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units - Man Page

decimal and binary prefixes


Decimal prefixes

The SI system of units uses prefixes that indicate powers of ten. A kilometer is 1000 meter, and a megawatt is 1000000 watt. Below the standard prefixes.

qquecto10^-30 = 0.000000000000000000000000000001
rronto10^-27 = 0.000000000000000000000000001
yyocto10^-24 = 0.000000000000000000000001
zzepto10^-21 = 0.000000000000000000001
aatto10^-18 = 0.000000000000000001
ffemto10^-15 = 0.000000000000001
ppico10^-12 = 0.000000000001
nnano10^-9  = 0.000000001
µmicro10^-6  = 0.000001
mmilli10^-3  = 0.001
ccenti10^-2  = 0.01
ddeci10^-1  = 0.1
dadeka10^ 1  = 10
hhecto10^ 2  = 100
kkilo10^ 3  = 1000
Mmega10^ 6  = 1000000
Ggiga10^ 9  = 1000000000
Ttera10^12  = 1000000000000
Ppeta10^15  = 1000000000000000
Eexa10^18  = 1000000000000000000
Zzetta10^21  = 1000000000000000000000
Yyotta10^24  = 1000000000000000000000000
Rronna10^27  = 1000000000000000000000000000
Qquetta10^30  = 1000000000000000000000000000000

The symbol for micro is the Greek letter mu, often written u in an ASCII context where this Greek letter is not available.

Binary prefixes

The binary prefixes resemble the decimal ones, but have an additional 'i' (and "Ki" starts with a capital 'K'). The names are formed by taking the first syllable of the names of the decimal prefix with roughly the same size, followed by "bi" for "binary".

Kikibi2^10 = 1024
Mimebi2^20 = 1048576
Gigibi2^30 = 1073741824
Titebi2^40 = 1099511627776
Pipebi2^50 = 1125899906842624
Eiexbi2^60 = 1152921504606846976
Zizebi2^70 = 1180591620717411303424
Yiyobi2^80 = 1208925819614629174706176


Before these binary prefixes were introduced, it was fairly common to use k=1000 and K=1024, just like b=bit, B=byte. Unfortunately, the M is capital already, and cannot be capitalized to indicate binary-ness.

At first that didn't matter too much, since memory modules and disks came in sizes that were powers of two, so everyone knew that in such contexts "kilobyte" and "megabyte" meant 1024 and 1048576 bytes, respectively. What originally was a sloppy use of the prefixes "kilo" and "mega" started to become regarded as the "real true meaning" when computers were involved. But then disk technology changed, and disk sizes became arbitrary numbers. After a period of uncertainty all disk manufacturers settled on the standard, namely k=1000, M=1000 k, G=1000 M.

The situation was messy: in the 14k4 modems, k=1000; in the 1.44 MB diskettes, M=1024000; and so on. In 1998 the IEC approved the standard that defines the binary prefixes given above, enabling people to be precise and unambiguous.

Thus, today, MB = 1000000 B and MiB = 1048576 B.

In the free software world programs are slowly being changed to conform. When the Linux kernel boots and says

hda: 120064896 sectors (61473 MB) w/2048KiB Cache

the MB are megabytes and the KiB are kibibytes.

See Also

The International System of Units.

Referenced By

bitmath(1), vnstat(1), vnstat.conf(5), vnstati(1).

2024-05-02 Linux man-pages 6.9.1