# Prefixes

A powerful feature of the metric system is its use of prefixes. The SI prefixes consist of a set of names and symbols that can be prepended to any SI unit’s name or symbol to modify its value. All SI prefixes have values that are multiples or submultiples of powers of 10. When prepended to a unit, the value of the unit is multiplied by the value of the prefix. For example the prefix “kilo”, symbol “k”, prepended to the unit “metre”, symbol “m”, gives a modified unit “kilometre”, symbol “km”, that has a value equal to 1000 metres.

With the exception of centi, deci, deca and hecto, each SI prefix has a value of 1000^{n}, where *n* is a non-zero integer from -8 to 8. The SI prefixes allow SI units to address very small and very large scales without numbers becoming cumbersome. The scales addressable by the standard SI prefixes have a range of 48 orders of magnitude, or 10^{48}.

##### SI prefixes

SI prefix | Symbol | Value | ||

yotta | Y | 10^{24} |
1000^{8} |
1 000 000 000 000 000 000 000 000 |

zetta | Z | 10^{21} |
1000^{7} |
1 000 000 000 000 000 000 000 |

exa | E | 10^{18} |
1000^{6} |
1 000 000 000 000 000 000 |

peta | P | 10^{15} |
1000^{5} |
1 000 000 000 000 000 |

tera | T | 10^{12} |
1000^{4} |
1 000 000 000 000 |

giga | G | 10^{9} |
1000^{3} |
1 000 000 000 |

mega | M | 10^{6} |
1000^{2} |
1 000 000 |

kilo | k | 10^{3} |
1000^{1} |
1 000 |

hecto | h | 10^{2} |
100 | |

deca | da | 10^{1} |
10 | |

10^{0} |
1000^{0} |
1 | ||

deci | d | 10^{-1} |
0.1 | |

centi | c | 10^{-2} |
0.01 | |

milli | m | 10^{-3} |
1000^{−1} |
0.001 |

micro | µ | 10^{-6} |
1000^{−2} |
0.000 001 |

nano | n | 10^{-9} |
1000^{−3} |
0.000 000 001 |

pico | p | 10^{-12} |
1000^{−4} |
0.000 000 000 001 |

femto | f | 10^{-15} |
1000^{−5} |
0.000 000 000 000 001 |

atto | a | 10^{-18} |
1000^{−6} |
0.000 000 000 000 000 001 |

zepto | z | 10^{-21} |
1000^{−7} |
0.000 000 000 000 000 000 001 |

yocto | y | 10^{-24} |
1000^{−8} |
0.000 000 000 000 000 000 000 001 |

Prefix symbols are printed in roman (upright) type, as are unit symbols, regardless of the type used in the surrounding text, and are attached to unit symbols without a space between the prefix symbol and the unit symbol. With the exception of da (deca), h (hecto), and k (kilo), all multiple prefix symbols are capital (upper case) letters, and all submultiple prefix symbols are lower case letters. All prefix names are printed in lower case letters, except at the beginning of a sentence.

The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or submultiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.

Similarly, prefix names are also inseparable from the unit names to which they are attached. Thus, for example, millimetre, micropascal, and meganewton are single words.

When units include exponents, for example, in square and cubic forms, the prefix is included in the exponentiation. For example, 1 km^{2} means one square kilometre, or the area of a square 1000 m × 1000 m, i.e. (1000 m)^{2}, and not 1000 (m)^{2}.

##### Examples

2.3 cm^{3} |
= 2.3 (cm)^{3} |
= 2.3 (10^{–2} m)^{3} |
= 2.3 × 10^{–6} m^{3} |

1 cm^{–1} |
= 1 (10^{–2} m)^{–1} |
= 10^{2} m^{–1} |
= 100 m^{−1} |

1 V/cm | = (1 V)/(10^{–2} m) |
= 10^{2} V/m |
= 100 V/m |

5000 μs^{−1} |
= 5000 (μs)^{−1} |
= 5000 (10^{−6} s)^{−1} |
= 5 × 10^{9} s^{−1} |

Compound prefix symbols, that is, prefix symbols formed by the juxtaposition of two or more prefix symbols, are not permitted. This rule also applies to compound prefix names.

Prefix symbols can neither stand alone nor be attached to the number 1, the symbol for the unit one. Similarly, prefix names cannot be attached to the name of the unit one, that is, to the word “one”.

Prefix names and symbols are used with a number of non-SI units, but they are never used with the non-SI units of time: minute (min), hour (h), day (d). However astronomers use milliarcsecond, which they denote mas, and microarcsecond, μas, which they use as units for measuring very small angles.

### Non-SI prefixes

Units used in the field of information technology are not included in the SI. These units include the bit, byte and pixel, and derived units such as bit per second, and byte per second. When SI prefixes are used with these units, they should be used only when referring strictly to multiples of powers of 10.

In information technology, it is often convenient to handle quantities in multiples of powers of 2, such as 2^{10}, or 1024. To avoid the incorrect usage of SI prefixes for multiples of powers of 2, there is a set of binary-based multiple prefixes, approved by the International Electrotechnical Commission (IEC), which should be used. For example, one kibibit is equal to 1024 bits, whereas one kilobit should refer only to 1000 bits. The rules for the use of IEC prefixes are similar to those of the SI prefixes.

IEC prefixes should not be used with SI units.

##### IEC prefixes

IEC prefix | Symbol | Value | ||

yobi | Yi | 2^{80} |
1024^{8} |
1 208 925 819 614 629 174 706 176 |

zebi | Zi | 2^{70} |
1024^{7} |
1 180 591 620 717 411 303 424 |

exbi | Ei | 2^{60} |
1024^{6} |
1 152 921 504 606 846 976 |

pebi | Pi | 2^{50} |
1024^{5} |
1 125 899 906 842 624 |

tebi | Ti | 2^{40} |
1024^{4} |
1 099 511 627 776 |

gibi | Gi | 2^{30} |
1024^{3} |
1 073 741 824 |

mebi | Mi | 2^{20} |
1024^{2} |
1 048 576 |

kibi | Ki | 2^{10} |
1024^{1} |
1 024 |

Note: The symbol for kibi is Ki, not ki. |

The value of each IEC prefix is equal to 1024^{n}, where *n* is a positive integer from 1 to 8. The name of the prefix is a portmanteau formed from the first two letters of the SI prefix whose value is equal to 1000^{n}, and the first two letters of the word “binary”

Each IEC prefix symbol is formed from the uppercase version of the first letter of the prefix name followed by the lower case letter “i”.

##### Examples

12 kilobits per second | = 12 kbit/s | = 12 × 1000^{1} bit/s |
= 12 000 bits per second |

12 kibibits per second | = 12 Kibit/s | = 12 × 1024^{1} bit/s |
= 12 288 bits per second |

8 megabytes per second | = 8 MB/s | = 8 × 1000^{2} B/s |
= 8 000 000 bytes per second |

8 mebibytes per second | = 8 MiB/s | = 8 × 1024^{2} B/s |
= 8 388 608 bytes per second |

4.5 gigabytes | = 4.5 GB | = 4.5 × 1000^{3} B |
= 4 500 000 000 bytes |

4.5 gibibytes | = 4.5 GiB | = 4.5 × 1024^{3} B |
= 4 831 838 208 bytes |

Although the IEC prefixes are not part of the SI, they are described here to avoid the incorrect usage of SI prefixes in the field of information technology.