Metric versus binary (computer) prefixes

Why does my 120 gigabyte hard disk only store 111 gigabytes?

The size discrepancy comes from the fact that manufacturers always use figures which show their product in the best way. Some would argue that it also stems from a cultural issue in the sense that many in the the US-led computing industry appear reluctant to join the rest of the planet in adopting & understanding the metric system.

Normally, the metric prefix ‘kilo‘ means 1000 or 10^3. But in computing parlance ‘kilo‘ has been taken to mean 1024 or 2^10. The metric prefix ‘mega‘ means 1,000,000= 10^6. However in computing terms ‘mega‘ means 1024×1024 = 1,048,576 = 2^20.

A new ISO standard attempts to work around this problem by adopting a new set of computing-specific prefixes – where 1024 bytes should now be referred to as 1 kibibyte (or 1.024 kilobytes). The table below details these prefixes…

Metric Computer
prefix abbrev power of 10 multiplier value prefix abbrev power of 2 multiplier value
Kilo k 10^3 1,000 Kibi Ki 2^10 1,024
Mega M 10^6 1,000,000 Mebi Mi 2^20 1,048,576
Giga G 10^9 1,000,000,000 Gibi Gi 2^30 1,073,741,824
Tera T 10^12 1,000,000,000,000 Tebi Ti 2^40 1,099,511,627,776

With small numbers, this difference is unimportant. But as the size of storage media has increased, the discrepancy has become quite significant. For example the difference between 1 terabyte (1,000,000,000,000 bytes) and 1 tebibyte (1,099,511,627,776 bytes) is almost 100 gigabytes!

To avoid confusion, and no doubt quite a few lawsuits, manufacturers will need to be much clearer in the future which prefix they are using!

  • Meantime, please click here to use our converter applet to convert metric to/from computer prefixes.

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