# SI base unit

Last updated The seven SI base unitsSymbolNameBase quantitys second timem metre lengthkg kilogram massA ampere electric currentK kelvin temperaturemol mole amount of substancecd candela luminous intensity

The SI base units are the standard units of measurement chosen for the seven base quantities chosen by the International System of Quantities: they are notably a basic set from which all other SI units can be derived. The units and their physical quantities are the second for time, the metre for measurement of length, the kilogram for mass, the ampere for electric current, the kelvin for temperature, the mole for amount of substance, and the candela for luminous intensity. The SI base units are a fundamental part of modern metrology, and thus part of the foundation of modern science and technology.

## Contents

The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology. [ citation needed ]

The names and symbols of SI base units are written in lowercase, except the symbols of those named after a person, which are written with an initial capital letter. For example, the metre (US English: meter) has the symbol m, but the kelvin has symbol K, because it is named after Lord Kelvin and the ampere with symbol A is named after André-Marie Ampère.

A number of other units, such as the litre (US English: liter), astronomical unit and electronvolt, are not formally part of the SI, but are accepted for use with SI.

## Definitions

On 20 May 2019, as the final act of the 2019 redefinition of the SI base units, the BIPM officially introduced the following new definitions, replacing the preceding definitions of the SI base units.

SI base units
NameSymbolMeasurePost-2019 formal definition  Historical origin / justification Dimension
symbol
second s time "The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s−1."  The day is divided in 24 hours, each hour divided in 60 minutes, each minute divided in 60 seconds.
A second is 1 / (24 × 60 × 60) of the day. Historically this day was defined as the mean solar day; i.e., the average time between two successive occurrences of local apparent solar noon.
T
metre m length "The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299792458 when expressed in the unit m s−1, where the second is defined in terms of νCs."  1 / 10000000 of the distance from the Earth's equator to the North Pole measured on the median arc through Paris.L
kilogram kg mass "The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J s, which is equal to kg m2 s−1, where the metre and the second are defined in terms of c and ∆νCs."  The mass of one litre of water at the temperature of melting ice. A litre is one thousandth of a cubic metre.M
ampere A electric current "The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602176634×10−19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of ∆νCs."  The original "International Ampere" was defined electrochemically as the current required to deposit 1.118 milligrams of silver per second from a solution of silver nitrate. Compared to the SI ampere, the difference is 0.015%. However, the most recent pre-2019 definition was: "The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force equal to 2×10−7 newtons per metre of length." This had the effect of defining the vacuum permeability to be
μ0 = 4π×10−7  H/m or N/A 2 or T⋅m/A or Wb/(A⋅m) or Vs/(A⋅m)
I
kelvin K thermodynamic temperature "The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380649×10−23 when expressed in the unit J K−1, which is equal to kg m2 s−2 K−1, where the kilogram, metre and second are defined in terms of h, c and ∆νCs."  The Celsius scale: the Kelvin scale uses the degree Celsius for its unit increment, but is a thermodynamic scale (0 K is absolute zero).Θ
mole mol amount of substance "The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles."  Atomic weight or molecular weight divided by the molar mass constant, 1 g/mol.N
candela cd luminous intensity "The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540×1012 Hz, Kcd, to be 683 when expressed in the unit lm W−1, which is equal to cd sr W−1, or cd sr kg−1 m−2 s3, where the kilogram, metre and second are defined in terms of h, c and ∆νCs."  The candlepower, which is based on the light emitted from a burning candle of standard properties.J
NameSymbolMeasurePost-2019 formal definition  Historical origin / justification Dimension
symbol

## 2019 redefinition of SI base units New SI: Dependence of base unit definitions on physical constants with fixed numerical values and on other base units that are derived from the same set of constants. The SI system after 1983, but before the 2019 redefinition: Dependence of base unit definitions on other base units (for example, the metre is defined as the distance travelled by light in a specific fraction of a second), with the constants of nature and artefacts used to define them (such as the mass of the IPK for the kilogram).

