# The Kilogram - the Unit of Mass

The 26th General Conference on Weights and Measures (CGPM) has adopted a revision of the International System of Units (SI) on 16th November 2018, effective from 20th May 2019. As a result, all SI units refer to fixed values of seven constants of nature. In the new SI, the kilogram will be derived from a fixed value of the Planck constant h (in conjunction with fixed values of the frequency of the unperturbed ground state hyperfine transition frequency of the 133Cs atom ΔvCs and of the speed of light in vacuum c) [1-4]:

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 6.626 070 15 × 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 ΔvCs.

After the first international key comparison of realisations of the new kilogram definition had been completed [5], the CCM Task Group on the Phases for the Dissemination of the kilogram following redefinition (CCM-TGPfD-kg) was able to determine the first consensus value for the dissemination of the unit of mass [6-9].

Based on this consensus value, the mass of the international prototype of the kilogram was determined as 1 kg − 0.002 mg with a standard uncertainty (k = 1) of 0.020 mg (relative value 2 × 10‑8) [8-9]. After 1 February 2021 [9], when disseminating the unit of mass, the kilogram, this uncertainty contribution must be taken into account. This uncertainty therefore replaces the former standard uncertainty (k = 1) of the mass of the international kilogram prototype of 0.010 mg (relative value 1 × 10-8), which was introduced with the redefinition on 20 May 2019 [7].

As a result of subsequent key comparisons of realisations of the new definition of the kilogram, the consensus value will be regularly updated and published on the websites of the CCM [12, 13]. The current consensus value and the corresponding corrections need to be taken into account in the dissemination of the mass unit. In certificates issued by PTB, the corrections required for the respective current consensus value are already included.

Literature

[1]  Resolutions of the 26th  meeting of the General Conference of Weights and Measures (CGPM), Versailles, 13-16 November 2018,
www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf

[2]  PTB: Research on the new SI,
www.ptb.de/cms/en/research-development/research-on-the-new-si.html

[3]  Mise en pratique for the definition of the kilogram in the SI,
www.bipm.org/utils/en/pdf/si-mep/SI-App2-kilogram.pdf

[4]  Bureau International des Poids et Mesures: The International System of Units (SI), 9th SI Brochure, 2019, www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf

[5]  Stock, M. et al.: Report on the CCM key comparison of kilogram realizations CCM.M-K8.2019, Metrologia 57 (2020) Tech. Suppl. 07030,
iopscience.iop.org/article/10.1088/0026-1394/57/1A/07030

[6]  Newell, D. B. et al.: The CODATA 2017 values of h, e, k, and NA for the revision
of the SI, Metrologia 55 (2018) L13
iopscience.iop.org/article/10.1088/1681-7575/aa950a

[7]  Consultative Committee for Mass and Related Quantities (CCM): Report of the 16th meeting (18-19 May 2017) to the International Committee for Weights and Measures, www.bipm.org/utils/common/pdf/CC/CCM/CCM16.pdf

[8]  Consultative Committee for Mass and Related Quantities: CCM detailed note on the dissemination process after the redefinition of the kilogram , Approved at the 17th CCM meeting, 16-17 May 2019, www.bipm.org/documents/20126/41489673/CCM_Note-on-dissemination-after-redefinition.pdf/3743d0d0-d8cc-325c-3219-547a6ea47a47

[9]  M. Stock, S. Davidson: Report on the Calculation of the CCM Consensus Value for the Kilogram 2020, www.bipm.org/documents/20126/48512025/Report+on+calculation+of+consensus+value+2020/cf6aba9a-ddaf-0a63-f3d4-5f146e6e28f1

[10] CCM Task Group on the Phases for the Dissemination of the kilogram following redefinition (CCM-TGPfD-kg): Calculation of the Consensus Value for the Kilogram 2020, www.bipm.org/documents/20126/49759984/Calculation+of+the+consensus+value+2020/99498411-54a2-ddfd-5054-4d7beb1ae45f

[11] Bureau International des Poids et Mesures: Beginning a new phase of the dissemination of the kilogram, www.bipm.org/en/-/2021-kg-consensus

[12] Consultative Committee for Mass and Related Quantities (CCM): Dissemination from the Consensus Value for the kilogram. February 2023, www.bipm.org/en/committees/cc/ccm

[13] CCM Task Group on the Phases for the Dissemination of the kilogram following redefinition (CCM-TGPfD-kg): Calculation of the Consensus Value for the Kilogram 2023. February 2023, www.bipm.org/en/committees/cc/ccm/wg/ccm-tgpfd-kg

### The international prototype of the kilogram

The international prototype of the kilogram is a cylinder 39 mm in height and 39 mm in diameter. It consists of an alloy of 90 % platinum and 10 % iridium (density of appr. 21500 kg/m3) and is maintained at the International Bureau of Weights and Measures (BIPM) in Sèvres near Paris. The national prototypes of the signatories of the Metre Convention are official copies of the international prototype of the kilogram, made of the same material with the same dimensions and surface properties.

### National prototype of the kilogram No. 52 of the Federal Republic of Germany

The national prototype of the kilogram of the Federal Republic of Germany is maintained under two bells jars at standard ambient conditions at the PTB in Braunschweig.

About every 10 years, its traceability to the international prototype at the BIPM is reconfirmed. The secondary standards of stainless steel are linked up with the national prototype once a year.

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## Prototype Balance of the PTB

The most accurate balances of the PTB are high-resolution 1 kg mass comparators. They are accommodated in a pressure-tight enclosures. Mass comparisons can be performed with standard deviations of less than 0,4 µg ( ≤ 4•10-10 kg).

Prototype balances are used for the:

• link up of PTB’s secondary standards with the national prototype
• realisation of the mass scale starting from 1 kg down to 100 g
• calibration of mass standards and weights (nominal values 100 g, 200 g, 500 g, 1 kg) with smallest uncertainties according to the CMC1  tables of the BIPM2
• mass determination of silicon spheres used as primary standards of the solid density and for the determination of the Avogadro constant

Furthermore, with these balances mass determinations are performed under vacuum conditions (≤ 0,1 Pa). Air buoyancy and sorption effects are investigated and corrected by means of comparison measurements in air and in vacuum.

1 Calibration and measurement capabilities
2 kcdb.bipm.org/appendixC/

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Mass comparator Mettler M_one

for measurements in a pressure-tight enclosure in air under constant pressure and in vacuum, automatic weight exchange mechanism with 6 positions, nominal load 1 kg, standard deviation (typ.) ≤ 0,4 µg

Mass comparator Sartorius CCL1007
for measurements in a pressure-tight enclosure in air under constant pressure and in vacuum, automatic weight exchange mechanism with 8 positions, nominal load 1 kg, standard deviation (typ.) ≤ 0,2 µg