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International System of Units
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{{short description|a system of units of measurement for base and derived physical quantities}}{{Redirect|SI}}{{broader|Outline of the metric system}}{{2019 SI redefinition|df=y}}{{Use dmy dates|date=May 2014}}File:International System of Units Logo.png|thumb|right|264px|The seven SI base units
{| ! Symbol !! Name !! Quantity
s second time
m metre length
kg kilogram mass
A ampere electric current
K kelvin temperature
mol mole (unit) >| amount of substance
cd candelacandelaThe International System of Units (SI, abbreviated from the French ) is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the second, metre, kilogram, ampere, kelvin, mole, candela, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.The base units are defined in terms of invariant constants of nature, such as the speed of light in vacuum and the charge of the electron, which can be observed and measured with great accuracy. Seven constants are used in various combinations to define the seven base units. Prior to 2019, artefacts were used instead of some of these constants, the last being the International Prototype of the Kilogram, a cylinder of platinum-iridium. Concern regarding its stability led to a revision of the definition of the base units entirely in terms of constants of nature, which was put into effect on 20 May 2019.NEWS,weblink Historic Vote Ties Kilogram and Other Units to Natural Constants, Materese, Robin, 2018-11-16, NIST, 2018-11-16, en, Derived units may be defined in terms of base units or other derived units. They are adopted to facilitate measurement of diverse quantities. The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves. The most recent derived unit, the katal, was defined in 1999.The reliability of the SI depends not only on the precise measurement of standards for the base units in terms of various physical constants of nature, but also on precise definition of those constants. The set of underlying constants is modified as more stable constants are found, or may be more precisely measured. For example, in 1983 the metre was redefined as the distance that light propagates in vacuum in a given fraction of a second, thus making the value of the speed of light in terms of the defined units exact.
The motivation for the development of the SI was the diversity of units that had sprung up within the centimetreâ€“gramâ€“second (CGS) systems (specifically the inconsistency between the systems of electrostatic units and electromagnetic units) and the lack of coordination between the various disciplines that used them. The General Conference on Weights and Measures (French: â€“ CGPM), which was established by the Metre Convention of 1875, brought together many international organisations to establish the definitions and standards of a new system and to standardise the rules for writing and presenting measurements. The system was published in 1960 as a result of an initiative that began in 1948. It is based on the metreâ€“kilogramâ€“second system of units (MKS) rather than any variant of the CGS. Since then, the SI has officially been adopted by all countries except the United States, Liberia, and Myanmar.WEB,weblink The World Factbook Appendix G, CIA, 2017-10-26, Both Myanmar and Liberia make substantial use of SI units, as do the scientific, military, and medical communities in the US. Countries such as the United Kingdom, Canada, and certain islands in the Caribbean have partially metricated, currently employing a mixture of SI, imperial, and US Customary units. For instance, road signs in the United Kingdom continue to use miles whilst produce in Canada and the United Kingdom continue to, in certain context, be advertised in pounds rather than kilograms. The incomplete processes of metrication in Canada and the United Kingdom illustrate the complex status of metrication internationally beyond the three countries (US, Myanmar, and Liberia) commonly cited as not having adopted the SI.

## {{anchor|Coherent SI units}} Units and prefixes

The International System of Units consists of a set of base units, derived units, and a set of decimal-based multipliers that are used as prefixes.{{rp|103â€“106}} The units, excluding prefixed units,For historical reasons, the kilogram rather than the gram is treated as the coherent unit, making an exception to this characterisation. form a coherent system of units, which is based on a system of quantities in such a way that the equations between the numerical values expressed in coherent units have exactly the same form, including numerical factors, as the corresponding equations between the quantities. For example, 1 N = 1 kg Ã— 1 m/s2 says that one newton is the force required to accelerate a mass of one kilogram at one metre per second squared, as related through the principle of coherence to the equation relating the corresponding quantities: {{math|1=F = m Ã— a}}.Derived units apply to derived quantities, which may by definition be expressed in terms of base quantities, and thus are not independent; for example, electrical conductance is the inverse of electrical resistance, with the consequence that the siemens is the inverse of the ohm, and similarly, the ohm and siemens can be replaced with a ratio of an ampere and a volt, because those quantities bear a defined relationship to each other.Ohm's law: {{nowrap|1=1 Î© = 1 V/A}} from the relationship {{nowrap|1=E = I Ã— R}}, where E is electromotive force or voltage (unit: volt), I is current (unit: ampere), and R is resistance (unit: ohm). Other useful derived quantities can be specified in terms of the SI base and derived units that have no named units in the SI system, such as acceleration, which is defined in SI units as m/s2.

