meaning of a metric prefix, such as “milli-”.

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

The unit of mass in SI, 20 May 2019 – present, one of the base unitsbase units. About 2.2046 pounds avoirdupois. Symbol, kg.

The kilogram, symbol kg, is the SI unit of mass, one of SI's 7 base units. It is defined by taking the fixed numerical value of the Planck constant to be 6.626 070 15 × 10⁻³⁴ when expressed in the unit J s, which is equal to kg m²s⁻¹, where the metre and the second are defined in terms of c and ΔνCs.

Resolutions Adopted.
Resolution 1, appendix 3.
26 CGPM, Versailles 13-16 November 2018.

Here “J s” is joule seconds. “ΔνCs” refers to the unperturbed ground state hyperfine transition frequency of the cesium 133 atom, which is fixed at exactly 9 192 631 770 hertz in the definition of the ampere. Specifying in hertz the value of a particular naturally-constant frequency is a way of defining the second. The meter is defined in terms of c, the speed of light.

In SI base units, the Planck constant is meter² kilogram second⁻¹. The meter has been fixed by defining the speed of light. The second has been fixed by defining the frequency of light emitted by certain cesium atoms. So defining the numerical value of the Planck constant fixes the size of the kilogram. Upon redefinition, the mass of the International Prototype was 1 kg with a relative uncertainty equal to that of the recommended value of Planck's constant just before it was made exact by definition. In the future, the prototype's mass must be determined experimentally. Its mass is no longer the exact mass of the kilogram.

The new definition will have no effect at all on everyday weighing, or even on most scientific work. But increasing potential precision opens the way to “the physics that is to be learned from the next decimal place — rather than merely the numerology of being able to quote a physical magnitude to 9 or 10 or even 12 digits.”"

The kilogram is the only SI unit that incorporates one of the decimal multiplier prefixes in its name. To be completely consistent, the gram should have been the unit of mass.

E. Richard Cohen.
Opening remarks.

International Conference on the Atomic Masses and Fundamental Constants, 5th, Paris, 1975.
Atomic Masses and Fundamental Constants 5.
New York and London: Plenum Press, 1976.
Page xxxi.

What was wrong with the old definition?

The kilogram was the only SI unit still defined by a physical prototype,

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.


losing mass scares


Option One: counting entities

One way of defining a unit of mass is to give a number of entities that have an unchanging, known mass (say, atoms of some particular isotope). For example, we could say (but don't) that a kilogram is the mass of 1,000,000,000,000,000 atoms of carbon-12. This option depends upon finding ways of counting atoms.

One way is with crystals of a element. In a crystal, atoms are arranged in a recurring, regular arrangement, for example, at the corners of a cube. Shape whose volume is known, you can calculate how many atoms it contains.

Option Two

fundametally based on mass, length and time. where did electromagnetic measurements fit in?

problem solved by Gauss and Weber with the invention of the watt-balance. On one side of the balance, electromagnets to create a force On the oter side, that force os quantifed in familar units. 


NIST: mechanical power is measured in units of mass, length, and time, then compared to electrical power as measured in units of voltage and resistance.


B. N. Taylor and P. J. Mohr.
On the redefinition of the kilogram.
Metrologia, vol 36, 63 (1999)

traced in the publications of the "Gang of 5" Ian M. Mills, Peter J. Mohr, Terry J. Quinn, Barry N. Taylor, Edwin R. Williams.

Redefinition of the kilogram: a decision whose time has come.
Metrologia, vol 42, no. 2, page 71 (28 February 2005).

Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005) Adapting the International System of Units to the twenty-first century.
Philosophical Transactions of the Royal Society A 369, pages 3907–3924 (2011)

The International Prototype Kilogram, 1889 to 2019

photo of the International Prototype of the Kilogram

During this period the kilogram's mass was defined by the mass of the International Prototype Kilogram, a platinum-iridium cylinder kept by the BIPM at Sèvres, France. Of three trial cylinders made in the 1880's, this one, KIII, was chosen because it was closest in mass to the mass of the Kilogram of the Archives, the previous prototype. The CIPM made the choice in 1883, and it was ratified by the first CGPM in 1889. The actual definition dates from the 1901 3rd CGPM.


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.

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).

The Kilogram des Archives, – 1889

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.

The mass of a cubic decimeter of water, before 1799

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. Thus, its mass depended upon the length of the meter, and the density of water.

The metric unit of mass 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 standard for the 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.

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.


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”:

NIST on the redefinition of the kilogram:

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