Storage Unit Converter (GB, GiB, TB, TiB, MB, MiB)

Background.

A new 1 TB external drive goes into a Windows laptop, and File Explorer reports 931 GB. Nothing is broken and nothing has been taken. The drive holds exactly the 1,000,000,000,000 bytes it was sold as. Windows divides that count by 2³⁰, which is 1,073,741,824, gets 931.3226, and prints the result with the label GB. Plug the same drive into a Mac running OS X 10.6 or later, which counts in powers of ten, and it shows as about 1 TB.

The root of it is that one word, gigabyte, has carried two meanings for decades. In the SI, giga means 10⁹ and nothing else, and drive makers follow it. Computer memory is built in powers of two, so the industry borrowed kilo, mega and giga for 2¹⁰, 2²⁰ and 2³⁰. NIST records the split: memory manufacturers usually mean 1,048,576 bytes by a megabyte, storage manufacturers 1,000,000. Both conventions can even share one line of a datasheet: Micron describes a DDR4 module as 8GB, meaning 8 × 2³⁰ bytes, and its transfer rate as 25.6 GB/s, meaning 10⁹ bytes per second.

The IEC's remedy, in IEC 60027-2, gave the binary multiples names of their own, kibi through pebi, written KiB to PiB. Bits form a third family, quoted with a lower-case b for network speeds and interfaces. Every result here also appears as a plain byte count, the one figure no labelling convention can change.

What is storage unit converter?

Digital storage is counted in bits and bytes, and the units on this converter fall into three families. Bit units use decimal prefixes: a megabit is 10⁶ bits. Decimal byte units follow the SI: a kilobyte is 10³ bytes, a gigabyte 10⁹, a petabyte 10¹⁵. Binary byte units follow IEC 60027-2: a kibibyte is 2¹⁰ = 1,024 bytes, a gibibyte 2³⁰, a pebibyte 2⁵⁰. The difference between a decimal unit and its binary partner grows from 2.4% at kilo to 12.59% at peta.

How to use this calculator.

1. 01Enter the amount and choose the unit it is written in. Capacities printed on a drive, a phone box or a broadband plan are decimal; sizes reported by Windows and memory capacities are binary, even when labelled GB.
2. 02Choose the unit you want. Any unit converts to any other, from bits to pebibytes.
3. 03Read the byte count to settle disagreements: two tools that report different figures for the same file usually show the same number of bytes.
4. 04Scan the ladder of MB, MiB, GB, GiB, TB and TiB to work out which convention a program is using.
5. 05Check the case of the b. Mb is megabits and MB megabytes, a factor of eight apart.

The formula.

Every conversion runs through bytes: result = value × bytes per source unit ÷ bytes per target unit. The decimal byte units hold 10³, 10⁶, 10⁹, 10¹² and 10¹⁵ bytes, using the SI prefixes defined by the BIPM. The binary units hold 2¹⁰, 2²⁰, 2³⁰, 2⁴⁰ and 2⁵⁰ bytes, using the IEC prefixes. Bit units take decimal prefixes and are divided by 8 to reach bytes, so 1 Mbit is 10⁶ ÷ 8 = 125,000 bytes. All of these factors are exact integers or exact fractions, so there is no approximation in any conversion.

The gap between partners follows from the definitions. Each binary step multiplies by 1,024 and each decimal step by 1,000, so at the nth tier the binary unit is 1.024ⁿ times the decimal one: 2.4% larger for KiB against kB, 4.8576% for MiB against MB, 7.3742% for GiB against GB, 9.9512% for TiB against TB and 12.59% for PiB against PB. The percentage depends only on the tier, never on the amount, but the absolute shortfall grows with the drive.

A worked example.

Frequently asked questions.

References& sources.

1. [1]National Institute of Standards and Technology. Prefixes for binary multiples (Reference on Constants, Units and Uncertainty), citing IEC 60027-2 second edition, 2000-11. Source of the binary prefixes used here — kibi Ki 2¹⁰, mebi Mi 2²⁰, gibi Gi 2³⁰, tebi Ti 2⁴⁰, pebi Pi 2⁵⁰, exbi Ei 2⁶⁰ — and of the statement quoted on this page that most memory manufacturers use megabyte to mean 2²⁰ = 1,048,576 bytes while manufacturers of computer storage devices usually use it to mean 1,000,000 bytes.
2. [2]Bureau International des Poids et Mesures. SI prefixes. Source of the decimal prefixes: kilo 10³, mega 10⁶, giga 10⁹, tera 10¹², peta 10¹⁵ and exa 10¹⁸, described as the prefixes for writing decimal multiples and submultiples of SI units. Also records the 2022 extension of the prefix range to ronna and quetta.
3. [3]Micron Technology. MTA8ATF1G64HZ 8GB DDR4 SDRAM SODIMM datasheet. Cited as the concrete example of both conventions appearing in one vendor document: the module capacity is given as 8GB (memory, binary — 8 × 2³⁰ bytes) while its transfer rate on the same line is given as 25.6 GB/s (decimal — 3200 MT/s × 8 bytes ÷ 1000).