### Base units

The SI base units are the building blocks of the system and all the other units are derived from them.{| class="wikitable" style="margin:1em auto 1em auto"
23}}Quantities Units and Symbols in Physical Chemistry, IUPACHTTPS://BOOKS.GOOGLE.COM/?ID=NOG0SXXEU64C&PG=PA240 >PAGES=238â€“244
DATE=1975-05-20 EDITOR-FIRST1=CHESTER H. EDITOR-FIRST2=PAUL NATIONAL BUREAU OF STANDARDS >LOCATION=WASHINGTON, D.C.,
!Unitname!Unitsymbol!Dimensionsymbol!Quantityname!Definition
!secondWithin the context of the SI, the second is the coherent base unit of time, and is used in the definitions of derived units. The name "second" historically arose as being the 2nd-level sexagesimal division ({{frac|1|60{{sup|2}}}}) of some quantity, the hour in this case, which the SI classifies as an "accepted" unit along with its first-level sexagesimal division the minute.
sT|time9192631770}} periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
!metre
mL|length{{val|299792458}}}} second.
!kilogramDespite the prefix "kilo-", the kilogram is the coherent base unit of mass, and is used in the definitions of derived units. Nonetheless, prefixes for the unit of mass are determined as if the gram were the base unit.
kgM|massPlanck constant h exactly to {{val>6.62607015u=J.s}} ({{nowrap2}}â‹…s{{sup|âˆ’2}}}}), given the definitions of the metre and the second.
!ampere
AI|electric current11.602176634|e=-19}}}} times the elementary charge e per second.
!kelvin
KÎ˜thermodynamic temperature>thermodynamictemperatureBoltzmann constant k to {{val>1.380649u=Jâ‹…Kâˆ’1}}, (J = kgâ‹…m2â‹…sâˆ’2), given the definition of the kilogram, the metre, and the second.
!mole
molNamount of substance>amount ofsubstance6.02214076|e=23}} elementary entities.When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit molâˆ’1 and is called the Avogadro number.
!candela
Notes
{{reflist|group=n}}

### Derived units

The derived units in the SI are formed by powers, products, or quotients of the base units and are potentially unlimited in number.{{rp|103}}{{rp|9}} Derived units are associated with derived quantities; for example, velocity is a quantity that is derived from the base quantities of time and length, and thus the SI derived unit is metre per second (symbol m/s). The dimensions of derived units can be expressed in terms of the dimensions of the base units.Combinations of base and derived units may be used to express other derived units. For example, the SI unit of force is the newton (N), the SI unit of pressure is the pascal (Pa)â€”and the pascal can be defined as one newton per square metre (N/m2).WEB, Units & Symbols for Electrical & Electronic Engineers,weblink Institution of Engineering and Technology, 1996, 8â€“11, 2013-08-19,weblink" title="web.archive.org/web/20130628212624weblink">weblink 2013-06-28, {| class="wikitable floatleft" style="margin:1em auto 1em auto;line-height:1.4"SI derived units with special names and symbols{{rp|25}}! Name! Symbol! Quantity! In SI base units! In other SI units
sr| solid angle m2/m2 1
|hertz
Hz| frequency sâˆ’1|
newton (unit)>newton N| force, weight kgâ‹…mâ‹…sâˆ’2|
pascal (unit)>pascal Papressure, Stress (physics)>stress kgâ‹…mâˆ’1â‹…sâˆ’2 N/m2
| joule
Jenergy, Mechanical work>work, heat kgâ‹…m2â‹…sâˆ’2 Nâ‹…m = Paâ‹…m3
| watt
WPower (physics)>power, radiant flux kgâ‹…m2â‹…sâˆ’3 J/s
| coulomb
C| electric charge or quantity of electricity sâ‹…A|
| volt
Vvoltage (electrical potential), Electromotive force>emf kgâ‹…m2â‹…sâˆ’3â‹…Aâˆ’1 W/A = J/C
F| capacitance kgâˆ’1â‹…mâˆ’2â‹…s4â‹…A2 C/V
ohm (unit)>ohm Î©electrical resistance>resistance, electrical impedance, Reactance (electronics)>reactance kgâ‹…m2â‹…sâˆ’3â‹…Aâˆ’2 V/A
Siemens (unit)>siemens S| electrical conductance kgâˆ’1â‹…mâˆ’2â‹…s3â‹…A2 Î©âˆ’1
Weber (unit)>weber Wb| magnetic flux kgâ‹…m2â‹…sâˆ’2â‹…Aâˆ’1 Vâ‹…s
tesla (unit)>tesla T| magnetic flux density kgâ‹…sâˆ’2â‹…Aâˆ’1 Wb/m2
henry (unit)>henry H| inductance kgâ‹…m2â‹…sâˆ’2â‹…Aâˆ’2 Wb/A
| degree Celsius
Â°C| temperature relative to 273.15 K K|
lumen (unit)>lumen lm| luminous flux cdâ‹…sr cdâ‹…sr
| lux
lx| illuminance mâˆ’2â‹…cd lm/m2
| becquerel
Bq| radioactivity (decays per unit time) sâˆ’1|
gray (unit)>gray Gy| absorbed dose (of ionising radiation) m2â‹…sâˆ’2 J/kg
| sievert
Sv| equivalent dose (of ionising radiation) m2â‹…sâˆ’2 J/kg
| katal
kat| catalytic activity molâ‹…sâˆ’1|
{| class="wikitable floatleft" style="margin:1em auto 1em auto;line-height:1.4"Examples of coherent derived units in terms of base units{{rp|24}}! SI derived unit! Symbol! Derived quantity! Typical symbol
| square metre
m2| areaA
| cubic metre
m3| volumeV
| metre per second
m/s| speed, velocityv
| metre per second squared
m/s2| accelerationa
| reciprocal metre
mâˆ’1| wavenumberÏƒ, á¹½
| kilogram per cubic metre
kg/m3| densityÏ
| kilogram per square metre
kg/m2| surface densityÏA
| cubic metre per kilogram
m3/kg| specific volumev
| ampere per square metre
A/m2| current densityj
Amperes per metre>ampere per metre A/m| magnetic field strengthH
| mole per cubic metre
mol/m3| concentrationc
| kilogram per cubic metre
kg/m3Mass concentration (chemistry)>mass concentrationÏ, Î³
| candela per square metre
cd/m2| luminanceLv
{| class="wikitable floatleft" style="margin:1em auto 1em auto;line-height:1.4" Examples of derived units that include units with special names{{rp|26}}! Name! Symbol! Quantity! In SI base units
Pascal-second>pascal second Paâ‹…s| dynamic viscosity mâˆ’1â‹…kgâ‹…sâˆ’1
| newton metre
Nâ‹…m| moment of force m2â‹…kgâ‹…sâˆ’2
|newton per metre
N/m| surface tension kgâ‹…sâˆ’2
| watt per square metre
W/m2| heat flux density kgâ‹…sâˆ’3
| joule per kelvin
J/K| heat capacity, entropy m2â‹…kgâ‹…sâˆ’2â‹…Kâˆ’1
| joule per kilogram kelvin
J/(kgâ‹…K)| specific heat capacity, specific entropy m2â‹…sâˆ’2â‹…Kâˆ’1
| joule per kilogram
J/kg| specific energy m2â‹…sâˆ’2
| watt per metre kelvin
W/(mâ‹…K)| thermal conductivity mâ‹…kgâ‹…sâˆ’3â‹…Kâˆ’1
| joule per cubic metre
J/m3| energy density mâˆ’1â‹…kgâ‹…sâˆ’2
| volt per metre
V/m| electric field strength mâ‹…kgâ‹…sâˆ’3â‹…Aâˆ’1
| coulomb per cubic metre
C/m3| electric charge density mâˆ’3â‹…sâ‹…A
| coulomb per square metre
C/m2| surface charge density, electric flux density mâˆ’2â‹…sâ‹…A
F/m| permittivity mâˆ’3â‹…kgâˆ’1â‹…s4â‹…A2
| henry per metre
H/mPermeability (electromagnetism)>permeability mâ‹…kgâ‹…sâˆ’2â‹…Aâˆ’2
| joule per mole
J/mol| molar energy m2â‹…kgâ‹…sâˆ’2â‹…molâˆ’1
| joule per mole kelvin
J/(molâ‹…K)| molar heat capacity, molar entropy m2â‹…kgâ‹…sâˆ’2â‹…Kâˆ’1â‹…molâˆ’1
| coulomb per kilogram
C/kgExposure (photography)>exposure kgâˆ’1â‹…sâ‹…A
| gray per second
Gy/s| absorbed dose rate m2â‹…sâˆ’3
| watt per square metre steradian
| katal per cubic metre
kat/m3| catalytic activity concentration mâˆ’3â‹…sâˆ’1â‹…mol
{{clear}}

