The New International System of Units based on Fundamental Constants

Beat Jeckelmann, Chief Science Officer, Federal Office of Metrology METAS, Bern-Wabern


At its 24th meeting in October 2011, the General Conference on Weights and Measures (CGPM) approved possible changes to the International System of Units, including new definitions for the kilogram, ampere, kelvin and mole. The final approval of the new SI will be made by the CGPM after its prerequisite conditions have been met. The earliest date for this change is 2014.


The International System of Units, known as the SI, is used throughout the world to express the results of measurements in almost all aspects of modern society, from advanced science and technology, via precision manufacturing to daily life. The roots of the SI go back to the Metre Convention signed in 1875 by 17 countries and now consisting of 55 signatories, but being applied in almost all countries of the world. The Convention established the General Conference of Weights and Measures (CGPM), a diplomatic body of representatives of each member state which meets usually every four years and has the authority to decide on any changes or extensions to the SI. In October 2011, the CGPM adopted a resolution [1] paving the way to a major revision of the SI.

The building blocks of the SI are the seven base units: second, metre, kilogram, ampere, kelvin, mole and candela. In recent years, possible new definitions of the base units were intensively discussed among specialists. In the course of the planned changes, especially the unit of mass, the kilogram, which is the last remaining unit defined in terms of an artefact, should be based on fundamental physical constants. The responsible committees of the Metre Convention have worked out a detailed proposition for the new SI which includes new definitions for the base units kilogram, ampere, kelvin and mole.

Why do we need a redefinition of SI base units?

In the current SI, the only unit still based on an artefact is the unit of mass. The kilogram is defined as the mass of a particular cylinder of an alloy of platinum (Pt) and iridium (Ir) conserved and used at the International Bureau of Weights and Measures (BIPM) in Sèvres, France. Copies of this kilogram prototype are kept by many National Metrology Institutes (NMI) around the world. Since 1889, these copies were compared three times with the international prototype. A series of copies was produced later and was compared only twice with the prototype. For both groups it has turned out that on average the mass of the national copies has increased with respect to the international prototype [2].

The relative change of about 50 μg/100 years on average is very small, but scientifically unsatisfactory and a possible problem and obstacle in the future. Due to the definition of the ampere, the electrical units are related to force and thus to the kilogram. A drift of the kilogram would induce a similar drift in the electrical units.

In modern electrical metrology, however, the Josephson and quantum Hall effects are used to realize very reproducible voltage and resistance values [3, 4] which, to our current knowledge, depend only on fundamental physical constants. To be used as practical standards, the value of the Josephson constant KJ = 2e/h and the von-Klitzing constant RK = h/e2 have to be known in SI units. Unfortunately, the best realizations of the volt and the ohm in the SI according to the current definitions are about two orders of magnitude less accurate than the reproducibility of quantum standards based on the Josephson and the quantum Hall effects. As a consequence, conventional values for RK and KJ were introduced in 1990 (RK-90 = 25812.807 Ω and KJ-90 = 483597.9 GHz V-1). This step drastically improved the worldwide consistency of electrical measurements. On the other hand however, it led to a practical subsystem in the SI which is unsatisfactory from the conceptional point of view.

Attempts to replace the kilogram

Much effort is being made to replace the kilogram artefact by a procedure relating the unit of mass to fundamental constants [5]. In the Avogadro experiment, the Avogadro constant NA is measured with high accuracy by counting atoms in a nearly perfect Si crystal. Combining the constant with other physical constants, NA can be linked to Planck’s constant h. Hence the Avogadro experiment offers the opportunity to relate the kilogram either to an atomic mass or to the Planck constant. Another promising experimental approach is the so called “watt balance”. It equalises mechanical and electrical power. When the electrical power is measured with quantum standards, mass can be related to Planck’s constant h [5] (see also box 3).

Of course, the results of the individual experiments and the two different approaches should agree. At present the CODATA task group on fundamental constants, taking into account all relevant experimental data available by the end of 2010, attributes an uncertainty of 44 parts in 109 to the value of the Planck constant [6]. An improvement of a factor of two is needed before the redefinition of the kg will be decided.

