Bytes converter for decimal and binary data units
This bytes converter translates sizes between bits, bytes and 13 larger units, from kilobit to pebibyte. It keeps the two prefix systems apart: decimal units such as MB and GB count in powers of 1000, while binary units such as MiB and GiB count in powers of 1024. Mixing them up is behind most "where did my storage go" questions.
Decimal (SI) versus binary (IEC) prefixes
The metric prefixes kilo, mega and giga have always meant 1000, one million and one billion. Early computers, however, used "kilobyte" for 1024 bytes because memory comes in powers of two. In 1998 the International Electrotechnical Commission added separate binary names with an "i": kibibyte, mebibyte, gibibyte and so on.
| Decimal unit | Bytes | Binary unit | Bytes | Gap |
|---|---|---|---|---|
| KB | 1,000 | KiB | 1,024 | 2.4% |
| MB | 1,000,000 | MiB | 1,048,576 | 4.9% |
| GB | 1,000,000,000 | GiB | 1,073,741,824 | 7.4% |
| TB | 10¹² | TiB | 1,099,511,627,776 | 10.0% |
| PB | 10¹⁵ | PiB | 1,125,899,906,842,624 | 12.6% |
The gap grows at every step, so it is easy to ignore for kilobytes and impossible to ignore for terabytes. The tool labels the decimal kilobyte "KB"; strict SI style writes it "kB", and both mean 1000 bytes here.
Why a 500 GB drive shows about 465 GB
Drive manufacturers label capacity in decimal units, so a 500 GB drive holds 500,000,000,000 bytes. Windows File Explorer divides by 1024³ but still prints "GB", so the same bytes appear as roughly 465 "GB", which are really gibibytes.
500 GB = 465.6612873 GiB
1000 GB = 931.3225746 GiB
2 TB = 1.818989404 TiB
4.7 GB = 4.377216101 GiB
1 GiB = 1.073741824 GBNothing is missing; the number is simply expressed in a larger unit. Recovery partitions and file system metadata can shave off a little more usable space, but most of the gap is pure arithmetic. RAM goes the other way: memory is built in powers of two, so a "16 GB" module actually holds 16 GiB.
Bits versus bytes
A byte is 8 bits. File and storage sizes are counted in bytes (capital B), while network speeds are quoted in bits per second (lowercase b). Because the "per second" is the same on both sides, converting megabits to megabytes also converts Mbps to MB/s: 100 Mbit = 12.5 MB, so a 100 Mbps line moves at most 12.5 MB per second.
Here is a worked download estimate. A 4.7 GB file is 4.7 × 8 = 37.6 Gbit, or 37,600 Mbit. At 100 Mbit/s that takes 376 seconds, a little over six minutes, before protocol overhead slows real transfers down. Network speeds use decimal prefixes, so 1 Gbit is 125 MB, not 128 MiB.
Which unit should you use?
- Decimal (KB, MB, GB, TB): drive and SSD capacities, network speeds, and file sizes in macOS Finder.
- Binary (KiB, MiB, GiB, TiB): RAM, Windows File Explorer and many command-line tools, often while still printing "KB", "MB" or "GB".
- Documentation and specs: write KiB or MiB explicitly whenever the difference matters, so readers do not have to guess.
Common mistakes
- Mb vs MB. A factor of 8 separates megabits from megabytes, and it is the most common error in bandwidth math.
- Mixed prefixes. The classic "1.44 MB" floppy held 1,474,560 bytes: 1440 KiB, labeled as if 1 MB were 1000 KiB. It is neither 1.44 MiB nor 1.44 MB.
- Power-of-two thinking for decimal units. 1 MB is 0.9536743164 MiB, not 1.
Why powers of two at all? Memory addresses are binary numbers, as the decimal to binary converter shows: 1024 is 10000000000 in binary. To make files smaller rather than just relabel them, try Gzip compression, and use the time converter to turn download seconds into minutes or hours.