### Prefixes

Prefixes are added to unit names to produce multiples and sub-multiples of the original unit. All of these are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand. For example, kilo- denotes a multiple of a thousand and milli- denotes a multiple of a thousandth, so there are one thousand millimetres to the metre and one thousand metres to the kilometre. The prefixes are never combined, so for example a millionth of a metre is a micrometre, not a millimillimetre. Multiples of the kilogram are named as if the gram were the base unit, so a millionth of a kilogram is a milligram, not a microkilogram.{{rp|122}}BOOK, Ambler, Thompson, Barry N., Taylor, 2008,weblink Guide for the Use of the International System of Units (SI) (Special publication 811), Gaithersburg, MD, National Institute of Standards and Technology, {{rp|14}} When prefixes are used to form multiples and submultiples of SI base and derived units, the resulting units are no longer coherent.{{rp|7}}The BIPM specifies 20 prefixes for the International System of Units (SI):
{{SI prefixes (infobox)}}

### Non-SI units accepted for use with SI

Many non-SI units continue to be used in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture, and their use has not been entirely replaced by their SI alternatives. The CIPM recognised and acknowledged such traditions by compiling a list of non-SI units accepted for use with SI:(File:CubeLitre.svg|right|thumb|upright=1.1|While not an SI-unit, the litre may be used with SI units. It is equivalent to (10 cm)3 = (1 dm)3 = 10âˆ’3 m3)Some units of time, angle, and legacy non-SI units have a long history of use. Most societies have used the solar 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 they were being measured. The radian, being {{sfrac|2Ï€}} of a revolution, has mathematical advantages but is rarely used for navigation. Further, the units used in navigation around the world are similar. 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 given below:{| class="wikitable"|+ Non-SI units accepted for use with the SI units! Quantity! Name! Symbol! Value in SI units
time| minute| min| 1 min = 60 s
| hour| h| 1 h = 60 min = 3600 s
| day| d
86400|u=s}}
| length| astronomical unit| au
149597870700|u=m}}
plane andphase angleDegree (angle)>degree| Â°| 1Â° = (Ï€/180) rad
Minute and second of arc>minute| â€²10800}}) rad
Minute and second of arc>second| â€³648000}}) rad
| area| hectare| ha| 1 ha = 1 hm2 = 104 m2
| volume| litre| l, L| 1 l = 1 L = 1 dm3 = 103 cm3 = 10âˆ’3 m3
mass| tonne (metric ton)| t| 1 t = 1000 kg
dalton (unit)>dalton| Da1.660539040e=-27|u=kg}}
| energy| electronvolt| eV
1.602176634u=J}}
logarithmicratio quantities| neper| Np In using these units it is important that thenature of the quantity be specified and thatany reference value used be specified.
| bel| B
| decibel| dB