New definitions of the base units were approved on 16 November 2018, and took effect 20 May 2019. The definitions of the base units have been modified several times since the Metre Convention in 1875, and new additions of base units have occurred. Since the redefinition of the metre in 1960, the kilogram had been the only base unit still defined directly in terms of a physical artefact, rather than a property of nature. This led to a number of the other SI base units being defined indirectly in terms of the mass of the same artefact; the mole, the ampere, and the candela were linked through their definitions to the mass of the International Prototype of the Kilogram, a roughly golfball-sized platinumiridium cylinder stored in a vault near Paris.

It has long been an objective in metrology to define the kilogram in terms of a fundamental constant, in the same way that the metre is now defined in terms of the speed of light. The 21st General Conference on Weights and Measures (CGPM, 1999) placed these efforts on an official footing, and recommended "that national laboratories continue their efforts to refine experiments that link the unit of mass to fundamental or atomic constants with a view to a future redefinition of the kilogram". Two possibilities attracted particular attention: the Planck constant and the Avogadro constant.

In 2005, the International Committee for Weights and Measures (CIPM) approved preparation of new definitions for the kilogram, the ampere, and the kelvin and it noted the possibility of a new definition of the mole based on the Avogadro constant.  The 23rd CGPM (2007) decided to postpone any formal change until the next General Conference in 2011.  [ needs update ]

In a note to the CIPM in October 2009,  Ian Mills, the President of the CIPM Consultative Committee – Units (CCU) catalogued the uncertainties of the fundamental constants of physics according to the current definitions and their values under the proposed new definition. He urged the CIPM to accept the proposed changes in the definition of the kilogram, ampere, kelvin, and mole so that they are referenced to the values of the fundamental constants, namely the Planck constant (h), the electron charge (e), the Boltzmann constant (k), and the Avogadro constant (NA).  This approach was approved in 2018, only after measurements of these constants were achieved with sufficient accuracy.

## Related Research Articles

The General Conference on Weights and Measures is the supreme authority of the International Bureau of Weights and Measures, the inter-governmental organization established in 1875 under the terms of the Metre Convention through which Member States act together on matters related to measurement science and measurement standards. The CGPM is made up of delegates of the governments of the Member States and observers from the Associates of the CGPM. Under its authority, the International Committee for Weights and Measures (ICWM) (French: Comité international des poids et mesures executes an exclusive direction and supervision of the BIPM. The kilogram is the base unit of mass in the metric system, formally the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering, and commerce worldwide, and is often simply called a kilo in everyday speech. Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events. The scope and application of measurement are dependent on the context and discipline. In the natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures. However, in other fields such as statistics as well as the social and behavioral sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales. The Metre Convention, also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations. The treaty created the International Bureau of Weights and Measures (BIPM), an intergovernmental organization under the authority of the General Conference on Weights and Measures (CGPM) and the supervision of the International Committee for Weights and Measures (CIPM), that coordinates international metrology and the development of the metric system. The International System of Units is the modern form of the metric system and is the most widely used system of measurement, based on the International System of Quantities. 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 mole (symbol: mol) is the unit of measurement for amount of substance in the International System of Units (SI). It is defined as exactly 6.02214076×1023 constitutive particles, which may be atoms, molecules, ions, or electrons. The Avogadro number, sometimes denoted N or N0, is the number of constituent particles (usually molecules, atoms or ions) that are contained in one mole, the international (SI) unit of amount of substance: by definition, exactly 6.02214076×1023, and it is dimensionless. It is named after the scientist Amedeo Avogadro (1776–1856). Metric system refers to the internationally recognised decimalised system of measurement known as the International System of Units (SI), or to one of its predecessors. It is in widespread use, and where it is adopted, it is the only or most common system of weights and measures. It is used to measure everyday things such as the mass of a sack of flour, the height of a person, the speed of a car, and the volume of fuel in its tank. It is also used in science, industry and trade.

