Metric prefix

A metric prefix is a special word that we add to a unit of measurement to show if we are talking about a bigger or smaller amount. For example, the word kilo can be added to gram to mean one thousand grams, which we call a kilogram. In the same way, the word milli can be added to metre to mean one thousandth of a metre, which we call a millimetre.

All metric prefixes we use today are based on ten. Each prefix has its own short symbol that we write before the unit’s symbol. These prefixes have been used in the metric system since it began in the 1790s. Today, special prefixes called SI prefixes are used around the world in the International System of Units. These prefixes help scientists, engineers, and everyday people talk about very big or very small amounts in a clear and easy way.

List of SI prefixes

Several terms redirect here including "Femto", "Ronna-", "Yotta", and "Zepto". For the character Femto, see Griffith (Berserk). For the name, see Ronna. For the prize-linked savings account, see Yotta Technologies. For the Finnish musician, see Yotto. For similar terms, see Yota (disambiguation). For the Indian Q-commerce company, see Zepto (company). For other uses, see Atto, Exa (disambiguation), Peta, Pico, Quetta (disambiguation), Ronto, and Tera.

The BIPM specifies twenty-four prefixes for the International System of Units (SI).

The first uses of prefixes in SI date back to the definition of kilogram after the French Revolution at the end of the 18th century. Several more prefixes came into use, and were recognised by the 1947 IUPAC 14th International Conference of Chemistry before being officially adopted for the first time in 1960.

The prefixes that were most recently adopted are ronna, quetta, ronto, and quecto. These prefixes were adopted in 2022, after a proposal from British metrologist Richard J. C. Brown. Before 2022, Q/q and R/r were the only Latin letters available for abbreviations, with all other Latin letters either being already used for other prefixes or units, easily confused with mathematical symbols, or a combination of these factors. The large prefixes ronna and quetta were adopted in anticipation of needs for use in data science, and because unofficial prefixes that did not meet SI requirements were already circulating. The small prefixes were also added to maintain symmetry.

The prefixes from peta to quetta are based on the Ancient Greek or Ancient Latin numbers from 5 to 10, referring to the 5th through 10th powers of 10³. The initial letter h has been removed from some of these stems and the initial letters z, y, r, and q have been added, ascending in reverse alphabetical order, to avoid confusion with other metric prefixes.

Rules

• The symbols for the units of measure are combined with the symbols for each prefix name. The SI symbols for kilometre, kilogram, and kilowatt, for instance, are km, kg, and kW, respectively. (The symbol for kilo is k.) Except for the early prefixes of kilo, hecto, and deca, the symbols for the prefixes for multiples are uppercase letters, and those for the prefixes for submultiples are lowercase letters.
• All of the metric prefix symbols are made from upper- and lower-case Latin letters except for the symbol for micro, which is uniquely a Greek letter mu (μ).
• The prefix symbols are always prepended to the symbol for the unit without any intervening space or punctuation. This distinguishes a prefixed unit symbol from the product of unit symbols, for which a space or mid-height dot as separator is required. So, for instance, while 'ms' means millisecond, 'm s' or 'm·s' means metre-second.
• Prefixes corresponding to an integer power of one thousand are generally preferred; the prefixes corresponding to tens (deci-, deca-) and hundreds (centi-, hecto-) are less common and are disfavoured in certain fields. Hence, 100 m is preferred over 1 hm (hectometre) or 10 dam (decametres). The prefixes deci- and centi-, and less frequently hecto and deca, are generally used for informal purposes; the centimetre (cm) is especially common. Some modern building codes require that the millimetre be used in preference to the centimetre. These prefixes are also commonly used to create metric units corresponding to older conventional units, for example hectares and hectopascals.
• Prefixes may not be used in combination on a single symbol. This includes the case of the base unit kilogram, which already contains a prefix. For example, milligram (mg) is used instead of microkilogram (μkg).
• During mathematical operations, prefixes are treated as multiplicative factors. For example, 5 km is treated as 5000 m, which allows all quantities based on the same unit to be factored together even if they have different prefixes.
• A prefix symbol attached to a unit symbol is included when the unit is raised to a power. For example, 1 km² denotes 1 km × 1 km = 10⁶ m², not 10³ m².

Usage

Metric prefixes are special labels we add to units of measurement to show if we need a bigger or smaller amount. For example, we can use these prefixes with units like grams or meters.

• The mass of an electron is about 1 rg (rontogram).
• The mass of 1 litre of water is about 1 kg (kilogram).
• The mass of the Earth is about 6 Rg (ronnagrams).
• The mass of Jupiter is about 2 Qg (quettagrams).

When we use metric prefixes with units that are squared or cubed, it changes the meaning in special ways:

• 1 km² means one square kilometre, or the area of a square that is 1000 m on each side. This equals 1,000,000 square metres, not just 1,000 square metres.
• 2 Mm³ means two cubic megametres, or the volume of two cubes that are 1,000,000 m on each side. This equals 2×10¹⁸ m³, not 2,000,000 cubic metres (2×10⁶ m³).