### Common notions of the metric units

The basic units of the metric system, as originally defined, represented common quantities or relationships in nature. They still do â€“ the modern precisely defined quantities are refinements of definition and methodology, but still with the same magnitudes. In cases where laboratory precision may not be required or available, or where approximations are good enough, the original definitions may suffice.While the second is readily determined from the Earth's rotation period, the metre, originally defined in terms of the Earth's size and shape, is less amenable; however, the fact that the Earth's circumference is very close to 40,000 km may be a useful mnemonic.
• A second is 1/60 of a minute, which is 1/60 of an hour, which is 1/24 of a day, so a second is 1/86400 of a day (the use of base 60 dates back to Babylonian times); a second is the time it takes a dense object to freely fall 4.9 metres from rest.
• The length of the equator is close to 40,000,000 metres (more precisely 40,075,014.2 metres). In fact, the dimensions of our planet were used by the French Academy in the original definition of the metre.
• The metre is close to the length of a pendulum that has a period of 2 seconds; most dining tabletops are about 0.75 metres high; a very tall human (basketball forward) is about 2 metres tall.
• The kilogram is the mass of a litre of cold water; a cubic centimetre or millilitre of water has a mass of one gram; a 1-euro coin, 7.5 g; a Sacagawea US 1-dollar coin, 8.1 g; a UK 50-pence coin, 8.0 g.
• A candela is about the luminous intensity of a moderately bright candle, or 1 candle power; a 60 W tungsten-filament incandescent light bulb has a luminous intensity of about 64 candela.
• A mole of a substance has a mass that is its molecular mass expressed in units of grams; the mass of a mole of carbon is 12.0 g, and the mass of a mole of table salt is 58.4 g.
• A temperature difference of one kelvin is the same as one degree Celsius: 1/100 of the temperature differential between the freezing and boiling points of water at sea level; the absolute temperature in kelvins is the temperature in degrees Celsius plus about 273; human body temperature is about 37 Â°C or 310 K.
• A 60 W incandescent light bulb consumes 0.5 amperes at 120 V (US mains voltage) and about 0.25 amperes at 240 V (European mains voltage).

## Lexicographic conventions

### Unit names

The symbols for the SI units are intended to be identical, regardless of the language used,{{rp|130â€“135}} but unit names are ordinary nouns and use the character set and follow the grammatical rules of the language concerned. 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.WEB,weblink Using Abbreviations or Symbols, 2004-07-14, 2013-12-11, Russ, Rowlett, University of North Carolina, WEB,weblink SI Conventions, 2013-12-11, National Physical Laboratory, The British and American spellings for certain SI units differ â€“ British English, as well as Australian, Canadian, and New Zealand English, uses the spelling deca-, metre, and litre whereas American English uses the spelling deka-, meter, and liter, respectively.{{rp|3}}

### Unit symbols and the values of quantities {{anchor|SI_writing_style}}

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 therefore the SI Brochure has specific rules in respect of writing them.{{rp|130â€“135}} The guideline produced by the National Institute of Standards and Technology (NIST)WEB,weblink NIST Guide to SI Units â€“ Rules and Style Conventions, 2009-12-29, Thompson, A., July 2008, Taylor, B. N., National Institute of Standards and Technology, 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.JOURNAL, 2008-05-09,weblink Interpretation of the International System of Units (the Metric System of Measurement) for the United States, Federal Register, 73, 96, 28432â€“28433, FR Doc number E8-11058, 2009-10-28,

#### General rules

General rulesExcept where specifically noted, these rules are common to both the SI Brochure and the NIST brochure. for writing SI units and quantities apply to text that is either handwritten or produced using an automated process:
• 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, {{val|7.3|e=2|u=m2}}, 22 K. This rule explicitly includes the percent sign (%){{rp |134}} and the symbol for degrees Celsius (Â°C).{{rp|133}} Exceptions are the symbols for plane angular degrees, minutes, and seconds (Â°, ′, and ″), which are placed immediately after the number with no intervening space.
• 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 a unit symbol without a separator (e.g., k in km, M in MPa, G in GHz, Î¼ in Î¼g). Compound prefixes are not allowed. A prefixed unit is atomic in expressions (e.g., km2 is equivalent to (km)2).
• Unit symbols are written using roman (upright) type, regardless of the type used in the surrounding text.
• Symbols for derived units formed by multiplication are joined with a centre dot (â‹…) or a non-breaking space; e.g., Nâ‹…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 sâˆ’1, mâ‹…sâˆ’1, or {{sfrac|m|s}}. A solidus must not be used more than once in a given expression without parentheses to remove ambiguities; e.g., kg/(mâ‹…s2) and kgâ‹…mâˆ’1â‹…sâˆ’2 are acceptable, but kg/m/s2 is ambiguous and unacceptable.
(File:981ms2.png|thumb|Acceleration due to gravity.Note the lowercase 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. E.g., 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 tesla, a measure of magnetic field strength, and "t" the symbol for tonne, a measure of mass. Since 1979, the litre may exceptionally be written using either an uppercase "L" or a lowercase "l", a decision prompted by the similarity of the lowercase letter "l" to the numeral "1", especially with certain typefaces or English-style handwriting. The American NIST recommends that within the United States "L" be used rather than "l".
• Symbols do not have a plural form, e.g., 25 kg, but not 25 {{Not a typo|kgs}}.
• Uppercase and lowercase prefixes are not interchangeable. E.g., the quantities 1 mW and 1 MW represent two different quantities (milliwatt and megawatt).
• The symbol for the decimal marker is either a point or comma on the line. In practice, the decimal point is used in most English-speaking countries and most of Asia, and the comma in most of Latin America and in continental European countries.JOURNAL, Marchâ€“April 2008, Period or Comma? Decimal Styles over Time and Place,weblink Science Editor, 31, 2, 42,weblink" title="web.archive.org/web/20130228062258weblink">weblink 2013-02-28, Amelia A., Williamson, 2012-05-19,
• Spaces should be used as a thousands separator ({{val|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.
• Because the value of "billion" and "trillion" varies between languages, the dimensionless terms "ppb" (parts per billion) and "ppt" (parts per trillion) should be avoided. The SI Brochure does not suggest alternatives.

