International System of Units

"SI" redirects here. For other uses, see Si.

For a topical guide to this subject, see Outline of the metric system.

The seven SI base units and the interdependency of their definitions. Clockwise from top: kelvin (temperature), second (time), metre (length), kilogram (mass), candela (luminous intensity), mole (amount of substance) and ampere (electric current).

The International System of Units (abbreviated SI from French: Le Système international d'unités) is the modern form of the metric system. It comprises a coherent system of units of measurement built around seven base units, 22 named and an indeterminate number of unnamed coherent derived units, and a set of prefixes that act as decimal-based multipliers. The standards, published in 1960, are based on the metre-kilogram-second system, rather than the centimetre-gram-second system, which, in turn, had several variants. The SI has been declared to be an evolving system; thus prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses, and as the precision of measurements improves. SI is the world's most widely used system of measurement, used in both everyday commerce and science.

The system has been nearly globally adopted. Only Burma, Liberia and the United States have not adopted SI units as their official system of weights and measures. In the United States metric units are not commonly used outside of science, medicine and the government; however, United States customary units are officially defined in terms of SI units. The United Kingdom has officially adopted a partial metrication policy, with no intention of replacing imperial units entirely. Canada has adopted it for most purposes, but imperial units are still legally permitted and remain in common use throughout a few sectors of Canadian society, particularly in the buildings, trades and railways sectors.

History

Main article: History of the metric system

The metric system was first implemented during the French Revolution (1790s) with just the metre and kilogram as standards. In the 1860s British scientists, working through the British Association for the Advancement of Science laid the foundations for a coherent system based on length, mass and time known as the base units. The inclusion of electrical units into the system was hampered until 1900 when Giovanni Giorgi identified the need to define one electrical quantity as a base unit alongside the original three base units. Meanwhile, in 1875, the Treaty of the Metre passed custodianship of the prototype kilogram and metre from French to international control. In 1921 the Treaty was extended to include all physical measurements and in 1948 an overhaul of the metric system was set in motion which resulted in the publication of the International System of Units in 1960. The 1960 Standard defined fifth and sixth base units—temperature and luminous intensity. In 1971 a seventh base unit, amount of substance was added to the definition of SI.

Uncoordinated development

Old boundary stone in Pontebba, marking the former border between Austria-Hungary and Italy; the myriametre (10 km), since deprecated, was in common use in Central Europe during the mid-nineteenth century.

The metric system was developed from 1791 onwards by a group of scientists commissioned by the Assemblée nationale and Louis XVI of France to create a unified and rational system of measures. The group, which included Antoine-Laurent Lavoisier (the "father of modern chemistry") and the mathematicians Pierre-Simon Laplace and Adrien-Marie Legendre, used the principles that had been proposed by the English cleric John Wilkins in 1668 and naming concepts developed from those proposed in 1670 by the French cleric Gabriel Mouton. On 1 August 1793, the National Convention adopted the new decimal metre with a provisional length as well as the other decimal units with preliminary definitions and terms. The law of 7 April 1795 (loi du 18 germinal) defined the terms gramme and kilogramme which replaced the former terms gravet (correctly milligrave) and grave, and on 22 June 1799, after Pierre Méchain and Jean-Baptiste Delambre completed their survey, the definitive standard metre was deposited in the French National Archives. On 10 December 1799 (a month after Napoleon's coup d'état), the law by which metric system was to be definitively adopted in France was passed.

During the first half of the nineteenth century there was little consistency in the choice of preferred multiples of the base units – typically the myriametre (10000 metres) was in widespread use in both France and parts of Germany, while the kilogram (1000 grams) rather than the myriagram was used for mass.

In 1832 Carl Friedrich Gauss implicitly defined a coherent system of units when he measured the earth's magnetic field in absolute units quoted in terms of millimetres, grams, and seconds. In the 1860s James Clerk Maxwell and William Thomson (later Lord Kelvin), working through the British Association for the Advancement of Science formulated the concept of a coherent system of units with base units and derived units. The principle of coherence was successfully used to define a number of units of measure based on the centimetre–gram–second (cgs) system of units (cgs) including the erg for energy, the dyne for force, the barye for pressure, dynamic viscosity in poise and the kinematic viscosity in stokes.

Metre Convention

The desire for international cooperation in metrology led to the signing in 1875 of the Metre Convention, a treaty that established three international organisations to oversee the keeping of metric standards:

• General Conference on Weights and Measures (Conférence générale des poids et mesures or CGPM) – a meeting every four to six years of delegates from all member states;
• International Bureau of Weights and Measures (Bureau international des poids et mesures or BIPM) – an international metrology centre at Sèvres in France; and
• International Committee for Weights and Measures (Comité international des poids et mesures or CIPM) – an administrative committee that meets annually at the BIPM.

Initially the convention only covered standards for the metre and the kilogram, new prototypes of which were manufactured by the British firm Johnson, Matthey & Co and accepted by the GCPM in 1889. It was only in 1921 that the convention was extended to include all physical units that the CGPM was able to address inconsistencies in the way that the metric system had been used.

Towards SI

In the nineteenth century, attempts to produce a coherent set of electrical units was beset with difficulties.

William Thomson, later Lord Kelvin, who, with James Clerk Maxwell, was one of the most influential figures in the theoretical development of the metric system.

