# Kilogram

### The Unit – kilogram, kg (manokaramu)

Mass and its related quantities, such as pressure and density, are amongst the most commonly encountered quantities in our everyday lives. They are used in everything from supermarkets to international trades; and from manufacturing and transport to scientific research.

The SI unit of mass is the kilogram (kg). Before 1889, the kilogram had been defined as the mass of a litre of water at 4 °C. The first General Conference on Weights and Measures (CGPM) in 1889 sanctioned the International Prototype Kilogram (IPK) to be used to define the kilogram. The IPK is a 90 % platinum and 10 % iridium highly-polished metallic cylinder with height 39 mm and diameter 39 mm. The IPK, along with its six official copies, are stored under specific conditions inside a vault at the Bureau International des Poids et Mesures (BIPM), which is located in Paris. This decision from the CGPM gave us the following definition of the kilogram, which still applies today:

*“The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.”*

The kilogram is the only SI unit still defined by a material artefact. The main issue with such a definition is that it is impossible to determine the stability of the IPK mass with any accuracy. On four occasions since the inception of the IPK, mass comparison studies between it and its copies have shown mass divergences of up to 70 µg. While it may be that the copies are gaining atoms, there is a possibility that it is the IPK that has changed. If so, the very definition of the kilogram could also be said to vary. As a consequence, the accuracy of other critical measurement units that currently depend on the kilogram, such as the newton (force), pascal (pressure), joule (energy) and ampere (current), could be called into question. The accuracy with which these units can be realised is, in fact, limited by the uncertainties in the stability of the IPK.

The need for a new definition of the kilogram – one based on a natural constant that is invariant over time – was established several decades ago. Since the 1970s, several national laboratories have been working towards redefining the kilogram in terms of Planck’s constant – a physical constant that links the amount of energy a photon carries with the frequency of its electromagnetic wave. There are two main approaches that provide sufficiently high accuracy:

One method involves counting the atoms in a pure silicon-28 sphere that weighs the same as the reference kilogram. This can be used to calculate the value of Avogadro’s constant which, in turn, can be converted into a value for Planck’s constant. The second method uses an apparatus known as the Kibble balance to obtain a value for Planck’s constant by comparing the gravitational force on a test mass with the electromagnetic force on a coil carrying current in a magnetic field. Only in recent years have the two different methods obtained results that agree with each other, and that are precise enough to fulfil the strict requirements around the redefinition of the kilogram. The redefinition is expected to happen in 2019.

Basing the definition of mass on Planck’s constant will not only make the kilogram more stable, but in principle, it will allow the kilogram to be realised in any corner of the earth, rather than relying on a physical artefact stored in Paris.

### Technical Capability

We are leading experts in mass, pressure, density and volume measurements. We have the capabilities to perform high-accuracy calibration of reference weights and pressure measuring instruments, and carry out measurements of the density and volumes of solid objects and liquids. We do this by using state-of-the-art mass comparators and balances, pressure balances, deadweight testers, differential pressure generators, barometers, densitometers and hydrostatic weighing, supported by ongoing research in methods and analysis. We can also provide advice on the measurement of other mass-related quantities, such as flow, force, torque and hardness.

### Our Research

Our main focus is on building a unique Kibble balance based on a twin pressure balance, which offers to be a relatively cost-effective way to disseminate the kilogram following the redefinition. Other mass research includes: improved methods and analysis of mass comparison, stability of mass artefacts following cleaning of surfaces, and automatic weighing systems. We’re interested in pressure balance elastic distortion and generation of small absolute and differential pressures. In density measurements, we focus on the development of electronic densitometers, calibration and reference liquids.

### Relevant Publications

1 C M Sutton, M T Clarkson and Yin Hsien Fung, “The MSL Kibble balance weighing mode^{”}, summary paper submitted to CPEM 2018.

2 M Stock, S Davidson, H Fang, M Milton, E de Mirandés, P Richard and C Sutton”, Maintaining and disseminating the kilogram following its redefinition”, Metrologia 54 (2017) S99.

3 C M Sutton, M T Clarkson and W M Kissling, “The feasibility of a watt balance based on twin pressure balances”, CPEM 2016 Conf. Digest., Ottawa, Canada, July 10 - 15, 2016.

4 M T Clarkson, C M Sutton and R Mason, “An apparatus for accurate measurement of the temperature dependence of permanent magnetization”, Measurement Science & Technology 25 (2014) 085902, published 8 July 2014.

5 C M Sutton and M T Clarkson, “A magnet system for the MSL watt balance”, Metrologia 51 (2014) S101-S106, published 31 March 2014.

6 C M Sutton, “Progress with MSL’s watt balance - and differences from other watt balances”, presented to the APMP TCM Technical Workshop, Taipei, Chinese Taipei, 25 - 26 November 2013.

7 C M Sutton, M P Fitzgerald and K Carnegie, “Improving the Performance of the Force Comparator in a Watt Balance based on Pressure Balances”, CPEM 2012 Conf. Digest., Washington DC, USA, pp.468-469, July 1-6, 2012.

8 K. Jones, L. A. Christian and C. M. Sutton, “Coil Correction for Oscillatory Calibration of a Watt Balance”, CPEM 2012 Conf. Digest., Washington DC, USA, pp. 330-331, July 1-6, 2012.

9 L A Christian, T J Stewart and C M Sutton, “Investigation of ac voltage measurement requirements for an oscillatory dynamic mode version of the watt balance”, CPEM 2010 Conf. Digest., Daejeon, Korea, pp.151-152, June 13-18, 2010.

10 C M Sutton, M P Fitzgerald and D G Jack, “The concept of a pressure balance based watt balance”, CPEM 2010 Conf. Digest., Daejeon, Korea, pp.131-132, June 13-18, 2010.

11 C M Sutton, “An oscillatory dynamic mode for a watt balance”, Metrologia**46** (2009) 467-472.

12 C M Sutton, “On Watt Balance Design for a Non-Artefact Kilogram”, Proceedings of Asia-Pacific Symposium on Mass, Force and Torque (APMF 2007), Oct 24 – 25, 2007.

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