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The New SI

Ian Mills, emeritus professor at the University of Reading, UK Roberto Marquardt, professor at the Université de Strasbourg, France

1The International System of Units is getting a Makeover

Metrology, the science of measurement, is part of the essential but largely hidden infrastructure of the modern world. We need it for high-technology manufacturing, human health and safety, the protection of the environment, global climate studies, information transfer and the basic science that underpins all these. Highly accurate measurements are no longer the preserve of only the physical sciences and engineering. The International System of Units, the SI (Système International d’unités), provides the internationally agreed means by which we make such measurements.

At a meeting of the General Conference on Weights and Measures (CGPM) held in Paris on 16 November 2018 a new and revised SI was approved, adapted for the 21st century.* These changes will be implemented on 20 May 2019, the next “World Metrology Day” and the day anniversary on which the Convention of the Metre was first signed in 1875. Of particular interest to chemists are the changes in the definition of the SI units kilogram and mole.

* See We Did It! Redefinition of SI adopted, video release by The BIPM, 20 Nov 2018

2... a good set of units

In this context the well-known opening sentence of Jane Austen’s novel Pride and Prejudice may be adapted to read: “It is a truth universally acknowledged that a single man in possession of a good fortune, must be in want of a good set of units.” In the last four words of this sentence Jane Austen wrote “must be in want of a wife,” but we have substituted “in want of a good set of units.” Perhaps we need both!

3Summary of the changes

The following is a brief summary of the changes that are being adopted in this new SI.

1. Each of the seven base units of the SI (second, metre, kilogram, ampere, kelvin, mole, and candela) is defined by an agreed reference that has to be readily available and easily realized experimentally by anyone anywhere at any time with sufficient precision (sufficiently low uncertainty) for our needs. Four of the seven base units, the kilogram, ampere, kelvin and mole, have revised definitions in the new SI as described below. The definitions of the second, metre and candela remain unchanged.

2. All of the new definitions will in future be expressed in terms of seven ‘defining constants’ which are believed to fulfil these requirements and are summarized below. The numerical values of these seven constants when expressed in SI units provides the definition of all SI units, both base and derived units.

3. The revised definition of the kilogram is chosen to fix the numerical value of the Planck constant h, that of the ampere to fix the numerical value of the elementary charge e, that of the kelvin to fix the numerical value of the Boltzmann constant k (kB), and that of the mole to fix the numerical value of the Avogadro constant NA (L), all these numerical values being expressed in terms of the corresponding SI unit. The definitions of the remaining three base units, the second, the metre, and the candela fix the numerical value of the caesium hyperfine splitting ΔνCs, the speed of light in vacuum c, and the luminous intensity of the specified source Iv, just as they do at present.

4seven defining constants

4. The values of the seven defining constants listed in Table 1 below are chosen to be consistent with the best experimental values at the time of adopting the new definitions, to preserve continuity.

5. To summarize, the International System of Units, the SI, is the system of units in which:

where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz, J, C, lm, and W, respectively, are related to the units second, metre, kilogram, ampere, kelvin, mole, and candela, with unit symbols s, m, kg, A, K, mol, and cd, respectively, according to Hz = s–1, J = m2 kg s–2, C = A s, lm = cd sr, and W = m2 kg s–3.


5Zero uncertainty

The numerical values of the seven defining constants have zero uncertainty. They are summarized in Table 2 below. Definitions based on defining constants are called explicit-constant definitions; they are based on the fundamental constants of nature, in contrast to explicit-unit definitions which are based on particular experimental procedures.


Defining a unit by specifying the numerical value of a fundamental constant may be understood as follows. The value of any quantity Q may always be represented as the product of its numerical value {Q} and a unit [Q], so that we may write Q = {Q} [Q] (for example c = 299 792 458 m/s for the speed of light in vacuum). If the quantity Q is itself a unit that we wish to define, this may be done either by specifying some convenient reference (such as the length of the prototype metre bar that was used to define the SI unit of length prior to 1980) or by specifying the numerical value {Q} when expressed in terms of the desired SI unit (such as the numerical value of the speed of light 299 792 458 expressed in the unit m/s used to define the metre since 1980). It is this second method of using defining constants that is now being adopted for all the seven base units of the SI.

6In the spirit of William Shakespeare

For chemists, the definition of the mole has an important conceptual consequence. It is namely equivalent to stating that “One mole contains exactly 6.022 140 76 × 1023 elementary entities,” quite in the spirit of William Shakespeare in As You Like It: “It is as easy to count atomies as to resolve the propositions of a lover.” In addition, the exact and fixed number of elementary entities defining a mole finally receives the name that has been used for it for decades without proper definition: the Avogadro number.

In general, the changes associated with the new SI will lead to reduced uncertainties in our knowledge of most of the fundamental constants of physics and chemistry in the new SI.