#### Printing SI symbols

The rules covering printing of quantities and units are part of ISO 80000-1:2009.WEB,weblink ISO 80000-1:2009(en) Quantities and Unitsâ€”Past 1:General, International Organization for Standardization, 2009, 2013-08-22, Further rules are specified in respect of production of text using printing presses, word processors, typewriters, and the like.

#### Examples of the variety of symbols in use around the world for kilometres per hour

Thailand road sign à¸•à¸ª-15-1-60.svg|ThailandGeschwindigkeitsanzeigeanlage aus.jpg|GermanyFlemish_speed_limits_border.svg|BelgiumNational-speed-limit-sign-uk.svg|United KingdomHastighedsbegraensninger i DK - Hirtshals IX 2012 ubt-004.jpg|DenmarkCrÃ©ancey-FR-21-limitation de vitesse-01.JPG|FranceSpeed limits notice Mysore.jpg|IndiaThe denominator "hour" (h) is often translated to the country language:Sekolah Had Laju 30 kmj.png|MalaysiaSweden road sign E11-9.svg|SwedenCountries with historical ties to the United States often mix up the international "km/h" with the American "MPH":Philippines old road signs - Regulatory - Speed limit (60).svg|PhilippinesSamoa - Speed Limit.svg|Samoa

## International System of Quantities

{{anchor|SI Brochure}}
SI Brochure
(File:SI Brochure Cover.jpg|thumb|right|Cover of brochure The International System of Units)The CGPM publishes a brochure that defines and presents the SI.{{SIbrochure8th}} Its official version is in French, in line with the Metre Convention.{{rp|102}} It leaves some scope for local interpretation, particularly regarding names and terms in different languages.For example, the United States' National Institute of Standards and Technology (NIST) has produced a version of the CGPM document (NIST SP 330) which clarifies local interpretation for English-language publications that use American EnglishBOOK, Barry N., Taylor, Ambler, Thompson, The International System of Units (SI) (Special publication 330),weblink 2017-08-04, National Institute of Standards and Technology, Gaithersburg, MD, 2008, The writing and maintenance of the CGPM brochure is carried out by one of the committees of the International Committee for Weights and Measures (CIPM).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.WEB,weblink The International Vocabulary of Metrology (VIM), The quantities and equations that provide the context in which the SI units are defined are now referred to as the International System of Quantities (ISQ).The system is based on the quantities underlying each of the seven base units of the SI. Other quantities, such as area, pressure, and electrical resistance, are derived from these base quantities by clear non-contradictory equations. The ISQ defines the quantities that are measured with the SI units.BOOK, International vocabulary of metrology â€“ Basic and general concepts and associated terms (VIM), 2012, International Bureau of Weights and Measures (BIPM): Joint Committee for Guides in Metrology, 3rd,weblink 2015-03-28, 1.16, The ISQ is defined in the international standard ISO/IEC 80000, and was finalised in 2009 with the publication of ISO 80000-1.S. V. Gupta, Units of Measurement: Past, Present and Future. International System of Units, p. 16, Springer, 2009. {{ISBN|3642007384}}.{{clear}}

## Realisation of units

File:Silicon sphere for Avogadro project.jpg|thumb|upright|Silicon sphere for the Avogadro project used for measuring the Avogadro constant to a relative standard uncertainty of {{val|2|e=âˆ’8}} or less, held by Achim LeistnerAchim LeistnerMetrologists 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 mise en pratiqueThis term is a translation of the official [French] text of the SI Brochure. of the base units is given in an electronic appendix to the SI Brochure.WEB,weblink What is a mise en pratique?, International Bureau of Weights and Measures, 2012-11-10, {{rp|168â€“169}}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."{{rp|111}} In the current (2016) 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.{{citation needed|date=November 2012}} 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 {{val|5|e=-8}} and at least one of these values should be better than {{val|2|e=-8}}. Both the Kibble balance and the Avogadro project should be included in the experiments and any differences between these be reconciled.WEB,weblink Recommendations of the Consultative Committee for Mass and Related Quantities to the International Committee for Weights and Measures, 12th Meeting of the CCM, 2010-03-26, Bureau International des Poids et Mesures, SÃ¨vres, 2012-06-27,weblink" title="web.archive.org/web/20130514081750weblink">weblink 14 May 2013, yes, WEB,weblink Recommendations of the Consultative Committee for Amount of Substance â€“ Metrology in Chemistry to the International Committee for Weights and Measures, 16th Meeting of the CCQM, 15â€“16 April 2010, Bureau International des Poids et Mesures, SÃ¨vres, 2012-06-27,weblink" title="web.archive.org/web/20130514072057weblink">weblink 14 May 2013, yes,
• When the kelvin is being determined, the relative uncertainty of the Boltzmann constant derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry be better than one part in {{val|e=-6}} and that these values be corroborated by other measurements.WEB,weblink Recommendations of the Consultative Committee for Thermometry to the International Committee for Weights and Measures, 25th Meeting of the CCT, 6â€“7 May 2010, Bureau International des Poids et Mesures, SÃ¨vres, 2012-06-27,weblink" title="web.archive.org/web/20130514064646weblink">weblink 14 May 2013, yes,

