I do not see the Raid 10 or 1+0 option in that Raid calculator. Only the 0+1 or Raid 01 is there (apart from the base raid levels). For what I understand the first level of RAID 10 would be Raid 1 which creates the mirror and then Raid 0 on top of that to create the performance effect. To then calculate the space available after everything is done for a RAID 10 we would use the following (Assuming all hard drives are the same size. If not then the smallest is the base space for all the rest):

M = Mirrored Discs
N = Number of Discs
C = Capacity of Discs

(N x C) / M = Space Available

In your case it would be:

M = 2
N = 4
C = 3TB

(4 x 3) / 4 = 6TB Space Available

So what you reckon about the final size is true. What I might think is happening is that the total REAL space available from each drive is been subtracted from the total final size. So if for example each 3TB hard drive is really a 2.7 or 2.8TB hard drive (The actual usable space you can work with in the hard drive). That is about 1.2TB to 800GB of missing space. So you would be going from the 6TB in theory to the real 4.8GB or 5.2GB. Maybe less, maybe more.