# kilogram

For the meaning of any metric prefix, go here.

Convert between kilograms or grams and other major units of mass.

The unit of mass in SI, equal to the mass of the International Prototype Kilogram, a platinum-iridium cylinder kept by the BIPM at Sèvres, France. The present definition dates from the 1901 3rd CGPM, though the Prototype was made in the 1880's.  About 2.2046 pounds avoirdupois. Symbol, kg.

The kilogram is one of SI's seven base units. It is unique in being the only SI unit still defined by a physical prototype, and the only one that incorporates one of the decimal multiplier prefixes in its name. To be completely consistent, the gram should have been the unit of mass.

In 1989, the CIPM interpreted the 1901 definition of the kilogram to make it the mass of the International Prototype just after it has been washed using procedures newly developed by the BIPM.1 Without such cleaning, the Prototype gains almost 1 microgram per year.

The standards which most accurately reflect the mass of the International Prototype are kilogram standards. The masses of submultiple standards (e.g., gram standards) and multiples are all necessarily less certain.

## The definition to come

Work has continued on replacing the definition that depends on the perishable Prototype with one based on fundamental physical constants. Recommendation 1, passed at the 94th meeting of the CIPM in 2005, anticipated that the kilogram would be redefined at the 24th CGPM in 2011. At that meeting (Paris, October 2011), the CGPM, in resolution 1, while not yet ready to redefine the kilogram and many other units, gave much fuller details of the form the redefinitions will take.

The value of the Planck constant will be made a matter of definition, rather than something to be determined experimentally. The new value will be exactly 6.626 06X × 10−34 joule-seconds, where X stands for one or more yet-to-be-determined digits.

In SI base units, the Planck constant is meter2 kilogram second−1. The second has been fixed by defining the frequency of light emitted by certain cesium atoms. The meter has been fixed by defining the speed of light. So defining the numerical value of the Planck constant fixes the size of the kilogram. Upon redefinition, the mass of the International Prototype will be 1 kg with a relative uncertainty equal to the recommended value of Planck's constant just before the redefinition. In the future, the prototype's mass will be determined experimentally.

The new definition will not be adopted before 2014 at the earliest, and, in any case, will have no effect at all on everyday life. Its purpose, besides freeing us from dependence on an artefact, is to give scientists the extra decimal places needed for some types of investigations.

1. Procès-Verbaux des Séances du Comité International des Poids et Mesures, vol. 57, pages 104-105 (1989) and Procès-Verbaux, vol. 58, 95-97 (1990).

contents

history of the kilogram

future of the kilogram

## History of the kilogram

The kilogram originated in the reforms of the French Revolution. Conceptually, it was to be the mass of a cubic decimeter of water at water's maximum density. It was originally called a grave, but the name was changed to kilogram in 1795. In the same year Lefèvre-Gineau was given the job of determining just how massive a cubic decimeter of water was. In the meantime, a provisional kilogram was made which was expected to be close enough to the final value for commercial purposes.

The method that Lefèvre-Gineau chose depends on the principle that the difference between the weight of an object in air and its weight immersed in water is the weight of the water it displaces. He made a hollow brass cylinder, just heavy enough to sink in water, whose dimensions were measured repeatedly. After corrections were made for changes in size due to thermal expansion, the cylinder's volume was calculated to be 11.28 cubic decimeters at 0°C. To weigh the cylinder, special weights were made of brass of the same density as the brass of the cylinder, to compensate for the buoyancy in air of the weights.

After months of subtle and precise work, the researchers concluded that the mass of a cubic decimeter of water at its maximum density was 99.92072% of the mass of the provisional kilogram.

To create platinum standards for the new system of weights and measures, the former royal jeweller, Marc Etienne Janety (Janetti), was recalled to Paris. (He had fled when the revolution started.) By 1796 he was making kilogram masses. One of these, a cylinder 39.4 millimeters in diameter and 39.7 millimeters high, was legally declared the official prototype of the kilogram in 1799. Since then it has been called the Kilogramme des Archives.

In the 1870s the French government sponsored a series of conferences (1870, 1872) to discuss how metric standards ought best be designed, produced and distributed. One of the conference's conclusions was that new standards ought to be made of a platinum-iridium alloy rather than pure platinum. The first attempts to do so were failures. The Metric Convention (1875), which led to the establishment of the BIPM, gave fresh impetus to the work, and preparation of the alloy was entrusted to the London firm of Johnson, Matthey, who specialized in precious metals. They did succeed in casting the alloy, the French produced standards from it, and the new standards were ready for distribution before the first CGPM in 1889. This conference recognized one of the new platinum-iridium standards—the one whose mass most closely matched that of the Kilogramme des Archives—as the new prototype of the kilogram. It is that object, made in the 1870s, which is referred to as the International Prototype Kilogram.

Modern measurements of the mass of water have shown that a cubic decimeter of water has a mass that is about 28 parts per million less than a kilogram—but that doesn't matter, because the kilogram hasn’t been defined in terms of the mass of a cubic decimeter of water since 1799, when the Kilogramme des Archives was accepted as the unit’s prototype.

### sources

Gerrit Moll, writing in 1831, on variations in the mass of the early standards for the kilogram.

## Future of the kilogram

The continued dependence of the kilogram on a physical prototype makes metrologists uneasy. The last time the International Prototype Kilogram was compared with the national standard kilograms, (1988 – 1992), it was less massive than the average of the masses of the national kilograms. The probable explanation is that the Prototype's mass has decreased, for some unknown reason, by about 30 micrograms over the past century. Besides, because of the risk of damaging it, the unique prototype can't be used very often—the use being comparisons with the various national standards laboratories' standard kilograms. Although currently the prototype meets all needs for accuracy, physicists have been searching for a way of defining the kilogram in terms of fundamental physical constants.

A means of defining the kilogram in terms of electric units has been proposed by B. P. Kibble at the National Physical Laboratory in Teddington, England, and explored there and at the United States’s National Institute of Standards and Technology. The method uses a movable coil of wire in a magnetic field and exploits the precision with which the volt and ohm can now be defined using quantum effects. From measurements of the coil's velocity, the acceleration due to gravity, the coil's velocity, and the current and voltage in the coil, the mass of the coil can be calculated. As of 1993, the accuracy was not as good as that obtained with the Prototype Kilogram, but in the future this or some similar technique is bound to lead to a definition that will supplant the Prototype Kilogram.

Terry J. Quinn.
The kilogram: The present state of our knowledge.
IEEE Transactions on Instrumentation and Measurement, volume 40, pages 81-85. (April 1991)

R. Steiner, E. R. Williams, D. B. Newell and R. Liu.
Towards an electronic kilogram: an improved measurement of the Planck constant and electron mass.
Metrologia, vol. 42, pages 431-441. (2005)

NIST on the “electronic kilogram”:

www.nist.gov/pml/div684/grp05/kilogram.cfm

NIST on the redefinition of the kilogram:

www.nist.gov/pml/div684/grp07/rekilo.cfm