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SI units > kilogram (kg)

# kilogram (kg)

The kilogram is the SI base unit of mass. It is currently defined by the mass of the International Prototype of the Kilogram.

Accurately measuring the mass of an object in kilograms is essential in many applications, from administering the optimum dose of a drug to correctly manufacturing materials with the desired properties.

In the International Bureau of Weights and Measures in France, there is a platinum-iridium alloy cylinder called the International Prototype of the Kilogram

## Redefinition

Currently, we compare the gravitational force on an object with the gravitational force on a reference piece of metal known as a 'standard weight'. The standard weight is in turn compared with the International Prototype Kilogram. However, this may have changed since it was produced in 1884, but we have no way of knowing. Contamination, cleaning or just time may have increased or decreased it.

In May 2019 we will compare the gravitational force on an object with a magnetic force using a Kibble balance. A kilogram will be therefore be defined using the Planck constant, a fixed numerical constant which will not change over time.

## Did you know?

• A 10 cm cube of water at 4 °C has a mass of a kilogram and a metre cube has a mass of a tonne (approximately).
• NPL is home to the 18th copy of the International Prototype of the Kilogram
• The Kibble balance was developed at NPL in the UK

## The science behind the unit

The kilogram is the only remaining base unit to be defined by a physical object. All standards of mass must ultimately be traceable to this one object, a cylinder of platinum-iridium alloy kept at the International Bureau of Weights and Measures (BIPM) in France.

As science and industry's requirement for a more accurate way to measure extreme weights increases, the search is on for a definition of the kilogram in terms of a fundamental constant to improve its long-term stability and to eliminate the necessity for traceability to a single physical artefact.

Two key approaches are being pursued: building an electrical kilogram and counting atoms.

The quantum electrical standards for voltage and resistance, which are based upon the Planck constant and the elementary charge, are more stable than the present kilogram. The kilogram can be accurately compared with these standards using a moving-coil watt balance. Here, the weight of a 1 kg mass is balanced against the electromagnetic force generated by a current-carrying coil hung in a magnetic field. The ratio of the force generated by the coil to the the current passing through it is calibrated in a second phase of the experiment, which measures the voltage generated by the coil as it is moved at a measured velocity through the magnetic field. As the voltage and the current are measured using quantum electrical standards, the kilogram can be defined in terms of a fixed value of the Planck constant plus the existing definitions of the metre and the second.

The second approach relates the kilogram to an atomic mass, so that it can be defined as the mass of a fixed number of atoms. The number of atoms in a perfect silicon crystal can be counted by measuring its volume and dividing this by the volume a single atom occupies. This volume is measured by combined X-ray and optical interference techniques. This process amounts to a very accurate measurement of the Avogadro constant (NA).

These methods can only be used to measure the base unit if they can measure exactly one kilogram on demand. The first step is getting the resolution. NPL has developed the Kibble balance, which balances the gravitational force with an electromagnetic force. The next step is to get repeatable results and the final step is to ensure that the individual electrical and atomic mass experiments are in agreement. Both the electrical kilogram researchers and the atom counters are pursuing the ultimate target of measuring a kilogram with an accuracy of a millionth of one percent, every time.

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