At the close of the nineteenth century three different systems of units of measure existed for electrical measurements – a CGS-based system for electrostatic units (also known as the Gaussian system), a CGS-based system for electromechanical units and an MKS-based system (the "International system") for electrical distribution systems. In 1900 Giovanni Giorgi published a paper in which he advocated using a fourth base unit alongside the existing three base units. The fourth unit could be either electric current or voltage or electrical resistance.

James Clerk Maxwell, who, with William Thomson, later Lord Kelvin, was one of the most influential figures in the theoretical development of the metric system.

In the late nineteenth and early twentieth centuries a number of non-coherent units of measure were developed such as the Pferdestärke or "metric horsepower" for power, the darcy for permeability and the use of "millimetres of mercury" for the measurement of both barometric and blood pressure. All these units incorporate standard gravity in their definitions.

At the end of Second World War, a number of different systems of measurement were in use throughout the world. Some of these systems were metric system variations, whereas others were based on customary systems of measure. It was recognised that additional steps were needed to promote a worldwide measurement system. After representations by the International Union of Pure and Applied Physics (IUPAP) and by the French Government, the 9th General Conference on Weights and Measures (CGPM), in 1948, asked the International Committee for Weights and Measures (CIPM) to conduct an international study of the measurement needs of the scientific, technical, and educational communities.

Based on the findings of this study, the 10th CGPM in 1954 decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. The six base units that were recommended are the metre, kilogram, second, ampere, degree Kelvin (later renamed kelvin), and candela. In 1960, the 11th CGPM named the system the International System of Units, abbreviated SI from the French name, Le Système international d'unités. The BIPM has also described SI as "the modern metric system". The seventh base unit, the mole, was added in 1971 by the 14th CGPM.

SI Brochure and conversion factors

Cover of brochure The International System of Units

The CGPM have published a brochure, the 8th edition of which appeared in 2006, in which the various recommendations that make up SI have been codified. This brochure leaves some scope for local interpretation, particularly in respect of language. The United States National Institute of Standards and Technology has produced a version of the CGPM document (NIST SP 330) which clarifies local interpretation in respect of English-language publications that use American English and another document (NIST SP 811) that gives general guidance for the use of SI in the United States.

The writing and maintenance of the CGPM brochure is carried out by one of the consultative committees of the International Committee for Weights and Measures (CIPM) – the Consultative Committee for Units (CCU). The CIPM nominates the chairman of this committee, but its membership is made up of representatives of various other international bodies rather than CIPM or CGPM nominees. This committee also provides a forum for the bodies concerned to provide input to the CIPM in respect of on-going enhancements to SI. In 2010 the CCU proposed a number of changes to the definitions of the base units used in SI. The CIPM meeting of October 2010 found that the proposal was not complete, and it is expected that the CGPM will consider the full proposal in 2014.

The definitions of the terms 'quantity', 'unit', 'dimension' etc. that are used in the SI Brochure are those given in the International Vocabulary of Metrology, a publication produced by the Joint Committee for Guides in Metrology (JCGM), a working group consisting of eight international standards organisations under the chairmanship of the director of the BIPM. The quantities and equations that define the SI units are now referred to as the International System of Quantities (ISQ), and are set out in the ISO/IEC 80000 Quantities and Units.

Appendix B of NIST SP 811, a list of conversion factor between SI and customary units, is an extension to the SI Brochure.

Units and prefixes

The International System of Units consists of a set of base units, a set of derived units, some of which have special names and a set decimal-based multipliers that are denoted as prefixes. The term "SI Units" includes all three categories, but the term "coherent SI units" includes only base units and coherent derived units.

Base units

Main article: SI base unit

Base units are the building blocks of SI – all other units of measure can be derived from the base units. When Maxwell first introduced the concept of a coherent system, he identified three quantities that could be used as base units – mass, length and time. Giorgi later identified the need for an electrical base unit – theoretically electrical current, potential difference, electrical resistance, electrical charge or any one of a number of other units could have been used as the base unit with the remaining units being then defined by the laws of physics – the unit of electric current was chosen for SI. The remaining three base units were added later.

SI base units

Unit name	Unit symbol	Quantity name	Definition (Incomplete)	Dimension symbol
metre	m	length	Original (1793): 1/10000000 of the meridian through Paris between the North Pole and the EquatorFG Current (1983): The distance travelled by light in vacuum in 1/299792458 second	L
kilogram	kg	mass	Original (1793): The grave was defined as being the weight [mass] of one cubic decimetre of pure water at its freezing point.FG Current (1889): The mass of the International Prototype Kilogram	M
second	s	time	Original (Medieval): 1/86400 of a day Current (1967): The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom	T
ampere	A	electric current	Original (1881): A tenth of the electromagnetic CGS unit of current. The [CGS] emu unit of current is that current, flowing in an arc 1 cm long of a circle 1 cm in radius creates a field of one oersted at the centre.IEC Current (1946): The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10−7 newton per metre of length	I
kelvin	K	thermodynamic temperature	Original (1743): The centigrade scale is obtained by assigning 0° to the freezing point of water and 100° to the boiling point of water. Current (1967): The fraction 1/273.16 of the thermodynamic temperature of the triple point of water	Θ
mole	mol	amount of substance	Original (1900): The molecular weight of a substance in mass grams.ICAW Current (1967): The amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12.	N
candela	cd	luminous intensity	Original (1946):The value of the new candle is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per square centimetre Current (1979): The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.	J
Note The original definitions of the various base units in the above table were made by the following authorities: FG = French Government IEC = International Electrotechnical Commission ICAW = International Committee on Atomic Weights

Derived units

Main article: SI derived unit

Derived units are formed by powers, products or quotients of the base units and are unlimited in number; Derived units are associated with derived quantities, for example velocity is a quantity that is derived from the base quantities of time and distance which, in SI, has the dimensions metres per second (symbol m/s). The dimensions of derived units can be expressed in terms of the dimensions of the base units.