The changes in the new SI will strengthen the philosophical foundation of our system of units in relation to our present understanding of theoretical and quantum physics. However, they will not affect the daily work in the laboratory in any sizeable manner.

7For the chemist working in the laboratory

What are the direct consequences of these changes to a chemist working in the laboratory? For example, the equation

C2H4O = CH4 + CO

has the meaning that one mole of oxirane (C2H4O) decomposes to yield one mole of methane (CH4) and one mole of carbon monoxide (CO). The new definition of the mole will not change this meaning. A chemist in the laboratory will continue to determine the amount of a chemical entity B, n(B), by weighing the corresponding mass m(B) and setting n(B) = m(B)/M(B), where M(B) is the molar mass of B. He/she will continue to state that 44.053 g of oxirane decomposes to yield 16.043 g methane and 28.010 g carbon monoxide. Truly, the molar mass M(B) = Mr(B) Mu will acquire an uncertainty component of less than 1 part in 109 due to the new uncertainty of the molar mass constant Mu = M(12C)/12 (see Table 2; the relative molar mass Mr(B) of any atom B is unchanged in the new SI). However, balances in chemistry laboratories will continue to yield masses (e.g. in the SI unit kg) with uncertainties that far exceed the uncertainty of the molar mass of any given chemical entity by orders of magnitude, so that the change in the new definition of the mole will never influence the result of the determinations of amount of substance in practice.


* This story was first published in Chemistry International in January 2019 (CI 41(1), pp. 32-35; https://doi.org/10.1515/ci-2019-0108)

Ian Mills <[email protected]> is emeritus professor of chemistry at the University of Reading, UK and an elected Fellow of the Royal Society. He was the President of Consultative Committee on Units of the International Bureau of Weights and Measures (BIPM) and retired from this role in 2013 after 18 years of service. In IUPAC, he served as chair of the Commission on Physicochemical Symbols, Terminology, and Units (Commission I.1), and also as chair of the Interdivisional Committee on Nomenclature and Symbols (IDCNS, preceding the current ICTNS) until 1999.

Roberto Marquardt <[email protected]> was President of the Physical and Biophysical Chemistry Division of IUPAC in 2014-15.

Title image from Light show dedicated to the redefinition of the SI at Sevres, The BIPM 7 Jan 2019

8World Metrology Day - 20 May 2019

The theme for World Metrology Day 2019 is The International System of Units – Fundamentally better. This theme was chosen because on 16 November 2018, the General Conference on Weights and Measures agreed perhaps one of the most significant revisions to the International System of Units (the SI) since its inception. Research into new measurement methods, including those using quantum phenomena, underpin the change, which comes into force on 20 May 2019. The SI is now based on a set of definitions each linked to the laws of physics and have the advantage of being able to embrace further improvements in measurement science and technology to meet the needs of future users for many years to come. <http://www.worldmetrologyday.org>




View video produced by the National Institute of Standards and Technology, published by The BIPM on Nov 5, 2018



  1. Marquardt, R., Meija, J., Mester, Z., et al. (2017). A critical review of the proposed definitions of fundamental chemical quantities and their impact on chemical communities (IUPAC Technical Report). Pure Appl. Chem., 89, pp. 951- 981; - https://doi.org/10.1515/pac-2016-0808
  2. Marquardt, R., Meija, J., Mester, Z., et al. (2018). Definition of the mole (IUPAC Recommendation 2017). Pure Appl. Chem., 90, pp. 175-180; - https://doi.org/10.1515/pac-2017-0106
  3. Mills, I.M, Mohr, P.J., Quinn, T.J., Taylor, B.N. and Williams, E. R. (2006). Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005). Metrologia, 43, pp. 227- 246; - https://doi.org/10.1088/0026-1394/43/3/006
  4. Mills, I.M., Mohr, P.J., Quinn, T.J., Taylor, B.N. and Williams, E.R. (2011). Adapting the International System of Units to the twenty-first century. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, pp. 3907-3924; - https://doi.org/10.1098/rsta.2011.0180
  5. Ullrich, J. Why we need the SI redefinition. EURAMET short videos (13 June 2018), - https://www.euramet.org/?news=40:678
  6. Bureau International des Poids et Mesures (BIPM), On the Future Revision of the SI (International System of Units or Système International d’Unités), - https://www.bipm.org/en/measurement-units/rev-si/
  7. MIls, I.M., The Kilogram in the New SI—part II Explicit Constant Definitions for the Kilogram and for the Mole (2011) Chem. Int. 33(5) pp. 12-15; - https://doi.org/10.1515/ci.2011.33.5.12


Mills, I., Marquardt, R. (15 May 2019) "The New SI - The International System of units is getting a Makeover" IUPAC 100 Stories. Retrieved from https://iupac.org/100/stories/the-new-si/. (Accessed: day month year)

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