Different options were discussed before reaching the final agreement on the new definitions of the SI units, effective from 20 May 2019, especially with regard to the kilogram, now defined in terms of the numerical value of the Planck constant (

On 16 November 2018, the General Conference of Weights and Measures – CGPM
(from the French Conférence Générale des Poids et Mesures) decided that, effective from 20 May 2019, the International System of Units,
the SI, is the system of units defined in terms of seven defining constants.
This is the result of three decades of progress in metrology (Stock et al.,
2019). It allows the dream of realizing the units at any time and place.
The new definition of the kilogram fixing the value of the Planck constant
abolished the previous one, which was referred to as an artefact. It allows the realization of mass at any scale using different technologies. The kilogram is no longer the mass of “the weight that was in Paris”, but it is defined by taking the fixed numerical value of

An evasive way to explain what a kilogram now is, avoiding mentioning the Planck constant, would be not to answer exactly what the new definition says, explaining instead that one of the possible ways of “realizing” the new kilogram is by counting atoms. Most people may have some idea of what an atom is, so they can imagine that by putting together a huge number of atoms one obtains a mass similar to that of the old platinum iridium artefact that served as an international prototype of the kilogram. So far the explanation could become understood even by elementary school pupils. The following immediate question will be of course how to gather and count so many atoms. This paves the way for explaining the efforts made during the last 20 years in order to measure the number of atoms existing inside special silicon spheres. In principle, this first answer, which avoids referring to the Planck constant, is not incorrect, since this so-called silicon route for the realization of an “atomic kilogram” and a second route using a special Kibble balance for the realization of an “electric kilogram” may provide both a link between the Planck constant and a macroscopic mass (Stenger and Göbel, 2012).

For a more advanced audience, possibly with university studies, or advanced pre-university studies, deserving of addressing the new definition of the kilogram based on the Planck's constant, more complex approaches are required. A friendly way of introducing the Planck constant

A second answer to the question of the relationship of

Anticipating the important difficulties that would arise in teaching the kilogram to be redefined, experimental solutions emerged already some years before its adoption. These approaches assumed that incorporating hands-on learning techniques will make it easier to understand something so complex.

In 2015 two experimental educational proposals for the understanding of the
kilogram definition based on fundamental constants were published: one for
the electric kilogram (Chao et al., 2015) and a second for the atomic kilogram (Davis, 2015), both to 1% relative uncertainty or less. The
first was a watt balance of LEGO blocks constructed at the National Institute of Standards and Technology – NIST. It allows explaining how the value of a mechanical force is precisely given by electrical measurements. Nevertheless, because the Kibble balance connects classical mechanics to quantum mechanics, addressing some equations of the quantum effects involved is inevitable. Using any version of didactic watt balances one may explain how to compensate for the mechanical power delivered by the gravitational attraction of a mass with the electrical power of a moving electromagnetic force, but not the relationship of the mass that is being weighed with the Planck constant

The second is a rather simple experiment conceived by Richard Stephen Davis to explain in 2015 how the kilogram would be redefined in 2018 in terms of the Planck constant, which is closely linked to the Avogadro and atomic mass constants. After measuring the volume and mass of a high-purity aluminium cube, he estimated the number

After comparing both experiments described, we found it more interesting and less expensive to implement the experiment with the high-purity aluminium cube, as proposed by Richard Davis, than a tabletop watt balance capable of measuring gram-level masses to 1 % relative uncertainty, like the LEGO balance quoted. With a homogenized aluminium cube (not free of imperfections and impurities) specially prepared by an Argentine manufacturer of electrolytic aluminium, the difference between the mass calculated counting atoms and the mass measured by weighing turned out to be 0.1 % or less. On the other hand, the experiment with the silicon cube, adapted to engineering students, makes it possible to simultaneously implement dimensional and mass precision measurements of interest for teaching metrology at that level.

Both experimental educational solutions for the realization of the kilogram
mentioned in the previous section were developed before the redefinition of
the SI. The purpose of such experiments changed after the redefinition. For
example, in the Kibble balance approach, the experiment was initially used
to measure

In the case of the experiment in a classroom setting with the aluminium cube
described, more conceptual changes need to be taken into account. As the molar mass constant was exactly 1 g mol

Along with the redefinition of the units, new ways of carrying out their
realizations came into effect. The so-called

If we want to use at present the didactic experiment of the aluminium cube, it should no longer be used to determine the values of certain constants which have been fixed but rather to obtain the mass of the cube following the corresponding

Experimental determination to 0.1 % of the mass of an aluminium
cube following the new definition of the kilogram traceable to the Planck constant. The cube volume is obtained by dimensional measurements

The previous definition of the kilogram referred to an artefact that involved the risk of
loss, damage, or change. The current definition of the kilogram based on a constant of nature solves the “artefact problem” and brings additional
benefits. For instance, it allows one to realize mass at any scale using different technologies. Additionally, having fixed the value of the elementary charge

Although fixing the value of the atomic mass constant

The data that support the findings of this study are available upon request to the author if required.

The author declares that he has no conflict of interest.

This article is part of the special issue “Sensors and Measurement Science International SMSI 2020”. It is a result of the Sensor and Measurement Science International, Nuremberg, Germany, 22–25 June 2020.

The author thanks Jorge Sánchez for his commitment to the hands-on teaching experiments.

This paper was edited by Klaus-Dieter Sommer and reviewed by two anonymous referees.