Some derived units have special names, for example the unit of force is the newton. Coherent units (such as those in SI) are derived units that contain no numerical factor other than 1: in the example above, one newton is the force required to accelerate a mass of one kilogram by one metre per second squared. Since the SI units of mass and acceleration are kg and m⋅s⁻² respectively and F ∝ m × a, the units of force (and hence of newtons) is formed by multiplication to give kg⋅m⋅s⁻². Since the newton is part of a coherent set of units, the constant of proportionality is 1.

Named units derived from SI base units

Name	Symbol	Quantity	Expressed in terms of other SI units	Expressed in terms of SI base units
radian	rad	angle	1	m/m
steradian	sr	solid angle	1	m2/m2
hertz	Hz	frequency		s−1
newton	N	force, weight		kg⋅m⋅s−2
pascal	Pa	pressure, stress	N/m2	kg⋅m−1⋅s−2
joule	J	energy, work, heat	N⋅m	kg⋅m2⋅s−2
watt	W	power, radiant flux	J/s	kg⋅m2⋅s−3
coulomb	C	electric charge or quantity of electricity		s⋅A
volt	V	voltage (electrical potential difference), electromotive force	W/A	kg⋅m2⋅s−3⋅A−1
farad	F	electric capacitance	C/V	kg−1⋅m−2⋅s4⋅A2
ohm	Ω	electric resistance, impedance, reactance	V/A	kg⋅m2⋅s−3⋅A−2
siemens	S	electrical conductance	A/V	kg−1⋅m−2⋅s3⋅A2
weber	Wb	magnetic flux	V⋅s	kg⋅m2⋅s−2⋅A−1
tesla	T	magnetic field strength	Wb/m2	kg⋅s−2⋅A−1
henry	H	inductance	Wb/A	kg⋅m2⋅s−2⋅A−2
degree Celsius	°C	temperature relative to 273.15 K		K
lumen	lm	luminous flux	cd⋅sr	cd
lux	lx	illuminance	lm/m2	m−2⋅cd
becquerel	Bq	radioactivity (decays per unit time)		s−1
gray	Gy	absorbed dose (of ionizing radiation)	J/kg	m2⋅s−2
sievert	Sv	equivalent dose (of ionizing radiation)	J/kg	m2⋅s−2
katal	kat	catalytic activity		s−1⋅mol
Notes 1. The radian and steradian, once given special status, are now considered dimensionless derived units. 2. The ordering of this table is such that any derived unit is based only on base units or derived units that precede it in the table.

Prefixes

Main article: Metric prefix

A prefix may be added to a unit to produce a multiple of the original unit. All multiples are integer powers of ten, and beyond a hundred(th) all are integer powers of a thousand. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth; hence there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, and multiples of the kilogram are named as if the gram was the base unit. Thus a millionth of a metre is a micrometre, not a millimillimetre, and a millionth of a kilogram is a milligram, not a microkilogram.

Standard prefixes for the SI units of measure

Multiples	Name		deca-	hecto-	kilo-	mega-	giga-	tera-	peta-	exa-	zetta-	yotta-
	Prefix		da	h	k	M	G	T	P	E	Z	Y
	Factor	100	101	102	103	106	109	1012	1015	1018	1021	1024
Fractions	Name		deci-	centi-	milli-	micro-	nano-	pico-	femto-	atto-	zepto-	yocto-
	Prefix		d	c	m	μ	n	p	f	a	z	y
	Factor	100	10−1	10−2	10−3	10−6	10−9	10−12	10−15	10−18	10−21	10−24

Non-SI units accepted for use with SI

Main article: non-SI units accepted for use with SI

Although, in theory, SI can be used for any physical measurement, it is recognised that some non-SI units still appear in the scientific, technical and commercial literature, and will continue to be used for many years to come. In addition, certain other units are so deeply embedded in the history and culture of the human race that they will continue to be used for the foreseeable future. The CIPM has catalogued a number of such non-SI units accepted for use with SI and published them in the SI Brochure thereby ensuring that their use is consistent across the globe. These units have been grouped as follows:

The litre is classed as a non-SI unit accepted for use with the SI.
Being one thousandth of a cubic metre, the litre is not a coherent unit of measure with respect to SI.

• Non-SI units accepted for use with the SI (Table 6):

Certain units of time, angles and legacy non-SI metric units have a long history of consistent use. Most of mankind has used the day and its non-decimal subdivisions as a basis of time and, unlike the foot or the pound, these were the same regardless of where it was being measured. The radian, being 1/2π of a revolution has mathematical niceties, but it is cumbersome for navigation, and, as with time, the units used in navigation have a large degree of consistency around the world. The tonne, litre and hectare were adopted by the CGPM in 1879 and have been retained as units that may be used alongside SI units, having been given unique symbols. The catalogued units are

minute, hour, day, degree of arc, minute of arc, second of arc, hectare, litre and tonne

• Non-SI units whose values in SI units must be obtained experimentally (Table 7).