## Evolution of the SI

### Changes to the SI

The International Bureau of Weights and Measures (BIPM) has described SI as "the modern metric system".{{rp|95}} Changing technology has led to an evolution of the definitions and standards that has followed two principal strands â€“ 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.Since 1960 the CGPM has made a number of changes to the SI to meet the needs of specific fields, notably chemistry and radiometry. These are mostly additions to the list of named derived units, and include the mole (symbol mol) for an amount of substance, the pascal (symbol Pa) for pressure, the siemens (symbol S) for electrical conductance, the becquerel (symbol Bq) for "activity referred to a radionuclide", the gray (symbol Gy) for ionising radiation, the sievert (symbol Sv) as the unit of dose equivalent radiation, and the katal (symbol kat) for catalytic activity.{{rp|156}}p. 221 â€“ McGreevy{{rp|156}}{{rp|158}}{{rp|159}}{{rp|165}}Acknowledging the advancement of precision science at both large and small scales, the range of defined prefixes pico- (10âˆ’12) to tera- (1012) was extended to 10âˆ’24 to 1024.{{rp|152}}{{rp|158}}{{rp|164}}The 1960 definition of the standard metre in terms of wavelengths of a specific emission of the krypton 86 atom was replaced with the distance that light travels in a vacuum in exactly {{sfrac|{{val|299792458}}}} second, so that the speed of light is now an exactly specified constant of nature.A few changes to notation conventions have also been made to alleviate lexicographic ambiguities. An analysis under the aegis of CSIRO, published in 2009 by the Royal Society, has pointed out the opportunities to finish the realisation of that goal, to the point of universal zero-ambiguity machine readability.{{Citation |last=Foster |first=Marcus P. |year=2009 |title=Disambiguating the SI notation would guarantee its correct parsing |journal=Proceedings of the Royal Society A |volume=465 |issue= 2104|pages=1227â€“1229 |doi=10.1098/rspa.2008.0343 |postscript=.}}

### 2019 redefinitions

File:Unit_relations_in_the_new_SI.svg | thumb |right |Dependencies of the SI base units on seven physical constantphysical constantAfter the metre was redefined in 1960, the kilogram remained the only SI base unit directly based on a specific physical artefact, the International Prototype of the Kilogram (IPK), for its definition and thus the only unit that was still subject to periodic comparisons of national standard kilograms with the IPK.WEB, Redefining the kilogram,weblink UK National Physical Laboratory, 2014-11-30, During the 2nd and 3rd Periodic Verification of National Prototypes of the Kilogram, a significant divergence had occurred between the mass of the IPK and all of its official copies stored around the world: the copies had all noticeably increased in mass with respect to the IPK. During extraordinary verifications carried out in 2014 preparatory to redefinition of metric standards, continuing divergence was not confirmed. Nonetheless, the residual and irreducible instability of a physical IPK undermined the reliability of the entire metric system to precision measurement from small (atomic) to large (astrophysical) scales.A proposal was made that:
• In addition to the speed of light, four constants of nature â€“ the Planck constant, an elementary charge, the Boltzmann constant, and the Avogadro number â€“ 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 base unit definitions should change emphasis from explicit unit to explicit constant definitions.

## History

File:Alter Grenzstein Pontebba 01.jpg|thumb|upright|Stone marking the Austro-Hungarian/Italian border at Pontebba displaying myriametres, a unit of 10 km used in Central Europe in the 19th century (but since (Deprecation|deprecated]]).WEB,weblink Amtliche MaÃŸeinheiten in Europa 1842, German, Official units of measure in Europe 1842,  Text version of MalaisÃ©'s book: , 2011-03-26, BOOK,weblink Theoretisch-practischer Unterricht im Rechnen, German, Theoretical and practical instruction in arithmetic, Ferdinand von, MalaisÃ©, MÃ¼nchen, 1842, 307â€“322, 2013-01-07, )

### The improvisation of units

| width1 = 140
| image1 = William Thomson 1st Baron Kelvin.jpg
| alt1 = William Thomson, (Lord Kelvin)
| caption1 = Thomson
| width2 = 153
| image2 = PSM V78 D529 James Clerk Maxwell.png
| alt2 = James Clerk Maxwell
| caption2 = Maxwell
| footer = William Thomson (Lord Kelvin) and James Clerk Maxwell played a prominent role in the development of the principle of coherence and in the naming of many units of measure.JOURNAL, Report on the Forty-third Meeting of the British Association for the Advancement of Science Held at Bradford in September 1873, 1874, First Report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units, Everett, 222â€“225, Special names, if short and suitable, would ... be better than the provisional designation 'C.G.S. unit of ...'.,weblink 2013-08-28,
}}

