Couple of comments:

1) 10TB with 15K disks in a new purchase wouldnt really make sense - I would probably go SSD.

2) Space calculation of usable -

If you wanted to use 600GB 15k disk (2.5 or 3.5?) it would be 10000 x 1.33 (RAID overhead) or 23 disks + spares. Depending on form factor you are dealing with 12 or 24 (or 30) disk enclosures and you need at least one spare per each. So 2 x 12 disk enclosure = 24 slots or 22 active disks; depending on how close you want to be you would need 3 enclosures of 3.5 disks and put 10 - 10 - 6 disk into them. 

Alternatively you could use 3.84TB SSD (3.65 space) and do it as 1 enclosure with 6 disks

Note: I used 33% to represent RAID5 style overhead here - in heavy write environments (non-SSD) you are by default writing in RAID10 (50%) and migrating to RAID5 over time - so if you are doing a lot of writing then you should add disks.

In all sizing exercises you really should be starting with what is the workload and what is needed to support it - but this will get you started.