Physicists often use units of measure that are based on natural phenomena, particularly when the quantities associated with these phenomena are many orders of magnitude greater than or less than the equivalent SI unit. The most common ones have been catalogued in the SI brochure together with consistent symbols and accepted values, but with the caveat that their physical values need to be measured.:

electronvolt, dalton/unified atomic mass unit, astronomical unit, speed of light, Planck constant and electron mass

• Other non-SI units (Table 8):

A number of non-SI units that had never been formally sanctioned by the CGPM have continued to be used across the globe in many spheres including health care and navigation. As with the units of measure in Tables 6 and 7, these have been catalogued by the CIPM in the SI brochure to ensure consistent usage, but with the recommendation that authors who use them should define them wherever they are used.

bar, millimetre of mercury, ångström, nautical mile, barn, knot, neper and [deci]bel

• Non-SI units associated with the CGS and the CGS-Gaussian system of units (Table 9)

The SI manual also catalogues a number of legacy units of measure that are used in specific fields such as geodesy and geophysics or are found in the literature, particularly in classical and relativistic electrodynamics where they have certain advantages: The units that are catalolgued are:

erg, dyne, poise, stokes, stilb, phot, gal, maxwell, gauss and œrsted.

Writing unit symbols and the values of quantities

Before 1948, the writing of metric quantities was haphazard. In 1879, the CIPM published recommendations for writing the symbols for length, area, volume, and mass, but it was outside its domain to publish recommendations for other quantities. Beginning in about 1900, physicists who had been using the symbol "μ" for "micrometre" (or "micron"), "λ" for "microlitre", and "γ" for "microgram" started to use the symbols "μm", "μL" and "μg", but it was only in 1935, a decade after the revision of the Metre Convention that the CIPM formally adopted this proposal and recommended that the symbol "μ" be used universally as a prefix for 10⁻⁶.

In 1948, the ninth CGPM approved the first formal recommendation for the writing of symbols in the metric system when the basis of the rules as they are now known was laid down. When, in 1960, the International System of Units was introduced, the rules that were put in place in 1948 were adapted for use with the new system. Since then the rules, apart from some minor modifications, have remained in place.

Writing the unit names

The CGPM rules state that the names of units follow the grammatical rules associated with common nouns: in English and in French they start with a lowercase letter (e.g., newton, hertz, pascal), even when the symbol for the unit begins with a capital letter. This also applies to "degrees Celsius", since "degree" is the unit. In German, however, the names of units, just like all German nouns, start with capital letters. The spelling of unit names is a matter for the guardians of the language concerned – the official British and American spellings for certain SI units differ – British English uses the spelling deca-, metre, and litre whereas American English uses the spelling deka-, meter, and liter, respectively.

Likewise, the plural forms of units follow the grammar of the language concerned: in English, the normal rules of English grammar are used, e.g. "henries" is the plural of "henry". However the units lux, hertz, and siemens have irregular plurals in that they remain the same in both their singular and plural form.

In English, when unit names are combined to denote multiplication of the units concerned, they are separated with a hyphen or a space (e.g. newton-metre or newton metre). The plural is formed by converting the last unit name to the plural form (e.g. ten newton-metres).

Representation of SI units in Chinese and Japanese

Chinese expressway distances road sign in eastern Beijing. Although the primary text is in Chinese, the distances use the internationally recognised numerals and symbols.

In Japanese and Chinese there exist logograms and the rules for the writing unit names adapted to suit the languages.

Japanese

A set of characters representing various metric units was created in Japan in the late 19th century. Characters exist for three base units: the metre (米), litre (升) and gram (克). These were combined with a set of six prefix characters—kilo- (千), hecto- (百), deca- (十), deci- (分), centi- (厘) and milli- (毛)—to form an additional eighteen single-character units. The seven length units (kilometre to millimetre), for example, are 粁, 粨, 籵, 米, 粉, 糎 and 粍. These characters, however, are not in common use today instead units are written out in katakana, a Japanese syllabary.

Chinese

The basic units are 米 mǐ "metre", 升 shēng "litre", 克 kè "gram", and 秒 mǐao "second". Some sample prefixes are 分 fēn "deci", 厘 lí "centi", 毫 háo "milli", and 微 wēi "micro". These are not combined into a single character, so for example centimetres are simply 厘米 límǐ.

The symbols for the metric units are internationally recognised Latin characters or, in respect of "Ω" or "μ", Greek characters.

Writing unit symbols and the values of quantities

Although the writing of unit names is language-specific, the writing of unit symbols and the values of quantities is consistent across all languages and as such the SI brochure has specific rules in respect of writing them. The guideline produced by NIST clarifies language-specific areas in respect of American English that were left open by the SI brochure, but is otherwise identical to the SI brochure.

