You buy a 1 TB drive, plug it in, and the computer reports about 931 GB. The drive is not short. Two counting systems are using nearly the same names for different sizes.
The arithmetic behind 931
| Step | Calculation | Result |
|---|---|---|
| Bytes on the label | 1 TB = 10¹² bytes | 1,000,000,000,000 B |
| To kibibytes | ÷ 1,024 | 976,562,500 KiB |
| To mebibytes | ÷ 1,024 | 953,674.32 MiB |
| To gibibytes | ÷ 1,024 | 931.32 GiB |
| To tebibytes | ÷ 1,024 | 0.9095 TiB |
The byte count is identical in every row. A manufacturer divides by 1,000 at each step; a binary display divides by 1,024. Because 1,024 is bigger, the same bytes produce a smaller number.
Two prefix systems with nearly the same names
Kilo, mega, giga and tera are SI prefixes meaning powers of 1,000. Early computing borrowed kilo for 1,024 because 1,024 = 2¹⁰ is close to 1,000 and memory is built in powers of two. To end the ambiguity, the International Electrotechnical Commission approved separate binary prefixes in December 1998, published as Amendment 2 to IEC 60027-2 in January 1999: kibi (Ki), mebi (Mi), gibi (Gi), tebi (Ti) and larger ones. NIST documents these prefixes and their adoption.
| Decimal unit | Bytes | Binary unit | Bytes | Binary unit is larger by |
|---|---|---|---|---|
| kB (kilobyte) | 1,000 | KiB (kibibyte) | 1,024 | 2.40% |
| MB (megabyte) | 1,000,000 | MiB (mebibyte) | 1,048,576 | 4.86% |
| GB (gigabyte) | 1,000,000,000 | GiB (gibibyte) | 1,073,741,824 | 7.37% |
| TB (terabyte) | 1,000,000,000,000 | TiB (tebibyte) | 1,099,511,627,776 | 9.95% |
The gap compounds with each prefix step, so it grows with size. A file measured in kilobytes barely changes; a drive measured in terabytes shows a number almost 10% lower. The trend continues past the converter's largest unit: one petabyte (10¹⁵ bytes) is about 11.2% smaller than one pebibyte (2⁵⁰ bytes), so large storage systems show an even bigger apparent shortfall when quoted in binary units.
Notice that the two percentages in this section are not the same number. A GiB is 7.37% larger than a GB, yet a GB figure reads 6.87% lower when shown in GiB, because each percentage is measured against a different base. The percent change versus percentage points guide explains why the base matters.
Common drive sizes in both units
| Label | Exact bytes | Binary equivalent |
|---|---|---|
| 64 GB | 64,000,000,000 | 59.60 GiB |
| 128 GB | 128,000,000,000 | 119.21 GiB |
| 256 GB | 256,000,000,000 | 238.42 GiB |
| 500 GB | 500,000,000,000 | 465.66 GiB |
| 1 TB | 1,000,000,000,000 | 931.32 GiB (0.91 TiB) |
| 2 TB | 2,000,000,000,000 | 1,862.65 GiB (1.82 TiB) |
| 4 TB | 4,000,000,000,000 | 3,725.29 GiB (3.64 TiB) |
| 8 TB | 8,000,000,000,000 | 7,450.58 GiB (7.28 TiB) |
Who uses which convention
- Drive and memory-card makers state capacity in decimal units: 1 GB is one billion bytes.
- Windows File Explorer divides by 1,024 but labels the result GB, which is why a 1 TB drive appears as about 931 GB.
- Apple says iOS 10 and earlier and OS X Leopard and earlier reported storage in binary units. Later versions report decimal capacity, so a 1 TB drive appears as about 1 TB on a current Mac.
- Command-line tools differ by option. On Linux, for example, GNU df -h reports powers of 1,024 with short suffixes such as G, while df -H uses powers of 1,000. The same drive can therefore print two different numbers from one tool.
- RAM is built in powers of two. A 16 GB memory module holds 16 GiB, which is 17,179,869,184 bytes or 17.18 decimal GB.
- Network speeds are stated in bits per second with decimal prefixes. 100 Mbps is 100,000,000 bits, or 12.5 MB, each second; the lowercase b matters.
Checking any capacity figure in three steps
- Find the exact byte count. A label of 2 TB means 2,000,000,000,000 bytes. A system information panel often lists the raw byte count of a drive, which is the most reliable figure to compare.
- Decide which divisor the display uses. If the reported number is about 7% below the label for GB, or about 9% below for TB, the display is dividing by 1,024 at each step.
- Convert the label with the same divisor and compare like with like. If the two now match, the difference was only notation.
Decimal labels are not a marketing trick invented to inflate numbers. Kilo, mega, giga and tera have meant powers of 1,000 in the SI since long before personal computers. NIST records that the IEEE Standards Board decided mega would mean 1,000,000 in its standards, with base-two meanings allowed only if explicitly stated. The binary prefixes exist so that both meanings can be written without confusion.
When the gap is bigger than the unit difference
Convert the label first. If the computer reports a total well below the binary equivalent in the table, the unit difference does not explain the rest. A laptop sold with a 256 GB drive should show about 238 GiB in total; anything less is usually recovery or system partitions created by the maker. Free space is lower still because the operating system and its files occupy part of the drive.
The same trap, one unit name with two sizes, appears outside computing. Land in Pakistan is measured in marlas that range from 225 to 272.25 square feet depending on the authority and records used, as the marla and kanal guide shows. In both cases the fix is to ask for the base quantity, bytes or square feet, before comparing.
What a unit conversion does not tell you
The converter re-expresses a stated number of bytes. It does not know how a filesystem stores files: space is allocated in fixed blocks, so a tiny file can occupy several kilobytes on disk, and compression can make files take less room than their size suggests. It also cannot tell which convention an unlabeled KB or GB uses. In the converter, kB means 1,000 bytes and KiB means 1,024 bytes; when a source writes GB, check whether it divides by 1,000 or 1,024 before comparing figures.