Data Storage Converter

Two kinds of kilobyte

A bit is a single 0 or 1, and a byte is 8 bits. Larger amounts use prefixes, and here the trouble starts, because two sets of prefixes are in use:

• Decimal (SI) prefixes step by 1,000: 1 kB = 1,000 bytes, 1 MB = 1,000,000 bytes, 1 GB = 1,000,000,000 bytes, and so on up to the petabyte. This is what kilo, mega and giga mean everywhere else in science, and what drive makers, network providers and many operating systems use.
• Binary (IEC) prefixes step by 1,024 (2¹⁰): 1 KiB = 1,024 bytes, 1 MiB = 1,048,576 bytes, 1 GiB = 1,073,741,824 bytes, up to 1 PiB = 1,125,899,906,842,624 bytes. Memory chips come in these sizes because computer addresses are binary.

For decades both were written “KB, MB, GB”, so “1 GB” could mean either amount. To end the ambiguity the International Electrotechnical Commission introduced the binary prefixes kibi, mebi, gibi, tebi and pebi (KiB, MiB, GiB, TiB, PiB) in 1998; they are now part of the international standard IEC 80000-13. The International Bureau of Weights and Measures states that the SI prefixes mean powers of ten only. This converter follows both: GB always means 10⁹ bytes and GiB always 2³⁰ bytes.

The conversion formula

Every conversion goes through bytes:

value

the amount you enter

bytes in one unit

1,000ⁿ for kB, MB, GB, TB, PB (n = 1 to 5); 1,024ⁿ for KiB to PiB; 1/8 for a bit

Every unit is a whole number of bits, so the calculator works with exact whole numbers (arbitrary-size integers) rather than floating-point approximations. Because the sizes are built only from 2s and 5s, every answer is a decimal that ends: the result is shown in full, digit for digit, unless it has more than 24 digits.

Worked examples

A “1 TB” drive in GiB. The maker’s terabyte is 1,000,000,000,000 bytes. A gibibyte is 1,073,741,824 bytes, so 1,000,000,000,000 ÷ 1,073,741,824 = 931.322574615478515625 GiB. A system that counts in powers of 1,024 but labels the result “GB” will show about 931 GB, roughly 6.9% fewer units than the box, although not a single byte is missing.

500 GB in GiB. 500,000,000,000 ÷ 1,073,741,824 = 465.6612873077392578125 GiB, which is why a 500 GB drive is listed as about 465 GB.

A 100 Mbit/s connection in MB per second. Divide bits by 8: 100 Mbit = 100,000,000 bits = 12,500,000 bytes = 12.5 MB. At full speed, with no overhead, a 5 GB download (40,000 Mbit) takes 40,000 ÷ 100 = 400 seconds, just under 7 minutes.

Why a new drive looks smaller than advertised

Drive capacities are sold in decimal units. Windows File Explorer divides the byte count by powers of 1,024 but still labels the result KB, MB, GB and TB, so a 1 TB drive appears as about 931 GB and a 2 TB drive as about 1.8 TB. Apple’s macOS (since Mac OS X 10.6 Snow Leopard) and iOS (since iOS 11) report storage in decimal units, so the same drive shows as 1 TB there. The gap grows with each prefix: a GiB is 7.4% larger than a GB, a TiB 9.95% larger than a TB.

A little of the space really is unavailable once a drive is formatted, because the file system reserves room for its own records, and phones set aside space for the operating system. That is a separate effect from the unit difference, and this converter does not estimate it.

Bits for speed, bytes for size

Internet and network speeds are quoted in bits per second (Mbit/s or Mbps, Gbit/s), normally with decimal prefixes. File sizes and download progress are usually shown in bytes. Divide a bit figure by 8 to get bytes: a 1 Gbit/s line moves at most 125 MB per second. Real transfers are somewhat slower because of protocol overhead and the speed of the other end.

Watch the capital letter: Mb or Mbit is megabits, MB is megabytes, eight times more. Percentages like the 6.9% above are easy to check with the percentage calculator, and very large byte counts in powers of two with the scientific calculator.