Data Storage Converter
Bits through petabytes, with a switch for the two counting conventions, because a gigabyte means two different things depending on who is doing the counting.
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Enter a number.
Pick the convention before you trust the number. Storage and network capacity is sold in decimal. Windows and most file managers report in binary but still write GB. Neither side usually says which it means, so a figure copied between them is off by a growing margin. The bits row is unaffected: there are 8 bits in a byte under both conventions.
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Reference table
| Unit | Symbol | Decimal | Binary |
|---|---|---|---|
| Bits | bit | 0.125 B | 0.125 B |
| Bytes | B | 1 B | 1 B |
| Kilobytes | KB | 1,000 B | 1,024 B |
| Megabytes | MB | 1,000,000 B | 1,048,576 B |
| Gigabytes | GB | 109 B | 1,073,741,824 B |
| Terabytes | TB | 1012 B | 240 B |
| Petabytes | PB | 1015 B | 250 B |
How far apart the two conventions get
| At this unit | Binary exceeds decimal by |
|---|---|
| Kilobyte | 2.4% |
| Megabyte | 4.9% |
| Gigabyte | 7.4% |
| Terabyte | 10.0% |
| Petabyte | 12.6% |
The gap compounds because each step multiplies by 1,024 instead of 1,000. At the kilobyte nobody notices 2.4 percent. At the terabyte, 10 percent is the difference between the number on the box and the number in your file manager, which is why the complaint only ever arrives about large drives.
The prefixes that would have fixed this
The IEC introduced binary prefixes in 1998 for exactly this problem. A kibibyte (KiB) is exactly 1,024 bytes, a mebibyte (MiB) is 1,024 KiB, a gibibyte (GiB) is 1,024 MiB. They are unambiguous, correct, and almost entirely ignored outside standards documents and a few Linux tools.
Because the unambiguous names never caught on, KB and MB and GB still carry both meanings, and the only reliable fix is to say which convention you mean. That is why this tool asks rather than assumes.
Common questions
Is a gigabyte 1,000 or 1,024 megabytes?
Both, depending on who is counting. Drive manufacturers and network operators use the decimal convention where a gigabyte is 1,000 megabytes. Windows and most file managers use the binary convention where it is 1,024. Neither is wrong, and neither usually says which it is using, which is why this tool makes you pick.
What are GiB, MiB and KiB?
They are the IEC binary prefixes, introduced in 1998 to end this ambiguity. A gibibyte is exactly 1,024 mebibytes and a mebibyte is exactly 1,024 kibibytes. They are unambiguous and correct, and almost nobody outside standards documents uses them, so the ambiguous terms remain in daily use.
Why does a 1 TB drive show as 931 GB?
The manufacturer sold you 1,000,000,000,000 bytes, which is a decimal terabyte. Your operating system divides by 1,024 four times and reports about 931 binary gigabytes. Nothing is missing from the drive; the two sides are counting in different bases. The gap is 10.0 percent at the terabyte.
How large is the gap between the two conventions?
It compounds at every step, measured from bytes: 2.4 percent at the kilobyte, 4.9 percent at the megabyte, 7.4 percent at the gigabyte, 10.0 percent at the terabyte and 12.6 percent at the petabyte. That is why the discrepancy on a large drive looks alarming when the same effect on a memory card doesn't.
Sources
- NIST Guide to the SI. Source for the decimal prefix values, where kilo is 1,000.
- IEC 80000-13 defines the binary prefixes kibi, mebi and gibi used above. The decimal and binary tables here are arithmetic from those two definitions rather than measured values.