### Metre Convention{| class"wikitable" style"font-size: 85%; float:right; margin-left: 1em;"|+ CGPM vocabulary

Technical standard>[Technical] standard5, 95
| prototype
Standard (metrology)>prototype [kilogram/metre]5,95
| noms spÃ©ciaux| [Some derived units have]special names
16,106
| mise en pratique| mise en pratique[Practical realisation]The 8th edition of the SI Brochure (2008) notes that [at that time of publication] the term "mise en pratique" had not been fully defined.
82, 171
A French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention, also called Treaty of the Metre, by 17 nations.Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, German Empire, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States, and Venezuela.{{rp|353â€“354}} Initially the convention only covered standards for the metre and the kilogram. In 1921, the Metre Convention was extended to include all physical units, including the ampere and others thereby enabling the CGPM to address inconsistencies in the way that the metric system had been used.BOOK, Lord Kelvin, His Influence on Electrical Measurements and Units, Paul, Tunbridge,weblink 42â€“46, 978-0-86341-237-0, Peter Pereginus Ltd, 1992, {{rp|96}}A set of 30 prototypes of the metre and 40 prototypes of the kilogram,The text "Des comparaisons pÃ©riodiques des Ã©talons nationaux avec les prototypes internationaux" () in article 6.3 of the Metre Convention distinguishes between the words "standard" (OED: "The legal magnitude of a unit of measure or weight") and "prototype" (OED: "an original on which something is modelled"). in each case made of a 90% platinum-10% iridium alloy, were manufactured by British metallurgy specialty firm and accepted by the CGPM in 1889. One of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mÃ¨tre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the remaining prototypes to serve as the national prototype for that country.JOURNAL, Robert A., Nelson, Foundations of the international system of units (SI), Physics Teacher, 1981, 597,weblink's%20LECDEM/A101/GetPDFServlet.pdf, {{inconsistent citations}}The treaty also established a number of international organisations to oversee the keeping of international standards of measurement:WEB,weblink The Metre Convention, Bureau International des Poids et Mesures, 2012-10-01,

### The Practical system of units

{{missing info|section|changeover centigradeâ†’Kelvin and candlepowerâ†’candela|date=December 2017}}In 1948, the 9th CGPM commissioned a study to assess the measurement needs of the scientific, technical, and educational communities and "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention".WEB,weblink BIPM - Resolution 6 of the 9th CGPM, Bipm.org, 22 August 2017, 1948, This working document was Practical system of units of measurement. Based on this study, the 10th CGPM in 1954 defined an international system derived from six base units including units of temperature and optical radiation in addition to those for the MKS system mass, length, and time units and Giorgi's current unit. Six base units were recommended: the metre, kilogram, second, ampere, degree Kelvin, and candela.The 9th CGPM also 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.WEB,weblink Resolution 7 of the 9th meeting of the CGPM (1948): Writing and printing of unit symbols and of numbers, 2012-11-06, International Bureau of Weights and Measures, These rules were subsequently extended and now cover unit symbols and names, prefix symbols and names, how quantity symbols should be written and used, and how the values of quantities should be expressed.{{rp|104,130}}

### Birth of the SI

(File:Metric_system_adoption_map.svg|thumb|upright=1.5|Countries where the metric system is mandatory in trade and commerce (green))In 1960, the 11th CGPM synthesised the results of the 12-year study into a set of 16 resolutions. The system was named the International System of Units, abbreviated SI from the French name, .{{rp|110}}WEB,weblink BIPM - Resolution 12 of the 11th CGPM, Bipm.org, 22 August 2017,

### Redefinition of the SI system

On 20 May 2019, the redefinition of the SI system in measurement by major countries came into its effect.

