# Kilogram

For other uses of 'kg' see kg (disambiguation)

The kilogram or kilogramme, (symbol: kg) is the SI base unit of mass. It is defined as being equal to the mass of the international prototype of the kilogram.

It is the only SI base unit that employs a prefix, and the only SI unit that is still defined in relation to an artifact rather than to a fundamental physical property.

## History

The kilogram was originally defined as the mass of one litre of pure water at a temperature of 3.98 degrees Celsius and standard atmospheric pressure. This definition was hard to realize accurately, partially because the density of water depends ever-so-slightly on the pressure, and pressure units include mass as a factor, introducing a circular dependency in the definition of the kilogram.

To avoid these problems, the kilogram was redefined as precisely the mass of a particular standard mass created to approximate the original definition. Since 1889, the SI system defines the unit to be equal to the mass of the international prototype of the kilogram, which is made from an alloy of platinum and iridium of 39 mm height and diameter, and is kept at the Bureau International des Poids et Mesures (International Bureau of Weights and Measures). Official copies of the prototype kilogram are made available as national prototypes, which are compared to the Paris prototype ("Le Grand Kilo") roughly every 10 years. The international prototype kilogram was made in the 1880s.

By definition, the error in the repeatability of the current definition is exactly zero; however, in the usual sense of the word, it can be regarded as of the order of 2 micrograms. This is found by comparing the official standard with its official copies, which are made of roughly the same materials and kept under the same conditions. There is no reason to believe that the official standard is any more or less stable than its official copies, thus giving a way to estimate its stability. This procedure is performed roughly once every forty years.

The international prototype of the kilogram seems to have lost about 50 micrograms in the last 100 years, and the reason for the loss is still unknown (reported in Der Spiegel, 2003 #26). The observed variation in the prototype has intensified the search for a new definition of the kilogram. It is accurate to state that any object in the universe (other than the reference metal in France) that had a mass of 1 kilogram 100 years ago, and has not changed since then, now has a mass of 1.000 05 kg. This perspective is counterintuitive and defeats the purpose of a standard unit of mass, since the standard should not change arbitrarily over time.

## The gram

The gram or gramme is the term to which SI prefixes are applied.

The gram was the base unit of the older cgs system of measurement, a system which is no longer widely used.

## Proposed future definitions

There is an ongoing effort to introduce a new definition for the kilogram by way of fundamental or atomic constants. The proposals being worked on are:

### Atom-counting approaches

• The Avogadro approach attempts to define the kilogram as a fixed number of silicon atoms. As a practical realization, a sphere would be used and its size would be measured by interferometry.
• The ion accumulation approach involves accumulation of gold atoms and measuring the electrical current required to neutralise them.

### Fundamental-constant approaches

• The Watt balance uses the current balance that was formerly used to define the ampere to relate the kilogram to a value for Planck's constant, based on the definitions of the volt and the ohm.
• The levitated superconductor approach relates the kilogram to electrical quantities by levitating a superconducting body in a magnetic field generated by a superconducting coil, and measuring the electrical current required in the coil.
• Since the values of the Josephson (CIPM (1988) Recommendation 1, PV 56; 19) and von Klitzing (CIPM (1988), Recommendation 2, PV 56; 20) constants have been given conventional values, it is possible to combine these values (KJ ≡ 4.835 979×1014 Hz/V and RK ≡ 2.581 280 7×104 Ω) with the definition of the ampere to define the kilogram as follows:
The kilogram is the mass which would be accelerated at precisely 2×10-7 m/s² if subjected to the per metre force between two straight parallel conductors of infinite length, of negligible circular cross section, placed 1 metre apart in vacuum, through which flow a constant current of exactly 6.241 509 629 152 65 × 1018 elementary charges per second.

When the weight of an object is given in kilograms, the property intended is almost always mass. Occasionally the gravitational force on an object is given in "kilograms", but the unit used is not a true kilogram: it is the deprecated kilogram-force (kgf), also known as the kilopond (kp). An object of mass 1 kg at the surface of the Earth will be subjected to a gravitational force of approximately 9.80665 newtons (the SI unit of force). Note that the factor of 980.665 cm/s² (as the CGPM defined it, when cgs systems were the primary systems used) is only an agreed-upon conventional value (3rd CGPM (1901), CR 70) whose purpose is to define grams force. The local gravitational acceleration g varies with latitude and altitude and location on the Earth, so before this conventional value was agreed upon, the gram-force was only an ill-defined unit. (See also gee, a standard measure of gravitational acceleration.)

### Examples

• Attogram: a research team at Cornell University made a detector using NEMS cantilevers with sub-attogram sensitivity.
• Yoctogram: can be used for masses of nucleons, atoms and molecules. It is a little large for light particles, but yocto- is the last official prefix in the sequence.
• The coefficient is close to the reciprocal of Avogadro's number: 1 unified atomic mass unit = 1.660 54 yg
• Although the unified atomic mass unit is often convenient as a unit, one may sometimes want to use yoctograms to relate easily to other SI values.
• Mass of a free electron: 0.000 91 yg
• Mass of a free proton : 1.672 6 yg
• Mass of a free neutron: 1.674 9 yg

## SI multiples

Multiple Name Symbol Multiple Name Symbol
100 gram g
101 decagram dag 10–1 decigram dg
102 hectogram hg 10–2 centigram cg
103 kilogram kg 10–3 milligram mg
106 megagram Mg 10–6 microgram µg
109 gigagram Gg 10–9 nanogram ng
1012 teragram Tg 10–12 picogram pg
1015 petagram Pg 10–15 femtogram fg
1018 exagram Eg 10–18 attogram ag
1021 zettagram Zg 10–21 zeptogram zg
1024 yottagram Yg 10–24 yoctogram yg