The 7 fixed constants, setting the scale of the SI

The International System of Units, the SI, will be the system of units in which [1]:

  • the ground state hyperfine splitting frequency of the caesium 133 atom Δν(133Cs)hfs is exactly 9 192 631 770 hertz, Hz,
  • the speed of light in vacuum c is exactly 299 792 458 metre per second, m s-1,
  • the Planck constant h is exactly 6.626 06X ×10-34 joule second, J s,
  • the elementary charge e is exactly 1.602 17X ×10-19 coulomb, C,
  • the Boltzmann constant k is exactly 1.380 65X ×1023 joule per kelvin, J K-1,
  • the Avogadro constant NA is exactly 6.022 14X ×1023 reciprocal mole, mol-1,
  • the luminous efficacy Kcd of monochromatic radiation of frequency 540 ×1012 hertz is exactly 683 lumen per watt, lm W-1.

Note: see Box 2

Concept of the new SI

With the recent progress made in the experimental determination of the Planck constant, the replacement of the last artefact within the SI is within reach. For the first time, it becomes possible to base the whole system on a set of exactly known values of fundamental constants. All units, base or derived, can then be constructed by consulting the laws of physics. In the SI, we have chosen to fix the size of seven base units by convention. For this reason, seven constants have to be selected. The set, proposed in this form for the first time in [7], is shown in box 1. From the point of view of fundamental physics one might argue that the SI is unnecessarily complicated and that basic units for time, length and mass would be sufficient. Indeed, in the view of many physicists it would be simpler to measure electrical quantities in terms of these three basic mechanical units. The kelvin and the mole are not essential since thermodynamic energy and the number of particles could be measured without introducing any special units. The candela, finally, is related to the sensitivity of the human eye and as such not necessarily related to physics. However, it should be realized that the SI should serve practical measurements as well as fundamental physics. The ampere, kelvin, mole and candela would not be necessary to make all the associated quantities measurable. But for practical applications, it is much more convenient to have these basic units. Along these lines it is not surprising that the constants listed in box 1 do not all have the same importance. The speed of light c and the Planck constant h are truly fundamental constants in modern physics as they are related to fundamental limitation principles described in the theories of special relativity and quantum mechanics. The Boltzmann constant k can be seen as conversion factor relating temperature and energy. The ground state hyperfine splitting frequency of the caesium 133 atom Δν(133Cs)hfs is the property of a specific atom. It cannot be expressed by more fundamental quantities in a simple way. The accuracy of the realization of the unit second linked to this constant is limited by the natural line width of the atomic transition. Considerable efforts are being made to define the unit of time through a more fundamental constant in the foreseeable future. The Avogadro constant NA and the luminous efficacy Kcd are chosen for practical reasons; they are usually not considered as “fundamental” by physicists.

With the fixed constants and with the help of the laws of physics, all units in the SI may be realized. The constants set the scale for the entire system. They are the building blocks and, as a consequence, it is no longer necessary to make a distinction between base and derived units. Nevertheless, for reasons of continuity with the past, the organs of the Metre Convention decided to keep the concept of base units and to propose formal definitions for them as listed in box 2 (see also [8] for more background information).

Proposed new definitions of the seven base units.

  • The second, s, is the unit of time; its magnitude is set by fixing the numerical value of the ground state hyperfine splitting frequency of the caesium 133 atom, at rest and at a temperature of 0 K, to be equal to exactly 9 192 631 770 when it is expressed in the unit s-1, which is equal to Hz.
  • The metre, m, is the unit of length; its magnitude is set by fixing the numerical value of the speed of light in vacuum to be equal to exactly 299 792 458 when it is expressed in the unit m s-1.
  • The kilogram, kg, is the unit of mass; its magnitude is set by fixing the numerical value of the Planck constant to be equal to exactly 6.626 06X ×10-34 when it is expressed in the unit s-1 m2 kg, which is equal to J s.
  • The ampere, A, is the unit of electric current; its magnitude is set by fixing the numerical value of the elementary charge to be equal to exactly 1.602 17X ×10-19 when it is expressed in the unit s A, which is equal to C.
  • The kelvin, K, is the unit of thermodynamic temperature; its magnitude is set by fixing the numerical value of the Boltzmann constant to be equal to exactly 1.380 6X ×10-23 when it is expressed in the unit s-2 m2 kg K-1, which is equal to J K-1.
  • The mole, mol, is the unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be equal to exactly 6.022 14X ×1023 when it is expressed in the unit mol-1.
  • The candela, cd, is the unit of luminous intensity in a given direction; its magnitude is set by fixing the numerical value of the luminous efficacy of monochromatic radiation of frequency 540 ×1012 Hz to be equal to exactly 683 when it is expressed in the unit s3 m-2 kg-1 cd sr, or cd sr W-1, which is equal to lm W-1.