Here are some more examples showing how prefixes work with math:

• 5 mV × 5 mA = 5×10⁻³ V × 5×10⁻³ A = 25×10⁻⁶ V⋅A = 25 μW.
• 5.00 mV + 10 μV = 5.00 mV + 0.01 mV = 5.01 mV.
• 5 cm = 5×10⁻² m = 5 × 0.01 m = 0.05 m.
• 9 km² = 9 × (10³ m)² = 9 × (10³)² × m² = 9×10⁶ m² = 9,000,000 m².
• 3 MW = 3×10⁶ W = 3 × 1,000,000 W = 3,000,000 W.

Application to units of measurement

The use of prefixes began with the metric system in the 1790s, long before the 1960 introduction of the SI. These prefixes can be used with any metric unit, whether part of the SI or not, like millidyne and milligauss. They can also sometimes be used with non-metric units, but not with non-SI units of time.

The kilogram, gram, milligram, microgram, and smaller units are commonly used for measuring mass. However, larger units like megagram and gigagram are rarely used; tonnes or scientific notation are used instead. The kilogram is the only unit in the International System of Units that includes a metric prefix.

The litre, millilitre, microlitre, and smaller are common for measuring volume. In Europe, the centilitre is often used for liquids, while the hectolitre is used for bulk products like grain or beer. Larger volumes are usually measured in kilolitres, megalitres, or gigalitres, or in cubic metres.

For measuring length, the kilometre, metre, centimetre, millimetre, and smaller units are common. The decimetre is rarely used. The micrometre is often called a micron, though this name is not officially recommended. For very small lengths, the ångström and femtometre are sometimes used. Large distances are usually measured using non-metric units like the solar radius, astronomical units, light years, and parsecs.

For time, prefixes are most commonly used for fractions of a second. Larger times are usually measured in minutes, hours, and days. Very long times in science are measured using the Julian year, with prefixes like megaannum (Ma) or gigaannum.

The SI unit for angle is the radian, but degrees and arc-minutes and arc-seconds are also used, especially in astronomy.

For temperature, prefixes are more commonly used with the kelvin to show very high or very low temperatures, like MK (megakelvin) or mK (millikelvin).

The joule and kilojoule are common for measuring energy. The kilowatt-hour is often used for electrical energy. The unit calorie has different definitions, with metric prefixes usually applied to the smaller gram calorie.

Non-standard prefixes

See also: Unit prefix § Unofficial prefixes

Obsolete metric prefixes

Some old prefixes used in the metric system are no longer used. The prefix for ten thousand, myria-, and early prefixes like double- (meaning 2×) and demi- (meaning half) were part of the original system in France in 1795 but were dropped later.

Other old prefixes include hebdo- for ten million and micri- for one hundred trillionth.

Double prefixes

In the past, people used double prefixes like micromillimetres (now called nanometres) and micromicrofarads (now picofarads). These are not used with today’s standard metric system.

Other old double prefixes included "decimilli-" (one ten-thousandth), which was shortened to "dimi-" in France until 1961.

There are no more letters left in the alphabet to create new prefixes. Some ideas suggest using compound prefixes like kiloquetta- for very large numbers, but this has not been officially approved.

Similar symbols and abbreviations

In everyday English, people often use the letter K to mean "thousand." For example, someone might say they have a 40K salary, meaning 40,000, or talk about the Y2K problem from the Year 2000 problem.

In news and money talks, m or M stands for million, b or B stands for billion (10⁹), and t or T stands for trillion (10¹²). In the medical and automotive fields in the United States, cc or ccm means cubic centimetres, which is the same as a millilitre.

Engineers used to use MCM to mean a thousand circular mils for big electrical cables, but now kcmil is the official term. In natural gas and oil, mm or MM stands for millions of British thermal units or therms, and MMbbl means millions of barrels. The letter M for thousand comes from old Roman numerals, where it means 1000.

Typography

Micro symbol

Main article: Micro-

When the prefixes mega- and micro- were first used in 1873, they needed a special symbol that was not just the letter M. They chose the Greek letter mu (μ) to show the difference.

Because many old typewriters and computer keyboards didn’t have a key for μ, people used other short ways to write it, like "mc", "mic", "M", or "u". By around 1960, "u" became the most common way to write it in typed documents. Even when computers replaced typewriters, this kept happening because common computer systems did not include the μ symbol.

Later, the standard ISO 8859-1 added the μ symbol for micro- at a special code point. This was also included in Unicode, where it is listed at U+03BC. Some fonts show this symbol and the Greek letter μ the same way, while others show them differently.

Keyboard entry

Most English-language keyboards do not have a key for μ, so people use special codes to type it. The way to do this depends on the type of computer you are using.

On Microsoft Windows computers:

• You can type it by holding Alt and pressing 0 1 8 1 on the number pad, or
• You can also type it using Alt and the codes b+5, or
• On older systems, you can type it by holding Alt and pressing 2 3 0 on the number pad;

On MacOS computers, you can type it by pressing ⌥ Opt+m or ⌥ Opt+Y.

On Linux computers:

• If you have a Compose key enabled, you can type it by pressing Compose+m+u
• With ibus version 1.5.19 or higher, you can type it by pressing Ctrl+⇧ Shift+u b 5 space
• On the VGA console, you can type it by holding Alt and pressing 1 8 1 on the number pad
• You can also type it by pressing right Alt+m (if the right alt key is set to act as AltGr).

Typesetting in LaTeX

The LaTeX system has a special package called SIunitx that helps write units of measurement clearly. For example, \qty{3}{\tera\hertz} will show up as "3 THz".