## Convert Disk TB to File TB

You may have noticed that when you buy a hard disk or other storage media, the reported size is always greater than the size presented for file storage in your computer once the disk is connected and formatted for use. Some of this difference is due to overhead caused by partition tables and file systems like GPT and NTFS, but a large part of the size difference is the way that the disk manufacturers calculate TB (powers of 10) versus the way that the computer operating system calculates TB (powers of 2).

Here is an example using 16T of purchased disk space and converting to base two for a resulting lower number of raw disk space according to computer calculations.

${\dfrac{16\times10^{12}}{1\times2^{40}}} \approx {14.55 \text{ TB base two}}$

$1-\dfrac{14.55}{16} \approx 9.06\% \text{ less than TB base ten}$

Note that the raw disk is usually low-level formatted by the manufacturer to mark bad sections as unusable prior to shipping. This could cause the initial usable size even in base 10 calculations to be less than reported on the box – normally manufacturers account for this by making the disk a little larger than needed so the usable base 10 size will still be above the number on the box after bad sectors have been excluded.

For scientific people, the conversion is based on the ratio of TiB (tebibytes or $2^{40}$ bytes) to TB (terabytes or $10^{12}$ bytes). I usually avoid the *bibytes discussion because it causes more confusion for end users. Computer software and hardware almost never uses the explicit units KiB ($2^{10}$), MiB ($2^{20}$), GiB ($2^{30}$), TiB ($2^{40}$) but this is implied and must be deduced by the user based on the context and obvious capacity difference from straight base 10 media sizes. I prefer to just say that the conversion is due to a difference in the base-two binary units vs the base-ten decimal units KB ($10^3$), MB ($10^6$), GB ($10^9$), TB ($10^{12}$).