A base unit is a unit adopted for measurement of a base quantity. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. The SI units, or Systeme International d'unites which consists of the metre, kilogram, second, ampere, Kelvin, mole and candela are base units. Metrology is the science of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in France, when a length standard taken from a natural source was proposed. This led to the creation of the decimal-based metric system in 1795, establishing a set of standards for other types of measurements. Several other countries adopted the metric system between 1795 and 1875; to ensure conformity between the countries, the Bureau International des Poids et Mesures (BIPM) was established by the Metre Convention. This has evolved into the International System of Units (SI) as a result of a resolution at the 11th Conference Generale des Poids et Mesures (CGPM) in 1960. Giovanni Giorgi was an Italian physicist and electrical engineer who proposed the Giorgi system of measurement, the precursor to the International System of Units (SI).

The molar mass constant, usually denoted by Mu, is a physical constant defined as the ratio of the molar mass of an element and its relative mass.

A conventional electrical unit is a unit of measurement in the field of electricity which is based on the so-called "conventional values" of the Josephson constant, the von Klitzing constant agreed by the International Committee for Weights and Measures (CIPM) in 1988, as well as ΔνCs used to define the second. These units are very similar in scale to their corresponding SI units, but are not identical because of the different values used for the constants. They are distinguished from the corresponding SI units by setting the symbol in italic typeface and adding a subscript "90" – e.g., the conventional volt has the symbol V90 – as they came into international use on 1 January 1990.

The kelvin is the base unit of temperature in the International System of Units (SI), having the unit symbol K. It is named after the Belfast-born, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907). In metrology, a standard is an object, system, or experiment that bears a defined relationship to a unit of measurement of a physical quantity. Standards are the fundamental reference for a system of weights and measures, against which all other measuring devices are compared. Historical standards for length, volume, and mass were defined by many different authorities, which resulted in confusion and inaccuracy of measurements. Modern measurements are defined in relationship to internationally standardized reference objects, which are used under carefully controlled laboratory conditions to define the units of length, mass, electrical potential, and other physical quantities. In 2019, the SI base units were redefined in agreement with the International System of Quantities, effective on the 144th anniversary of the Metre Convention, 20 May 2019. In the redefinition, four of the seven SI base units – the kilogram, ampere, kelvin, and mole – were redefined by setting exact numerical values for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela were already defined by physical constants and were subject to correction to their definitions. The new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

The history of the metric system began in the Age of Enlightenment with notions of length and weight taken from natural ones, and decimal multiples and fractions of them. The system became the standard of France and Europe in half a century. Other dimensions with unity ratios were added, and it went on to be adopted by the world. The metric system was developed during the French Revolution to replace the various measures previously used in France. The metre is the unit of length in the metric system and was originally based on the dimensions of the earth, as far as it could be measured at the time. The litre, is the unit of volume and was defined as one thousandth of a cubic metre. The metric unit of mass is the kilogram and it was defined as the mass of one litre of water. The metric system was, in the words of French philosopher Marquis de Condorcet, "for all people for all time". The following outline is provided as an overview of and topical guide to the metric system – various loosely related systems of measurement that trace their origin to the decimal system of measurement introduced in France during the French Revolution. The scientific community examined several alternative approaches to redefining the kilogram before deciding on a redefinition of the SI base units in November 2018. Each approach had advantages and disadvantages.

1. "The International System of Units (SI), 9th Edition" (PDF). Bureau International des Poids et Mesures. 2019.
2. Ian Mills, President of the CCU (October 2009). "Thoughts about the timing of the change from the Current SI to the New SI" (PDF). CIPM. Retrieved 23 February 2010.
3. Ian Mills (29 September 2010). "Draft Chapter 2 for SI Brochure, following redefinitions of the base units" (PDF). CCU. Retrieved 1 January 2011.