Decimal versus binary byte units, with the gap calculated
Every SI decimal byte unit set against its IEC 80000-13 binary counterpart, with the gap between the two calculated for each rung of the ladder, plus what each advertised storage capacity actually reports on a system that counts in binary. Every byte count here is a power of 1,000 or of 1,024 computed at build time, not a rounded figure quoted from elsewhere.
Decimal SI units against IEC binary units
Decimal units are powers of 1,000 and are what storage, memory cards, bandwidth and app stores are sold in. The IEC 80000-13 binary units are powers of 1,024. The last column is calculated: it is how much larger the binary unit is than the decimal one at that rung, and it grows with every step.
| Decimal unit | Bytes | Binary unit | Bytes | Binary larger by |
|---|---|---|---|---|
| Kilobyte (KB) | 1,000 | Kibibyte (KiB) | 1,024 | 2.40% |
| Megabyte (MB) | 1,000,000 | Mebibyte (MiB) | 1,048,576 | 4.86% |
| Gigabyte (GB) | 1,000,000,000 | Gibibyte (GiB) | 1,073,741,824 | 7.37% |
| Terabyte (TB) | 1,000,000,000,000 | Tebibyte (TiB) | 1,099,511,627,776 | 9.95% |
| Petabyte (PB) | 1,000,000,000,000,000 | Pebibyte (PiB) | 1,125,899,906,842,624 | 12.59% |
| Exabyte (EB) | 1,000,000,000,000,000,000 | Exbibyte (EiB) | 1,152,921,504,606,846,976 | 15.29% |
What an advertised capacity looks like in binary units
Each row takes the decimal capacity a drive is sold as, converts it to the binary unit that software such as Windows File Explorer counts in, and shows the shortfall against the number on the box. Windows prints the decimal prefix name (GB, TB) while counting in gibibytes and tebibytes, which is what creates the apparent loss. No capacity is actually missing.
| Sold as | Bytes on the drive | The same capacity in binary units | Apparent shortfall |
|---|---|---|---|
| 64 GB | 64,000,000,000 | 59.60 GiB | 6.87% |
| 128 GB | 128,000,000,000 | 119.21 GiB | 6.87% |
| 256 GB | 256,000,000,000 | 238.42 GiB | 6.87% |
| 500 GB | 500,000,000,000 | 465.66 GiB | 6.87% |
| 512 GB | 512,000,000,000 | 476.84 GiB | 6.87% |
| 1 TB | 1,000,000,000,000 | 931.32 GiB | 6.87% |
| 2 TB | 2,000,000,000,000 | 1.82 TiB | 9.05% |
| 4 TB | 4,000,000,000,000 | 3.64 TiB | 9.05% |
| 8 TB | 8,000,000,000,000 | 7.28 TiB | 9.05% |
| 16 TB | 16,000,000,000,000 | 14.55 TiB | 9.05% |
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Two units, one set of names
A kilobyte in the SI sense is 1,000 bytes, because the prefix kilo means one thousand everywhere else in measurement. Early computing borrowed the prefix for 1,024, the nearest power of two, and the two meanings coexisted for decades because at the kilo rung they differ by less than three percent.
The gap compounds. By the giga rung it is 7.37 percent and by the tera rung 9.95 percent, which is the point at which it stops being a rounding curiosity and starts generating support tickets. The first table is that divergence in full.
IEC 80000-13 resolved the ambiguity by giving the binary multiples their own names: kibi, mebi, gibi, tebi, pebi and exbi, contracted from kilo binary, mega binary and so on. When a figure is written GiB it is unambiguously binary. When it is written GB it is meant to be decimal, whatever the software producing it actually calculated.
Which convention each system uses
Storage manufacturers, memory card makers, network operators and app stores quote decimal units. So does macOS, which moved to decimal reporting in Mac OS X 10.6 Snow Leopard, and so does iOS, which is why an Apple device's figures line up with the number on the box.
Windows File Explorer divides by 1,024 at every step while still writing KB, MB and GB. Linux is mixed: many tools accept a flag to switch, and several now print GiB by default. RAM is the one place where binary is genuinely correct, because memory is addressed in powers of two, so a 16 GB memory module really does hold 16 GiB.
That split is the whole content of the second table. A 1 TB drive holds exactly 1,000,000,000,000 bytes, as advertised. Windows divides that by 1,024 three times, arrives at 931.32, and writes GB after it. Nothing was reserved by formatting and nothing is missing.
The other eightfold trap
Storage is counted in bytes and bandwidth in bits, and a byte is eight bits. MB and Mb are different units, and reading a lowercase b as an uppercase B is an eightfold error rather than a seven percent one.
A 100 Mbps connection moves at most 12.5 MB per second, so a 1 GB file takes around 80 seconds at full rate, not 10. Download time estimates that come out badly wrong are usually this mistake rather than the decimal and binary one.
Both traps can stack. A file listed as 1 GiB downloaded over a link quoted in megabits is two unit conversions away from an honest estimate, and getting either one wrong changes the answer by more than the other.
Frequently asked questions
Is 1 GB 1000 MB or 1024 MB?
1 GB is 1,000 MB in the decimal SI sense used by storage makers, carriers, macOS and iOS. The 1,024 figure belongs to the gibibyte: 1 GiB is 1,024 MiB, or 1,073,741,824 bytes. Software that prints GB while dividing by 1,024 is using the older, loose meaning of the prefix.
Why does a 1 TB drive show as 931 GB?
Because 1,000,000,000,000 bytes divided by 1,024 three times is 931.32, and Windows writes GB after that figure instead of GiB. The drive holds exactly what the box says. It is one quantity expressed in two units, not lost capacity.
What is the difference between GB and GiB?
A gigabyte is 1,000,000,000 bytes and a gibibyte is 1,073,741,824 bytes, so a gibibyte is 7.37 percent larger. GiB and its relatives are defined in IEC 80000-13 and exist precisely so that a figure can be stated without ambiguity.
Do phones and Apple devices measure storage the same way?
Apple reports storage in decimal units on macOS and iOS, so those figures match the advertised capacity and the shortfall in the second table does not appear. Any remaining difference on an Apple device is the operating system and preinstalled files taking up space, not the unit.
Can I republish these tables?
Yes, under Creative Commons Attribution 4.0 International (CC BY 4.0). Credit UnitGlide, https://unitglide.net and you may copy, adapt and republish them, commercial use included. The embed on this page keeps the credit attached and stays current.
Sources
- NIST: Prefixes for binary multiples, for the IEC 80000-13 binary prefixes and the names kibi, mebi, gibi and tebi.
- BIPM, SI Brochure, for the decimal SI prefixes as powers of 1,000.
- Apple Support: how storage capacity is measured on Apple devices, for Apple reporting storage in decimal units on macOS and iOS.