# Computer (Digital) Storage Units Converter

## Calculator Use

Convert digital storage units among bits and bytes in both decimal and binary units.

This conversion calculator uses two different sets of prefixes for bits and bytes.

- Binary prefixes (base 2) - for example, kibi, mebi, gibi and tebi are binary notation where 1 kibibyte = 1024 bytes, 1 mebibyte = 1024 kibibytes, 1 gibibyte = 1024 mebibytes, etc.
- Metric or Decimal prefixes (base 10) - for example, kilo, mega, giga and tera are decimal notation where 1 kilobyte = 1000 bytes, 1 megabyte = 1000 kilobytes, 1 gigabyte = 1000 megabytes, etc.

Metric prefixes are common SI units in decimal notation. In common SI decimal notation using joules as an example, 1 kilojoule = 1000 joules, 1 megajoule = 1000 kilojoules, 1 gigajoule = 1000 megajoules, etc.

## How to Convert Units of Bytes

To simply convert from any unit in binary into binary bytes, for example, from 5 gibibytes to bytes, just
* multiply by* the value in the right column in the

**Binary Bytes Reference**table below.

Since 1 GiB = 2^{30}B, we can divide both sides by 1 GiB to show that 1 = 2^{30}B / GiB and this is our conversion ratio.

Multiply 5 GiB by 1 (the conversion ratio), GiB will cancel and we will be left with byte units B.

5

~~GiB~~× 2^{30}B /~~GiB~~= 5,368,709,120 B

To convert from bytes back into units in the left column
* divide by* the value in the right column or, multiply by the reciprocal, 1/x.

5,368,709,120

~~B~~/ 2^{30}~~B~~/ GB = 5 GB

To convert among any units in the left column, say from A to B, you can multiply by the factor for A to convert A into bytes then divide by the factor for B to convert out of bytes. Or, you can find the single factor you need by dividing the A factor by the B factor.

For example, to convert from gibibytes to tebibytes you would multiply by 2^{30} then divide by 2^{40}. Or, multiply by 2^{30}/2^{40} = 2^{(30-40)} = 2^{-10}. So, to convert directly from gibibytes to tebibytes you multiply by 2^{-10}.

To understand how to also convert the units follow this example. Say you want to convert decimal units from exabytes to bytes. Since you can multiply anything by 1 and still retain the original value, but in different units, set it up so that EB will cancel out leaving you with B.

Since: 1 EB = 10

^{18}B, dividing both sides by 10^{18}

1 B = 1 / 10^{18}EB = 10^{-18}EB 1 B = 10^{18}EB, 1 B / 10^{18}EB = 1We can write the conversion as:

1 EB =

1 EB × (1 B / 10^{18}EB) =

1 EB * (10^{0}B / 10^{18}EB) =

1 EB * (10^{(0 - 18)}) [B / EB ] = 10^{-18}B

And we now have our factor for conversion from exabytes to bytes since 1 * 2

^{60}= 2^{60}.

Knowing that 1 EB = 2^{60} B we can now find the conversion factor for converting back. Dividing both sides of the equation by 2^{60} we get 10^{18} EB = 1 B. So, the conversion factor to convert from bytes to exabytes is 10^{18}.

### Metric (or Decimal) Digital Storage Units Refernce

^{0}

^{0}

^{1}

^{3}

^{2}

^{6}

^{3}

^{9}

^{4}

^{12}

^{5}

^{15}

^{6}

^{18}

^{7}

^{21}

^{8}

^{24}

^{9}

^{27}

^{10}

^{30}

^{0}

^{0}

^{1}

^{3}

^{2}

^{6}

^{3}

^{9}

^{4}

^{12}

^{5}

^{15}

^{6}

^{18}

^{7}

^{21}

^{8}

^{24}

^{9}

^{27}

^{10}

^{30}

### Binary Digital Storage Units Refernce

kibibyte (KiB) is not the same as kilobyte (KB). Even though you will find that computer storage units are reported in KB or MB or TB they actually are referring to base 2 units where 2^{10} = 1024, for kiibibyts .......... historically these units or used but confusion..... formalized the units ....

^{10}

^{20}

^{30}

^{40}

^{50}

^{60}

^{70}

^{80}

^{90}

^{100}

^{3}

^{10}

^{20}

^{30}

^{40}

^{50}

^{60}

^{70}

^{80}

^{90}

^{100}

## Percent Difference in Binary to Metric Storage Sizes

Percent differences are showing how much greater the metric equivalent units are.

Binary Storage Unit | Metric Storage Unit | Percent Difference |
---|---|---|

1 Byte (B) | 1.000 Byte (B) | 0.0% |

1 Kibibyte (KiB) | 1.024 Kilobyte (kB) | 2.4% |

1 Mebibyte (MiB) | 1.049 Megabyte (MB) | 4.9% |

1 Gibibyte (GiB) | 1.074 Gigabyte (GB) | 7.4% |

1 Tebibyte (TiB) | 1.100 Terabyte (TB) | 10.0% |

1 Pebibyte (PiB) | 1.126 Petabyte (PB) | 12.6% |

1 Exbibyte (EiB) | 1.153 Exabyte (EB) | 15.3% |

1 Zebibyte (ZiB) | 1.181 Zettabyte (ZB) | 18.1% |

1 Yobibyte (YiB) | 1.209 Yottabyte (YB) | 20.9% |

* Be sure you are using and converting among the actual units you intend. As of 2023 there still exists some unit confusion. Historically, KB (kB), MB, GB, TB, and others, were symbols used in both metric and binary systems (kilo-, mega-, giga-, tera-). This has been confusing to non-experts since the two systems represent different actual sizes. See above table. In 1998 and 1999 the International Electrotechnical Commission defined and formalized the explicit prefixes kibi-, mebi-, gibi-, tebi- (KiB, MiB, GiB, TiB) and the like for binary prefixes and binary symbols leaving kB, MB, GB, TB etcetera, for metric decimal notation. See, Timeline of Binary Prefixes.

** This calculator uses the additional binary unit prefixes robi- and quebi- although they have not been officially adopted. The metric counterparts ronna- and quetta- have been formally introduced and adopted and some assume that the natural binary equivalents robi- and quebi- will eventually be adopted. See, Binary prefix.