International System of Units

• 1. Introduction

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  The International System of Units rests on seven exact numbers, and one of them is 299792458. That is the speed of light in vacuum, measured in metres per second, fixed forever by international agreement. Light no longer measures the metre. The metre is defined by light. This inversion sits at the heart of the modern metric system, known worldwide by the abbreviation SI, from its French name Systeme international d'unites. It is the only system of measurement with official status in nearly every country, the shared language of science, technology, industry, and everyday commerce. But how did the world settle on seven base units and not some other number? Why does a kilogram of mass hide inside a constant about energy and frequency? And what made scientists abandon the physical objects they once trusted to define a unit? The answers run from a treaty signed in 1875 to a vote taken in November 2018.

• 2. Seven Constants

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  Nine billion, one hundred ninety-two million, six hundred thirty-one thousand, seven hundred seventy. That exact figure, 9192631770, is the hyperfine transition frequency of caesium-133, and it anchors the second. The SI is built from seven defining constants, each a fixed numerical value paired with units. Alongside the caesium frequency sit the speed of light, the Planck constant of 6.62607015, the elementary charge of 1.602176634, the Boltzmann constant of 1.380649, the Avogadro constant of 6.02214076, and the luminous efficacy of 683. These seven values were not discovered to be round. They were fixed by decision, chosen to ensure continuity with the older definitions of the base units. The nature of the defining constants ranges from fundamental features of nature to one purely technical constant. From these seven numbers, every unit in the system can be constructed. The base units are defined in terms of the defining constants, and so are the derived units that follow. This is why the kilogram, once a lump of metal, can now be expressed through the Planck constant given the definitions of the metre and the second.

• 3. The Seven Pillars

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  The second, symbol s, measures time as the duration of 9192631770 periods of caesium radiation. It is one of seven base units, each tied to a base physical quantity. The metre carries the symbol m and measures length as the distance light travels in vacuum in a fraction of a second. The kilogram, symbol kg, measures mass. The ampere, symbol A, measures electric current as the flow of roughly 6.2415090744 elementary charges per second. The kelvin, symbol K, measures thermodynamic temperature through the Boltzmann constant. The mole, symbol mol, measures amount of substance as 6.02214076 elementary entities. The candela, symbol cd, measures luminous intensity through radiation at a frequency of 540 times ten to the twelfth hertz. The choice of which quantities to treat as base, and even how many to use, is not fundamental or unique. It is a matter of convention. The base units serve as a preferred set for analysing how units relate to one another.

• 4. Building Outward

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  Metre per second is the coherent derived unit of velocity, and it shows how the system grows. Derived units are products of powers of the base units. When the numeric multiplier equals one, the unit is coherent, and together the base and coherent derived units form a coherent system. Twenty-two coherent derived units have been given special names and symbols. Among them are the newton for force, the pascal for pressure, the joule for energy, the watt for power, and the volt for electric potential difference. The pascal can be defined as one newton per square metre. Some of these units do double duty. The joule per kelvin is the coherent unit for two distinct quantities, heat capacity and entropy. The ampere is the coherent unit for both electric current and magnetomotive force, a base unit in one role and a derived unit in the other. The radian and the steradian have no base units at all, yet are treated as derived units for historical reasons. A coherent system carries a quiet advantage. Equations between numerical values take exactly the same form as the equations between the physical quantities themselves.

• 5. Powers Of Ten

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  Kilo stands for a factor of 1000, which is why driving distances are given in kilometres rather than metres. The SI provides twenty-four metric prefixes spanning decimal powers from ten to the minus thirtieth all the way to ten to the thirtieth. The most recent prefixes were adopted in 2022. Most correspond to integer powers of 1000, and the only exceptions are those for ten, one tenth, a hundred, and one hundredth. Conversion between SI units for the same quantity always passes through a power of ten, which is why the SI is called a decimal system. Prefixes are never combined. A millionth of a metre is a micrometre, not a millimillimetre. The kilogram carries a special wrinkle. Because its name already includes a prefix, multiples and sub-multiples of mass are formed as if the gram were the base unit. A millionth of a kilogram is therefore a milligram, not a microkilogram. The kilogram is the only coherent SI unit whose name and symbol include a prefix.

• 6. Definition Versus Reality

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  Metrologists draw a careful line between the definition of a unit and its realisation. A definition is a declaration that seven constants hold exact numerical values. A realisation is the procedure that turns that definition into a measured quantity with a known uncertainty. For each base unit the BIPM publishes a mise en pratique, French for putting into practice, describing the current best ways to realise the unit. Because the defining constants are separated from the unit definitions, better measurements can change the mise en pratique without revising the definition itself. As science and technology develop, new and potentially superior realisations may be introduced. In 2016 the consultative committees of the CIPM decided that more than one mise en pratique would be developed for each unit. For the kilogram, at least three separate experiments must yield values within tight uncertainty bounds, and both the Kibble balance and the Avogadro project must be included, with any differences reconciled. For the kelvin, the Boltzmann constant must be derived from two fundamentally different methods, such as acoustic gas thermometry and dielectric constant gas thermometry.

• 7. The Long Road

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  The concept of a system of units emerged a hundred years before the SI. In the 1860s, James Clerk Maxwell and William Thomson, later Lord Kelvin, working under the British Association for the Advancement of Science and building on Carl Gauss, developed the centimetre-gram-second system, or cgs, in 1874. The cgs formalised the idea of a coherent system, where base units combine into derived units without extra factors. A French-inspired push for cooperation led to the Metre Convention of 1875, signed by 17 nations, which created the General Conference on Weights and Measures and laid the foundation of the MKS system. At the close of the 19th century, three rival systems governed electrical measurement, and dimensional analysis broke down depending on whether one used the ESU or EMU approach. In 1901 Giovanni Giorgi resolved the anomaly by proposing a fourth base unit. Electric current, named the ampere, was chosen, and the resulting MKSA system was approved in 1946. In 1948 the 9th CGPM commissioned a study toward a single practical system. The 10th CGPM in 1954 defined a system of six base units, and in 1960 the 11th CGPM adopted the SI. Degree Kelvin became kelvin in 1968, and in 1971 the mole became the seventh base unit.

• 8. Retiring The Artefact

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  For decades a single cylinder defined the kilogram. The International Prototype of the Kilogram, the IPK, was the last physical artefact on which base units depended, directly the kilogram and indirectly the ampere, mole, and candela. That dependence forced periodic comparisons of national standards against the IPK. During the 2nd and 3rd Periodic Verification of National Prototypes, a troubling divergence appeared. The official copies stored around the world had all noticeably increased in mass relative to the IPK. Extraordinary verifications carried out in 2014 did not confirm continuing divergence, but the residual and irreducible instability of a physical object undermined the reliability of the whole system from atomic to astrophysical scales. The fix was to abolish the artefact. A proposal fixed the Planck constant, the elementary charge, the Boltzmann constant, and the Avogadro constant to exact values, retired the IPK, and shifted base unit definitions from explicit unit to explicit constant. The new definitions were adopted at the 26th CGPM on the 16th of November 2018 and came into effect on the 20th of May 2019. The European Union adopted the change through Directive 2019/1258. With the artefact gone, the distinction between base and derived units became, in principle, unnecessary, yet it was kept because it is useful and historically well established.