### Historical definitions

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, for which the unit of electric current was chosen for SI. Another three base units (for temperature, amount of substance, and luminous intensity) were added later.The early metric systems defined a unit of weight as a base unit, while the SI defines an analogous unit of mass. In everyday use, these are mostly interchangeable, but in scientific contexts the difference matters. Mass, strictly the inertial mass, represents a quantity of matter. It relates the acceleration of a body to the applied force via Newton's law, {{nowrap|1=F = m Ã— a}}: force equals mass times acceleration. A force of 1 N (newton) applied to a mass of 1 kg will accelerate it at 1 m/s2. This is true whether the object is floating in space or in a gravity field e.g. at the Earth's surface. Weight is the force exerted on a body by a gravitational field, and hence its weight depends on the strength of the gravitational field. Weight of a 1 kg mass at the Earth's surface is {{nowrap|m Ã— g}}; mass times the acceleration due to gravity, which is 9.81 newtons at the Earth's surface and is about 3.5 newtons at the surface of Mars. Since the acceleration due to gravity is local and varies by location and altitude on the Earth, weight is unsuitable for precision measurements of a property of a body, and this makes a unit of weight unsuitable as a base unit.{| class="wikitable" style="margin:1em auto 1em auto"23}}Quantities Units and Symbols in Physical Chemistry, IUPACHTTPS://BOOKS.GOOGLE.COM/?ID=NOG0SXXEU64C&PG=PA240 >PAGES=238â€“244 DATE=1975-05-20 EDITOR-FIRST1=CHESTER H. EDITOR-FIRST2=PAUL NATIONAL BUREAU OF STANDARDS >LOCATION=WASHINGTON, D.C., !Unitname!DefinitionInterim definitions are given here only when there has been a significant difference in the definition.
!second|
• Prior: {{sfrac|1|{{val|86400}}}} of a day of 24 hours of 60 minutes of 60 seconds
• Interim (1956): {{sfrac|{{val|31556925.9747}}}} of the tropical year for 1900 January 0 at 12 hours ephemeris time.
• Current (1967): The duration of {{val|9192631770}} periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
!metre|
• Prior (1793): {{sfrac|{{val|10000000}}}} of the meridian through Paris between the North Pole and the Equator.FG
• Interim (1889): The Prototype of the metre chosen by the CIPM, at the temperature of melting ice, represents the metric unit of length.
• Interim (1960): {{val|1650763.73}} wavelengths in a vacuum of the radiation corresponding to the transition between the 2p{{sup|10}} and 5d{{sup|5}} quantum levels of the krypton-86 atom.
• Current (1983): The distance travelled by light in vacuum in {{sfrac|{{val|299792458}}}} second.
!kilogram|
• Prior (1793): The grave was defined as being the mass (then called weight) of one litre of pure water at its freezing point.FG
• Interim (1889): The mass of a small squat cylinder of ~47 cubic centimetres of platinum-iridium alloy kept in the Pavillon de Breteuil{{citation needed|reason=Though this is the location of the BIPM in Saint-Cloud,weblink indicates that [...] the IPK, which is kept by the [BIPM] in SÃ¨vres, France. (This borders onto, but is distinct from Saint-Cloud.)|date=July 2018}}, France. Also, in practice, any of numerous official replicas of it.This object is the International Prototype Kilogram or IPK called rather poetically Le Grand K.WEB,weblink Redefining the Kilogram, The Past, Erik M., Secula, 7 October 2014, Nist.gov, 22 August 2017,weblink 2017-01-09,
• Current (2019): The kilogram is defined by setting the Planck constant h exactly to {{val|6.62607015|e=-34|u=J.s}} ({{nowrap|1=J = kgâ‹…m{{sup|2}}â‹…s{{sup|âˆ’2}}}}), given the definitions of the metre and the second. Then the formula would be {{nowrap|1=kg = {{sfrac|h|{{val|6.62607015|e=-34}}â‹…m{{sup|2}}â‹…s{{sup|âˆ’1}}}}}}
!ampere|
• Prior (1881): A tenth of the electromagnetic CGS unit of current. The [CGS] electromagnetic unit of current is that current, flowing in an arc 1 cm long of a circle 1 cm in radius, that creates a field of one oersted at the centre.BOOK,weblink 322, Magnetism and Electricity, McKenzie, A. E. E., Cambridge University Press, 1961, IEC
• Interim (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 {{val|2|e=-7}} newtons per metre of length.
• Current (2019): The flow of {{sfrac|1|{{val|1.602176634|e=-19}}}} times the elementary charge e per second.
!kelvin|
• Prior (1743): The centigrade scale is obtained by assigning 0 Â°C to the freezing point of water and 100 Â°C to the boiling point of water.
• Interim (1954): The triple point of water (0.01 Â°C) defined to be exactly 273.16 K.In 1954 the unit of thermodynamic temperature was known as the "degree Kelvin" (symbol Â°K; "Kelvin" spelt with an upper-case "K"). It was renamed the "kelvin" (symbol "K"; "kelvin" spelt with a lower case "k") in 1967.
• Previous (1967): {{sfrac|273.16}} of the thermodynamic temperature of the triple point of water
• Current (2019): The kelvin is defined by setting the fixed numerical value of the Boltzmann constant k to {{val|1.380649|e=-23|u=Jâ‹…Kâˆ’1}}, (J = kgâ‹…m2â‹…sâˆ’2), given the definition of the kilogram, the metre, and the second.
!mole|
• Prior (1900): A stoichiometric quantity which is the equivalent mass in grams of Avogadro's number of molecules of a substance.ICAW
• Interim (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.
• Current (2019): The amount of substance of exactly {{val|6.02214076|e=23}} elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit molâˆ’1 and is called the Avogadro number.
!candela|
• Prior (1946): The value of the new candle (early name for the candela) 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 {{val|5.4|e=14}} hertz and that has a radiant intensity in that direction of {{sfrac|1|683}} watt per steradian.

Note: both old and new definitions are approximately the luminous intensity of a whale blubber candle burning modestly bright, in the late 19th century called a "candlepower" or a "candle".
Notes
{{reflist|group=n}}The Prior definitions of the various base units in the above table were made by the following authorities: All other definitions result from resolutions by either CGPM or the CIPM and are catalogued in the SI Brochure.

{hide}cmn|colwidth=30em|
• {{annotated link|Introduction to the metric system{edih}
• {{annotated link|Outline of the metric system}}
• {{annotated link|List of international common standards}}
• {{annotated link|Metreâ€“tonneâ€“second system of units}}
Organisations
• {{annotated link|Institute for Reference Materials and Measurements}}
Standards and conventions
• {{annotated link|Unified Code for Units of Measure}}
}}

## Notes

{{Reflist|group="Note"}}

## References

{{Reflist}}

{{Commons category|International System of Units}}
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