File Size & Storage Unit Conversion

Binary units of storage

Every file you save is a pattern of bits. A bit is a single binary digit, either 0 or 1, and it is the smallest unit of storage. Bits are bundled into larger units so sizes are quicker to write and read.

Each unit in the table is bigger than the one before: a bit to a nibble is 4 times, a nibble to a byte is 2 times, and every step after the byte is 1024 times the one before, where 1024 is 2 to the power of 10. Counted in bytes, that gives 1 KiB = 2^10, 1 MiB = 2^20, 1 GiB = 2^30 and 1 TiB = 2^40 bytes.

Converting between units

Moving from a larger unit down to a smaller one, multiply by 1024 once for each step. Moving from a smaller unit up to a larger one, divide by 1024 once for each step. Bits and bytes work differently: multiply by 8 to turn bytes into bits, and divide by 8 to turn bits into bytes, because a byte is 8 bits.

For example, a 3 GiB game holds 3 × 1024 = 3072 MiB, which is 3072 × 1024 = 3 145 728 KiB. Going the other way, 20 480 bits is 20 480 ÷ 8 = 2560 bytes, which is 2560 ÷ 1024 = 2.5 KiB.

storage_gib = 5
print("Bytes: " + str(storage_gib * 1024 ** 3))
print("Mebibytes: " + str(storage_gib * 1024))

Output:

Bytes: 5368709120
Mebibytes: 5120

Binary and decimal prefixes

Binary prefixes — kibi-, mebi-, gibi-, tebi- — step up in 1024s. Decimal prefixes — kilo-, mega-, giga-, tera- — step up in 1000s, so 1 kilobyte is 1000 bytes and a 2 TB drive is 2 000 000 000 000 bytes. A 2 TiB drive holds noticeably more, so use whichever prefix the question gives.

Data capacity is the total storage a set of files and any extra data needs, written in a suitable unit. Convert it by multiplying or dividing by the power of 1024 that matches the units, or by 1000 for decimal prefixes.