You’ve just bought a new hard disk or USB flash disk with one capacity specified, but when you install it or plug it in, Windows shows another capacity? Various thoughts are running through your head: had the manufacturer fooled you, or is that a piece of defective hardware, or something else? Do I need to make a complaint? In this article, we’ll try to explain why you see less capacity on your hard disk than the manufacturer specified and the whole confusion about units and byte calculations.
Take a look at these screenshots from my computer; I have a hard disk with a capacity of 1 TB, according to its specification, but Windows only shows 931.39 GB (almost 70 GB less than what the manufacturer specified! ):
* To open this prompt press Win key + R to open the Run dialog box and enter: diskmgmt.msc
And here is the result of my USB flash disk, Windows shows 14.5 GB, although the manufacturer specified the capacity of 16 GB (1.5 GB is missing here):
As we mentioned, this can cause a lot of confusion, so let’s try to demystify this mess. In my high school I had learned that 1 KB = 1024 B, 1 MB = 1024 KB, 1 GB = 1024 MB, and so on; so, we used binary addressing, where multiples are based on powers of 2 (210 = 1024).
The confusion came later, with the standard IEEE 1541-2002, which had to define the use of prefixes for binary multiples of units of measurement related to digital electronics and computing.
IEEE 1541 sets new recommendations to represent these quantities and unit symbols unambiguously:
- a set of units to refer to quantities used in digital electronics and computing:
- bit (symbol ‘b’), a binary digit;
- byte (symbol ‘B’), a set of adjacent bits (usually, but not necessarily, eight) operated on as a group;
- octet (symbol ‘o’), a group of eight bits;
- a set of prefixes to indicate binary multiples of the aforesaid units:
- kibi (symbol ‘Ki’), 210 = 1024;
- mebi (symbol ‘Mi’), 220 = 1048576;
- gibi (symbol ‘Gi’), 230 = 1073741824;
- tebi (symbol ‘Ti’), 240 = 1099511627776;
- pebi (symbol ‘Pi’), 250 = 1125899906842624;
- exbi (symbol ‘Ei’), 260 = 1152921504606846976;
- that SI prefixes are not used to indicate binary multiples;
- a set of prefixes to indicate decimal multiples:
- kilo (symbol ‘K’), 103 = 1000;
- mega (symbol ‘M’), 106 = 1000000;
- giga (symbol ‘G’), 109 = 1000000000;
- tera (symbol ‘T’), 1012 = 1000000000000;
- peta (symbol ‘P’), 1015 = 1000000000000000;
- exa (symbol ‘E’), 1018 = 1000000000000000000;
The bi part of the prefix comes from the word binary, so for example, kibibyte means a kilobinary byte, that is 1024 bytes. And kilobyte is 1000 bytes, according to this notation.
This standard was issued in 2002, and after a trial period of two years, in 2005, IEEE 1541-2002 was elevated to a full-use standard by the IEEE Standards Association – and was reaffirmed on 27 March 2008.
OK, this solves one part of the puzzle, so if you had learned in your school that 1 MB = 1024 KB, overwrite that entry in your brain with the fresh one: 1 MB = 1000 KB, and 1 MiB = 1024 KB.
The second part of the confusion why you see less capacity on your hard disk than what the manufacturer specified is the fact that hard disk manufacturers traditionally use the standard decimal meanings of the prefixes.
So, regardless of the new standard, hard disk manufacturers had used decimal meanings of the prefixes, and at the other side for cache memory and random access memory (RAM) binary meanings of the prefixes were used. This has even resulted in litigation against hard drive manufacturers, who report drive capacities in standard decimal multiples of bytes, while some operating systems report the size using the larger binary interpretation of traditional prefixes.
And finally, the third part to solve this puzzle is Microsoft itself, because it uses SI units (based on decimal system) to express values based on binary system, for example Windows use KB, MB and GB instead of KiB, MiB and GiB, respectively.
If you put all these three pieces together, you have a key to solve this confusion and analyse the screenshots I provided.
Firstly, let’s analyse a 1 TB hard disk from my screenshot, where Windows shows 931.39 GB capacity. In the following calculations you can use the provided Windows calculator, or this Web service Unit Juggler, because it easily convert unites to one another. OK, so manufacturer promised 1 TB and that theoretically represents 1000000000000 B (decimal addressing is used). Since Windows use binary meanings, as we previously mentioned, we have:
1000000000000 B / 1024 = 976562500 KB / 1024 = 953674.31640625 MB / 1024 = about 931.32 GB.
So how would you interpret these numbers? The manufacturer obviously gave you some extra storage space, about 0.07 GB (931.39 GB – 931.32 GB). Hence “theoretically“, as manufacturers don’t deliver you exact capacity of 1000000000000 B, the actual value is always above or below that one.
Another example is my USB flash disk, where the manufacturer promised a capacity of 16 GB, but Windows shows only 14.5 GB. Also notice the precise capacity in bytes: 15674765312. You can easily calculate that in this case the manufacturer took from you 16000000000 – 15674765312 = 325234688 bytes ! Let’s repeat the procedure I did above for my hard disk:
16000000000 B / 1024 = 15625000 KB / 1024 = 15258.7890625 MB / 1024 = about 14.90 GB
This means that manufacturer really took some storage space from you (promised 14.90 GB – actual 14.5 GB…).
* I will repeat this once again: Windows improperly use GB, to indicate binary addressing (that values are actually in GiB).
Linux Xubuntu properly shows the capacity of my USB flash drive:
Gigabytes (GB) are properly displayed, but the result is rounded to one decimal. You can easily check this value of 15674765312 bytes:
15674765312 B / 1000 = 15674765.312 KB = 15674.765312 MB = 15.674765312 GB (or 15,7 GB, rounded up to one decimal number).
Linux Mint KDE uses a new notation:
I hope this article clears up this confusion regarding capacities,
Why you see less capacity on your hard disk than manufacturer specified
Detailed explanation why you see less capacity on your hard disk than the manufacturer specified and the whole confusion about units and byte calculations.