How To Convert Data Sizes

Digital storage is measured in bytes, and a byte is eight bits. Bits are the smallest unit and appear in network speeds, while bytes are the unit of storage capacity.

Two conventions coexist. The decimal convention uses powers of a thousand, so a kilobyte is 1000 bytes, a megabyte is a million and a gigabyte is a billion.

The binary convention uses powers of 1024, which is two to the tenth. A kibibyte is 1024 bytes, a mebibyte is 1,048,576 and a gibibyte is 1,073,741,824.

The gap between the two grows with each step because the ratio 1024 over 1000 compounds. At the kilobyte it is 2.4 percent, at the gigabyte it is about 7.4 percent and at the terabyte it is nearly ten percent.

This is why a drive sold as one terabyte, using decimal units, appears as about 931 gigabytes in an operating system that displays binary units. The capacity has not changed; the unit has.

The International Electrotechnical Commission defined the binary prefixes kibi, mebi, gibi, tebi and pebi to remove the ambiguity. A kibibyte is always 1024 bytes and a kilobyte is always 1000.

The converter expresses every unit as a size in bytes and converts by multiplying the value by the source factor and dividing by the target factor. That keeps every pair consistent, including bits.

The bit to byte conversion is fixed at eight in both conventions. Eight bits make a byte regardless of whether the byte is counted in decimal or binary units.

Network speeds are usually quoted in bits per second, so a one gigabit link moves 1,000,000,000 bits per second, which is 125,000,000 bytes per second, or 125 megabytes per second.

Storage is usually quoted in bytes, so a one terabyte drive is 1,000,000,000,000 bytes in decimal terms, which equals about 0.9095 tebibytes.

A common mistake is to assume the prefixes always mean a power of 1024. Modern standards reserve the SI prefixes for powers of a thousand and the binary prefixes for powers of 1024.

A second trap is to compare a network speed in bits with a storage size in bytes without dividing by eight, which overstates the transfer rate eightfold.

Cloud storage and phone plans are quoted in decimal gigabytes, while the file manager on the same device shows binary units. A 128 gigabyte phone shows about 119 gibibytes of space before the operating system takes its share.

Internet plans are sold in megabits per second, so a 100 megabit connection downloads at about 12.5 megabytes per second. Dividing by eight converts the marketing figure into a file-transfer rate.

Backups and archives are sized in terabytes, and the gap between decimal and binary units grows with each step. A 10 terabyte array holds about 9.09 tebibytes, a difference of nearly a terabyte.

Memory is usually quoted in binary units because it is addressed in powers of two, while storage is quoted in decimal units by convention. Knowing which is which explains most capacity confusion.

Scientific data sets can reach petabytes, where the prefix arithmetic still holds but the numbers are large. One petabyte is a thousand terabytes, or about 0.888 pebibytes.

The calculator models the fixed relationships between the units and nothing more. It does not know which convention a manufacturer used on a label, so check the unit and treat the output as exact arithmetic on the number you entered.