General rules

General rules for writing SI units and quantities apply to text that is either hand-written or produced using an automated process:

• Symbols are mathematical entities, not abbreviations, and as such do not have an appended period/full stop (.) unless the rules of grammar demand one for another reason such as denoting the end of a sentence.
• A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator (e.g., "k" in "km", "M" in "MPa", "G" in "GHz"). Compound prefixes are not allowed.
• Symbols for derived units formed by multiplication are joined with a centre dot (·) or a non-break space; for example "N·m" or "N m".
• Symbols for derived units formed by division are joined with a solidus (/), or given as a negative exponent. E.g., the "metre per second" can be written m/s, m s⁻¹, m·s⁻¹, or m/s. Only one solidus should be used; e.g., kg/(m·s²) and kg·m⁻¹·s⁻² are acceptable, but kg/m/s² is ambiguous and unacceptable.

Acceleration due to gravity.
Note the lower case letters (neither "metres" nor "seconds" were named after people), the space between the value and the units and the superscript "2" to denote "squared"

• The first letter of symbols for units derived from the name of a person is written in upper case, otherwise they are written in lower case. For example, the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa", but the symbol for mole is written "mol". Thus "T" is the symbol for teslas, a measure of magnetic field strength and "t" the symbol for tonnes, a measure of mass. Since 1979 the litre may exceptionally be written using either an upper case "L" or a lower case "l", a decision prompted by the similarity of the lower case letter "l" to the numeral "1", especially with certain type-faces or English-style handwriting. The American National Institute of Standards and Technology recommends that within the United States "L" be used rather than "l".
• Symbols of units do not have a plural form; e.g., "25 kg", not "25 kgs".
• Upper-case and lower-case prefixes are not interchangeable—the quantities "1 mW" and "1 MW" represent two different quantities, the former is the typical power requirement of a hearing aid (1 milliwatt or 0.001 watts) and the latter typical power requirement of a suburban train (1 megawatt or 1000000 watts).
• The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line." In practice, the decimal point is used in English-speaking countries and most of Asia, and the comma in most of Latin America and in continental European languages.
• Spaces should be used as a thousands separator (1000000) in contrast to commas or periods (1,000,000 or 1.000.000) to reduce confusion resulting from the variation between these forms in different countries.
• Any line-break inside a number, inside a compound unit, or between number and unit should be avoided. Where this is not possible, line breaks should coincide with thousands separators.
• Since the value of "billion" and "trillion" can vary from language to language, the dimensionless terms "ppb" (parts per billion) and "ppt" (parts per trillion) should be avoided. However, no alternative is suggested in the SI Brochure.

Printing SI symbols

Further rules are specified in respect of production of text using printing presses, word processors, typewriters and the like.

• Symbols are written in upright (Roman) type (m for metres, s for seconds), so as to differentiate from the italic type used for quantities (m for mass, s for displacement). By consensus of international standards bodies, this rule is applied independent of the font used for surrounding text.
• The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., "2.21 kg", "7.3×10² m²", "22 K". This rule explicitly includes the per cent sign (%) and the symbol for degrees of temperature (°C). Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.
• In Chinese, Japanese, and Korean language computing (CJK), some of the commonly used units, prefix-unit combinations, or unit-exponent combinations have been allocated predefined single characters taking up a full square. Unicode includes these in its CJK Compatibility and Letter like Symbols subranges for back compatibility, without necessarily recommending future usage. These are summarised in Unicode symbols. The cursive ℓ, a letter-like symbol, has been used in a number of countries in addition to China and Japan as a symbol for the litre, but this is not currently recommended by any standards body.
• In print, the space used as a thousands separator (commonly called a thin space) is typically narrower than that used between words.

Realisation of units

A silicon sphere for the Avogadro project used for measuring the Avogadro constant to a relative uncertainty of 2×10⁻⁸ or less.

Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis on which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a quantity of the same kind as the unit. A description of the practical realisation (French: Mise en pratique) of the base units is given in an electronic appendix to the SI brochure.

The published mise en pratique is not the only way in which a base unit can be determined: the SI brochure states that "any method consistent with the laws of physics could be used to realise any SI unit." In the current (2012) exercise to overhaul the definitions of the base units, various consultative committees of the CIPM have required that more than one mise en pratique shall be developed for determining the value of each unit. In particular:

• At least three separate experiments be carried out yielding values having a relative standard uncertainty in the determination of the kilogram of no more than 5×10⁻⁸ and at least one of these values should be better than 2×10⁻⁸. Both the Watt balance and the Avogadro project should be included in the experiments and any differences between these be reconciled.
• When determining the kelvin, the relative uncertainty of Boltzmann constant derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry be better than one part in 10⁻⁶ and that these values be corroborated by other measurements.

Post 1960 changes

The preamble to the Metre Convention read "Desiring the international uniformity and precision in standards of weight and measure, have resolved to conclude a convention ...". Changing technology has led to an evolution of the definitions and standards that has followed two principal strands - changes to SI itself and clarification of how to use units of measure that are not part of SI, but are still nevertheless used on a worldwide basis.

