What the data size converter does
The data size converter changes a value between eleven units of digital data: bit, byte (B), kilobyte (KB), megabyte (MB), gigabyte (GB), terabyte (TB), petabyte (PB), kibibyte (KiB), mebibyte (MiB), gibibyte (GiB) and tebibyte (TiB). Type on either side; the All Units list repeats the quantity in every unit.
Two families share the list: KB, MB, GB, TB and PB step by powers of ten (1 KB = 1,000 B), while KiB, MiB, GiB and TiB step by powers of two (1 KiB = 1,024 B). The byte is exactly 8 bits in both: 100 Mbit is 12.5 MB. A rate times a duration is a size — arithmetic on the standard calculator, durations on the time converter, speeds on the speed converter.
Worked examples
One byte, one bit. 1 B is exactly 8 bit, and a 100 Mbit/s line moves 12.5 MB (12,500,000 B, or 12,207.03125 KiB) each second.
The two ladders. Decimal: 1 KB = 1,000 B, 1 MB = 1,000 KB, 1 GB = 1,000,000,000 B, 1 TB = 1,000 GB, 1 PB = 1,000 TB. Binary: 1 KiB = 1,024 B, 1 MiB = 1,048,576 B, 1 GiB = 1,073,741,824 B, 1 TiB = 1,024 GiB.
The gap. 1 GiB = 1.073741824 GB, 7.3741824% more than a decimal gigabyte; read the other way, 1 GB = 0.9313225746 GiB, about 6.9% less. It widens at the next rung: 1 TiB = 1.0995116278 TB, and 1 TB = 0.9094947018 TiB.
The drive in the operating system. A 500 GB drive holds 465.661287308 GiB, a 1 TB drive 931.322574615 GiB, a 256 GB SSD 238.418579102 GiB. Windows prints 465 GB and 931 GB — the same bytes divided by 2³⁰. Memory is different: 16 GiB is 17,179,869,184 B, or 17.179869184 GB.
Where the factors come from
The bit is the base unit of information; the byte is 8 bits. Werner Buchholz coined “byte” in June 1956 at IBM, respelling “bite” so it would not be read as “bit”. IEC 80000-13 codified the 8-bit byte and its B symbol; the octet is the same 8 bits.
Decimal prefixes come from the SI: k = 10³, M = 10⁶, G = 10⁹, T = 10¹², P = 10¹⁵, with kilo keeping its lowercase k. The IEC binary prefixes Ki, Mi, Gi and Ti, adopted in December 1998 and now in IEC 80000-13, mean 2¹⁰ to 2⁴⁰: 1 GiB = 1,073,741,824 B and 1 GB = 1,000,000,000 B exactly. Storage makers follow the SI series; RAM and Windows keep the binary habit.
Reading results and limits
- Display rule.
- Results carry 12 significant digits with at most 10 decimal places, thousands separators and
0 for zero. - Ten-decimal cap and exponents.
- The ten-decimal cap decides some readouts: exact 1 GB in GiB is 0.9313225746154785…, printed as 0.9313225746, and 1 TB in TiB prints as 0.9094947018. Outside 10⁻¹⁰–10¹⁵ results switch to exponential form with six decimals: 1 byte in TiB reads 9.094947e-13 TiB, while 1 bit in GiB, just above the cut, reads 0.0000000001 GiB.
- Stored values and swaps.
- Twelve significant digits round large exact integers too: 1 TiB is exactly 1,099,511,627,776 B, displayed as 1,099,511,627,780 B. A swap carries the displayed value: 1 GB → GiB shows 0.9313225746, and swapping back leaves the byte row at 999,999,999.983 B.
Representative readouts:
| Input (left card) |
Row |
Readout |
| 1 GB |
Gibibyte |
0.9313225746 GiB |
| 1 GiB |
Gigabyte |
1.073741824 GB |
| 1 bit |
Gigabyte |
0.0000000001 GB |
| 1 PB |
Bit |
8.000000e+15 bit |
| 1 byte |
Tebibyte |
9.094947e-13 TiB |