Have you ever wondered why your computer says your disk drive has a lower capacity than the package it came in? For example, let’s say you just bought a shiny new 2.5″ 5 TB portable hard drive. You plugged it in; you waited in suspense as its five platters and ten heads finally overcame and defeated inertia in a Herculean struggle; and, at long last, Windows recognized it and told you there was 4.55 TB of free space available on your brand new, empty disk.
What the heck, man? Where’d the other 0.45 TB go?
Surprise! It was never actually there. Or it’s still there. Depends on how you want to look at it. 🙂 The explanation is that in this scenario there are two different measurement systems in use that are erroneously using the same labels. In the early age of computing, two factions battled for dominance using the same terminology and abbreviations for two distinct measurement systems that are almost the same but not quite. The terminology has since been clarified and standardized, but some software has yet to catch up (e.g. Windows).
The storage manufacturers are actually using the correct terminology for the numbers they’re giving. They use a “decimal” system whose units are based on powers of 10. For example, gigabytes and terabytes, abbreviated GB and TB, are one billion (109) and one trillion (1012) bytes, respectively. Each next larger or smaller unit is a simple multiplication or division by 1,000, respectively. For example:
- 1,000 (103) bytes are 1 kilobyte (KB)
- 1,000,000 (106) bytes are 1 megabyte (MB)
- 1,000,000,000 (109) bytes are 1 gigabyte (GB)
- … and so on.
The numbers that Windows reports to you are actually in a “binary” measurement system based on powers of 2 where a GB and a TB are 1,073,741,824 (230) and 1,099,511,627,776 (240) bytes, respectively. The properly standardized names are gibibytes and tebibytes, abbreviated GiB and TiB. Why such weird names? Apparently someone wanted to wedge “binary” into the middle of “gigabyte” and friends to differentiate them from their powers-of-10 variants. And why such weird numbers? Because computers and their programmers like to do math by factors of 2-to-the-power-of-some-number (binary logarithm) since this makes nicer looking numbers in bases 2, 8, and 16 of course! And each next larger or smaller unit is a simple increment or decrement of the exponent by 10. For example:
- 210 (1,024) bytes are 1 kibibyte (KiB)
- 220 (1,048,576) bytes are 1 mebibyte (MiB)
- 230 (1,073,741,824) bytes are 1 gibibyte (GiB)
- … and so forth.
So, as you can see, each one of these binary units is larger, in bytes, than the corresponding decimal unit, resulting in your disk capacity appearing lower, according to Windows, than the advertised number! And this difference only increases as the capacities grow larger.
The tl;dr is that 5 TB is the same quantity as 4.55 TiB; similar to how 1 yard is the same quantity as 0.9144 meter. It’s made confusing by the fact that some programs, such as Windows, use the wrong label—it’s telling you TB when it means TiB, a subtle but important difference!