I have a 2 TB hard drive on my Windows, but I only see the number 1.81 TB displayed in the disk’s properties and 1863 GB in Disk Management. Why? Where did all those extra spaces go?
For the longest time, I always think that’s because it’s calculated in binary but never thought why it’s always smaller but not greater. Well, I was only partially right.
Hard drive manufacturers use the International System of Units (SI) convention when labeling their hard disk capacities. The prefixes used in SI such as Kilo-, Mega-, Giga-, Tera, Peta, Exab, Zetta, Yotta are all decimal-based. So, a 2 TB hard drive basically means it has the capacity of 2,000,000,000,000 or 10^12 bytes.
But as we all know, computers are made in binary and don’t really like the idea of having a decimal number floating around in the system. So in 1999, the International Electrotechnical Commission (IEC) introduced a new set of prefixes, Kibi-, Mebi-, Gibi-, Tebi-, Peta-, Exbi-, Zebi, Yobi, to be used in specifying binary multiples of a quantity, hoping to clarify the ambiguity between the decimal-based and binary-based systems. The names come from the first two letters of the original SI prefixes followed by bi, short for “binary”.
Operating systems like Windows never uses a decimal-based SI system to display the capacity of hard drive space. It always uses the binary numbers instead. So the 1.81 TB shown in the disk properties above really means 1.81 TiB (Tebibyte).
2 * (10^12 / 2^40) = 1.8189894 TiB
Same as in the Disk Management window above, it really should say 1863.02 GiB instead.
2 * (10^20 / 2^30) = 1862.64 GiB
Noticed the subtle difference there? That’s because of the extra space, 397,791,232 bytes in this case, the hard drive has.
2,000,397,791,232 / 2^30 = 1,863 GiB
So, when you buy a hard drive labeled as 2 TB, you are getting 2 TB (2,000 GB) storage spaces. When Windows tells you that there are only 1.81 TB in it, what it really says is that there are 1.81 TiB. The GB/TB info you see in Windows is misleading, causing more confusions to end users.
Really, Microsoft is the one to blame here. It’s been over 15 years since the Kibi system was introduced and you still haven’t adapted it in your system. Why?
/update on Sept. 23, 2016/
Because nobody else is on the program either.
If you look around you, you’ll find that nobody (to within experimental error) uses the terms kibibyte and KiB. When you buy computer memory, the amount is specified in megabytes and gigabytes, not mebibytes and gibibytes. The storage capacity printed on your blank CD is indicated in megabytes. Every document on the Internet (to within experimental error) which talks about memory and storage uses the terms kilobyte/KB, megabyte/MB, gigabyte/GB, etc. You have to go out of your way to find people who use the terms kibibyte/KiB, mebibyte/MiB, gibibyte/GiB, etc.
In other words, the entire computing industry has ignored the guidance of the IEC.
Now let’s blame on the hard drive manufactory for ruining the binary world we all love in the first place.