Note: the symbol X in the presentation of the constants represents one or more additional digits to the numerical values of the constants, using values based on the most recent CODATA adjustment.

Benefits of the new SI

The proposed changes make the SI fit for the future measurement needs. Replacing the kilogram prototype by a unit based on fundamental constants makes the system invariable over time. The electrical units can directly be realized through quantum effects within the SI with the highest accuracy and the conventional values RK-90 and KJ-90 become obsolete. In addition, the uncertainties of important fundamental constants are either eliminated or appreciably reduced.

Next steps

The proposed changes will be implemented as soon as the experimental results for the Planck constant are consistent and accurate enough. The target relative uncertainty for h is < 20 parts in 109.

There is concern about the proposed wording in the definition of the base units [see e.g. 9]. As they stand now, the definitions are hardly understandable for the non-expert reader. This is especially true for the units where the fixed constant does not belong to the same quantity as the unit to be defined (e.g. the unit of mass, the kg, is defined by a fixed value of h which is an angular momentum). For this reason, the CGPM invites the relevant committees [1] "... to continue the work towards improved formulations for the definitions of the SI base units in terms of fundamental constants, having as far as possible a more easily understandable description for users in general, consistent with scientific rigour and clarity." In this context, it is of great importance that the wider public and the user communities express their opinion about the proposed new SI. Feedback addressed to the author of this article is welcome.



[1] Resolution 1, 24th Meeting of the General Conference on Weights and Measures, October 2011
[2] G. Girard; The third periodic verification of national prototypes of the kilogram (1988-1992), Metrologia 31, pp. 317-336, 1994.
[3] B. Jeanneret and S. P. Benz; Application of the Josephson effect in electrical metrology, Eur. Phys. J. Special Topics 172, pp. 181-206, 2009.
[4] B. Jeckelmann and B. Jeanneret; The quantum Hall effect as an electrical resistance standard, Rep. Prog. Phys. 64, pp. 1603-1655, 2001.
[5] W. Schwitz, B. Jeckelmann, P. Richard; Towards a new kilogram definition based on a fundamental constant, C.R. Phys. 5, p. 881-892, 2004.
[6] CODATA internationally recommended values of the Fundamental Physical Constants 2010
[7] I. M. Mills, P. J. Mohr, T. J. Quinn, B. N. Taylor, E. R. Williams; Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005), Metrologia 43, pp. 227-246, 2006
[8] The “New SI”: Online (May 2011)
[9] U. Feller; The International System of Units – a case for reconsideration, Accred. Qual. Assur. 16, p.143, 2011.
[10] A. Eichenberger, H. Baumann, B. Jeanneret, B. Jeckelmann, P. Richard and W. Beer; Determination of the Planck constant with the METAS watt balance, Metrologia 48, pp. 133-141, 2011.


METAS operates a watt balance experiment to contribute to the efforts leading to a new definition of the kilogram based on fundamental constants. In the watt balance, electrical power and mechanical power are compared in a two phase measurement sequence. First results of the experiment were published in 2011 [10]. Currently, METAS is developing an improved apparatus, designed to reach the required relative uncertainty of < 20 parts in 109.

METAS is the National Metrology Institute of Switzerland, located in Bern-Wabern. Reliable, comparable and, internationally recognized metrology is an essential prerequisite for trade in measurable goods, industrial manufacturing, research, measurable services, transportation and the protection and safety of people and environment. To fulfil this mission, METAS focuses on two main objectives:

  • The measurements required for the protection and safety of our society are always completed correctly and according to legal regulations - in trade, transportation, public safety, healthcare and environmental protection.
  • The measurement, verification, and certification infrastructure is available to the Swiss economy and to industry for research, production, and services as required for scientific, technical or economic reasons and for quality assurance.

Therefore, the metrological activities of METAS mainly focus on measurement units and the testing of measurement equipment. The activities of METAS are designed to enable its customers to measure, verify, or evaluate conformity correctly and as accurately as possible.


[Released: January 2012]