Changes to the SI

Since 1960 the CGPM has made a number of changes to SI. These include:

• The 13th CGPM (1967) renamed the "degree Kelvin" (symbol °K) to the "kelvin" (symbol K)
• The 14th CGPM (1971) added the mole (symbol mol) to the list of base units.
• The 14th GCPM (1971) added the pascal (symbol Pa) for pressure and the siemens (symbol S) for electrical conductance to the list of named derived units.
• The 15th CGPM (1975) added the becquerel (symbol Bq) for "activity referred to a radionuclide" and the gray (symbol Gy) for ionizing radiation to the list of named derived units
• In order to distinguish between "absorbed dose" and "dose equivalent", the 16th CGPM added the sievert (symbol Sv) to the list of named derived units as the unit of dose equivalent.
• The 16th CGPM (1979) clarified that in a break with convention either the letter "L" or the letter "l" may be used as a symbol for the litre.

A sphygmomanometer - the traditional device that measures blood pressure using mercury in a manometer. Pressures are recorded in "millimetres of mercury" - a non-SI unit

• The 21st CGPM (1999) added the katal (symbol kat) for catalytic activity to the list of named derived units.
• In its original form (1960), the SI defined prefixes for values ranging from the pica (symbol p) having a value of 10⁻¹² to the tera (symbol T) having a value of 10¹². The list was extended at the 12th CGPM (1964), the 15th CGPM (1975) and at the 19th CGPM (1991) to give the current range of prefixes.

In addition, advantage was taken of developments in technology to redefine many of the base units enabling the use of higher precision techniques.

Retention of non-SI units

Although, in theory, SI can be used for any physical measurement, it is recognised that some non-SI units still appear in the scientific, technical and commercial literature, and will continue to be used for many years to come. In addition, certain other units are so deeply embedded in the history and culture of the human race that they will continue to be used for the foreseeable future. The CIPM has catalogued such units and included them in the SI brochure so that they can be used consistently.

The first such group are the units of time and of angles and certain legacy non-SI metric units. Most of mankind has used the day and its subdivisions as a basis of time with the result that the second, minute, hour and day, unlike the foot or the pound, were the same regardless of where it was being measured. The second has been catalogued as an SI unit, its multiples as units of measure that may be used alongside the SI. The measurement of angles has likewise had a long history of consistent use - the radian, being 1/2π of a revolution has mathematical niceties, but it is cumbersome for navigation, hence the retention of the degree, minute and second of arc. The tonne, litre and hectare were adopted by the CGPM in 1879 and have been retained as units that may be used alongside SI units, having been given unique symbols.

Physicists often use units of measure that are based on natural phenomena such as the speed of light, the mass of a proton (approximately one dalton), the charge of an electron and the like. These too have been catalogued in the SI brochure with consistent symbols, but with the caveat that their physical values need to be measured.

In the interests of standardising health-related units of measure used in the nuclear industry, the 12th CGPM (1964) accepted the continued use of the curie (symbol Ci) as a non-SI unit of activity for radionuclides; the becquerel, sievert and gray were adopted in later years. Similarly, the millimetre of mercury (symbol mmHg) was retained for measuring blood pressure.

Worldwide adoption of SI

Top view of the 2 kg weight with a credit card to show the weight's size)

Bottom view of the 2 kg showing the lead plug and assayer's stamp.

A commercial quality hexagonal 2 kg weight manufactured in 1979 with a lead plug and assayer's mark that is similar to, but which predates OIML recommendation R52.

The change to SI had little effect everyday life in countries that used the metric system - the metre, kilogram, litre and second remained unchanged as did the way in which they were used - most of the changes only affected measurements in the workplace. The CGPM has a role of recommending changes, but had no formal role in the enforcement of such changes although another inter-governmental organisation, the International Organization of Legal Metrology (OIML) had a formal role in providing a forum for the harmonisation of national legislation in respect of metrology. The formal adoption of SI varied from country to country: when those countries that had not yet adopted the metric system did so, they adopted SI directly. There was no "standard" way in which countries where the metric system was in use migrated to using SI.

In 1960, the world's largest economy was that of the United States, followed by the United Kingdom, West Germany, France, Japan, China and India. Of these the principal non-metric countries were the United States and the United Kingdom. France and Germany had been using the metric system for about a century, China had been using the metric system for 35 years while India and Japan had adopted the metric system within the preceding five years. Other non-metric countries were those where the United Kingdom or the United States had considerable influence.

United Kingdom and the former Empire

See also: Metrication in the United Kingdom, Metrication in Australia, Metrication in New Zealand, and Metrication in Canada

Even though the use of metric units were legalised for trade in 1864, the United Kingdom had signed the Metre Convention in 1884 and Parliament had defined the yard and the pound in terms of the metre and the kilogram in 1897, the United Kingdom continued to use the imperial system of measure and to export the imperial system of units to the Empire. In 1932, the system of Imperial Preference was set up at the Ottawa Conference. Although Ireland left the Commonwealth in 1948 and South Africa in 1961, both continued their close economic ties with the Commonwealth.

Metrication logo of the Board of Trade

When the SI standard was published in 1960, the only major Commonwealth country to have adopted the metric system was India. In 1965, after numerous false starts the then Federation of British Industry informed the British Government that its members favoured the adoption of the metric system. The rationale behind the request was that 80% of British exports were to countries that used the metric system or that were considering changing to the metric system. The Board of Trade, on behalf of the Government, agreed to support a ten-year metrication programme. The government agreed to a voluntary policy requiring minimal legislation and costs being to be borne where they fell. SI would be used from the outset. The rest of the Commonwealth, South Africa and Ireland followed within a few years; in some counties such as South Africa and Australia metrication was mandatory rather than voluntary.

