space is only a fraction of explored space, but I'll keep that out of the calculation for now. Lets assume a simple square of 8,000 x 8,000 light years with an average thickness of 1,000 light years. That is a volume of 64 billion light years. Some googling indicates that there are around 0.0025 star systems per cubic light year.…