By 1980 all apart from the United Kingdom, Canada and Ireland had effectively completed their programs. In the United Kingdom the breakdown of voluntary metrication in the mid-1970s coincided with the United Kingdom's obligations as part of the EEC to adopt the metric system, resulting in legislation to force metrication in certain areas and the eurosceptic movement adopting an anti-metrication stance and the United Kingdom seeking a number of derogations from the relevant EEC directives. Once the metrication of most consumer goods was completed in 2000, aspects of British life, especially in government, commerce and industry used SI. Although SI or units approved for use alongside SI are used in most areas where units of measure are regulated imperial units are widely encountered in unregulated areas such as the press and everyday speech. The situation in Ireland, apart from road signs which were metricated in the early 2000s, is similar to that in the United Kingdom.

United States

Main article: Metrication in the United States

Even though Congress legalised the use of the metric system in 1866, signed the Metre Convention in 1875 and under the Mendenhall Order in 1893 defined the pound and the yard in terms of the kilogram and metre respectively, the United States continued to use customary units - when the SI standard was published in 1960, the United States was one of the largest countries that did not use the metric system, though as a result of their Spanish heritage, metric units were used widely in Puerto Rico.

On February 10, 1964, the National Bureau of Standards (now the National Institute of Standards and Technology) issued a statement that it was to use SI except where this would have an obvious detrimental effect. In 1968 the United States Congress authorised the U.S. Metric Study the first volume of which was delivered in 1970. This was followed in 1975 by Congress passing the Metric Conversion Act of 1975. Voluntary metrication was to be coordinated by the United States Metric Board (USMB), but public response included resistance, apathy, and sometimes ridicule. The board was disbanded in 1982.

ANMC logo

The 1988 Omnibus Foreign Trade and Competitiveness Act, an act that removed international trade barriers amended the Metric Conversion Act of 1975 and designating the metric system as "the Preferred system of weights and measures for United States trade and commerce". The legislation stated that the federal government has a responsibility to assist industry, especially small business, as it voluntarily converts to the metric system of measurement. Exceptions were made for the highway and construction industries; the Department of Transportation planned to require metric units by 2000, but this plan was cancelled by the 1998 highway bill TEA21. However the U.S. military uses of the metric system widely, partly because of the need to work with armed services from other nations.

Although overall responsibility for labeling requirements of consumer goods lies with Congress and are therefore covered by federal law, details of labelling requirements for certain commodities are controlled by state law or by other authorities such as the Food and Drug Administration, Environmental Protection Agency and Alcohol and Tobacco Tax and Trade Bureau. The federal Fair Packaging and Labeling Act (FPLA), originally passed in 1964, was amended in 1992 to require consumer goods directly under its jurisdiction to be labelled in both customary and metric units. Some industries are engaged in efforts to amend this law to allow manufacturers to use only metric labelling. The National Conference on Weights and Measures has developed the Uniform Packaging and Labeling Regulations (UPLR) which provides a standard approach to those sections of packaging law that are under state control. Acceptance of the UPLA varies from state to state - fourteen states accept it by merely citing it in their legislation. During the first decade of the 21st century, the EU directive 80/181/EEC had required that dual unit labelling cease by the end of 2009. This was backed up by requests from other nations including Japan and New Zealand to permit metric-only labelling as an aid to trade with those countries. Opinion in the United States was split - a bill to permit metric-only labelling at the federal level was to have been introduced in 2005 but Significant opposition from the Food Marketing Institute, representing U.S. grocers, has delayed the introduction of the bill. During a routine decennial review of the directive in 2008, the EU postponed the sunset clause for dual units indefinitely.

Meanwhile, in 1999 the UPLA was amended to permit metric-only labelling and automatically became law in those states that accept UPLA "as is". By 1 January 2009, 48 out of 50 states permit metric-only labelling, either through UPLA or through their own legislation. As of February 2013 the use of metric (and therefore SI) units in the United States follows no coherent pattern. Dual-unit labelling on consumer goods is mandatory. Some consumer goods such as soft drinks are sold in metric quantities, others such as milk are sold in customary units. The engineering industry is equally split. The automotive industry is largely metric, but aircraft such as the Boeing 787 Dreamliner were designed using customary units.

European Union

Main article: European units of measurement directives

In 1960, all the largest industrialised nations that had an established history of using the metric system were members of the European Economic Community (EEC).

In 1972, in order to harmonise units of measure as part of a program to facilitate trade between member states, the EEC issued directive 71/354/EEC. This directive catalogued units of measure that could be used for "economic, public health, public safety and administrative purposes" and also provided instructions for a transition from the existing units of measure that were in use. The directive replicated the GCPM SI recommendations and in addition pre-empted some of the additions whose use had been recommended by the CIPM in 1969, but had not been ratified by the CGPM. The directive also catalogued units of measure whose status would be reviewed by the end of 1977 (mainly coherent cgs units of measure) and also catalogued units of measure that were to be phased out by the end of 1977 including the use of obsolete names for the sale of timber such as the stere, the use of units of force and pressure that made use of the acceleration due to gravity, the use of non-coherent units of power such as the Pferdestärke (PS), the use of the calorie as a measure of energy and the stilb as a measure of luminance. The directive was silent in respect of the use of colloquial units such as the pond, pfund, livre and the like, thereby effectively prohibiting their use as well.

Banana market stall in Kerala, India - the trader is using hexagonal weights - a shape that is consistent with metric weights.

When the directive was revisited during 1977, some of the older units that were being reviewed were retained as being permitted where they were still in use, but others were phased out while the directive was aligned with SI. The directive was however overhauled to accommodate British and Irish interests in retaining the imperial system in certain circumstances. It was reissued as directive 80/181/EEC. During subsequent revisions, the directive has reflected changes in the definition of SI. The directive also formalised the use of Supplementary units which, in 1979 were permitted for a period of ten years. The cut-off date for the use of supplementary units was extended a number of times and in 2009 was extended indefinitely.

India

Main article: Metrication in India

India was one of the last countries to start a metrication program before the advent of SI. When it became independent in 1947, both imperial and native units of measure were in use. Her metrication program started in 1956 with the passing of the Standards of Weights and Measures Act. Part of the act fixed the value of the steer (a legacy unit of mass) to 0.9331 kg exactly; elsewhere the Act declared that from 1960 all non-metric units of measure were to be illegal.

Four years after the Indian Government announced its metrication program, SI was published. The result was that initial metrication program was a conversion to the cgs system of units. Fifty years later, many of the country's schoolbooks still use cgs or imperial units Originally the Indian Government had planned to replace all units of measure with metric units by 1960. In 1976 a new Weights and Measures Act replaced the 1956 Act which, amongst other things, required that all weighing devices be approved before being released onto the market place. However, in 2012, it was reported that traditional units were still encountered in small manufacturing establishments and in the marketplace alongside cgs, SI and imperial measures, particularly in the poorer areas.

The use of the Indian numbering system of crores and lakhs is widespread and is often found alongside or in place of the western numbering system.

"New SI"

Main article: New SI definitions

Relations between proposed SI units definitions (in colour) and seven physical constants (in grey) with fixed numerical values in the proposed system.

When the metre was redefined in 1960, the kilogram was the only SI base unit that relied on a specific artefact. Moreover, after the 1996–1998 recalibration, a clear divergence between the various prototype kilograms was observed.

At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artifacts that were then in use. At a meeting of the CCU held in Reading, United Kingdom in September 2010, a resolution and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed to in principle. The proposals that the CCU put forward were:

• In addition to the speed of light, four constants of nature – Planck's constant, an elementary charge, Boltzmann constant and Avogadro's number – be defined to have exact values.
• The international prototype kilogram be retired
• The current definitions of the kilogram, ampere, kelvin and mole be revised.
• The wording of the definitions of all the base units be tightened up

The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time". The CIPM did however sponsor a resolution at the 24th CGPM in which the changes were agreed in principle and which were expected to be finalised at the CGPM's next meeting in 2014.

See also

Dimensional analysis History of measurement International vocabulary of metrology ISO/IEC 80000 List of international common standards Long and short scales Names of large numbers Names of small numbers		Non-SI units mentioned in the SI Order of magnitude SI base unit SI derived unit Metric prefixes List of scientific units named after people
Organisations
Institute for Reference Materials and Measurements (IRMM)		CODATA
Standards and conventions
Coordinated Universal Time (UTC) ISO/IEC 80000		Unified Code for Units of Measure

References

• [SI Brochure] International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), ISBN 92-822-2213-6 
• [NIST 330] Thompson, Ambler; Taylor, Barry N. (2008). The International System of Units (SI) (Special publication 330). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 2008-06-18. 

• [NIST] Thompson, Ambler; Taylor, Barry N. (2008). Guide for the Use of the International System of Units (SI) (Special publication 811). Gaithersburg, MD:: National Institute of Standards and Technology. 

Further reading

• International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry, 2nd edition, Oxford: Blackwell Science. ISBN 0-632-03583-8. Electronic version.
• Unit Systems in Electromagnetism
• MW Keller et al. Metrology Triangle Using a Watt Balance, a Calculable Capacitor, and a Single-Electron Tunneling Device
• "The Current SI Seen From the Perspective of the Proposed New SI". Barry N. Taylor. Journal of Research of the National Institute of Standards and Technology, Vol. 116, No. 6, Pgs. 797–807, Nov–Dec 2011.

External links

Official

• BIPM Bureau International des Poids et Mesures (SI maintenance agency) (home page)
  • BIPM brochure (SI reference)
• ISO 80000-1:2009 Quantities and units – Part 1: General
• NIST Official Publications
  • NIST Special Publication 330, 2008 Edition: The International System of Units (SI)
  • NIST Special Publication 811, 2008 Edition: Guide for the Use of the International System of Units
  • NIST Special Pub 814: Interpretation of the SI for the United States and Federal Government Metric Conversion Policy
• Rules for SAE Use of SI (Metric) Units
• International System of Units at the Open Directory Project
• EngNet Metric Conversion Chart Online Categorised Metric Conversion Calculator
• U.S. Metric Association. 2008. A Practical Guide to the International System of Units

History

• LaTeX SIunits package manual gives a historical background to the SI system.

Research

• The metrological triangle
• Recommendation of ICWM 1 (CI-2005)

Pro-metric advocacy groups

• The UK Metric Association
• The US Metric Association

Pro-customary measures pressure groups

• Pro-customary measures groups at the Open Directory Project