Kilogram

"kg" redirects here. For other uses, see KG (disambiguation).

The subject of this article is affected by the 2019 redefinition of the SI base units, which came into effect on May 20, 2019. As such, it may need to be revised to reflect those changes.

Kilogram
General information
Unit system	SI base unit
Unit of	mass
Symbol	kg
Conversions
1 kg in ...	... is equal to ...
Avoirdupois	≈ 2.205 pounds
British Gravitational	≈ 0.0685 slugs

The kilogram, also kilogramme, is the base unit of mass in the metric system, formally the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering, and commerce worldwide, and is often called a kilo.

The kilogram was originally defined in 1795 as the mass of a litre of water. This was a convenient definition, but hard to replicate precisely. In 1799, the Kilogramme des Archives, a platinum artefact, replaced it as a standard mass sample. Later, the International Prototype Kilogram (IPK) became the standard of the unit of mass for the metric system, and remained so until 20 May 2019. In spite of best efforts to maintain it, the IPK diverged from its replicas by approximately 50 micrograms since their manufacture late in the 19th century. This led to efforts to develop measurement technology precise enough to allow replacing the kilogram artefact with a definition based directly on physical fundamental constants. This was achieved in 2018, with a definition in terms of the Planck constant. Thus, the kilogram is now defined in terms of the second and the metre, eliminating the need for the IPK. The new definition was approved by the General Conference on Weights and Measures (CGPM) on 16 November 2018. The Planck constant relates a light particle's energy, and hence mass, to its frequency. The new definition only became possible when instruments were devised to measure the Planck constant with sufficient accuracy based on the IPK definition of the kilogram.

Definition

As of 20 May 2019, the definition of the kilogram is based on a fixed assignment of the Planck constant as 6.62607015×10⁻³⁴ kg⋅m²⋅s⁻¹, yielding a definition of the kilogram in terms of the second and the metre in a consistent system of units based on physical constants only.

Previous definitions

The development of the first metric system began about 1790. The initial mass unit was the grave, which evolved into the kilogram. The gram, 1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimetre of water at the melting point of ice. The Kilogramme des Archives was manufactured as a prototype in 1799 and served as a basis for the International Prototype Kilogram (IPK) in 1875. It had a mass equal to the mass of 1 dm³ of water under atmospheric pressure and at the temperature of its maximum density, which is approximately 4 °C.

A replica of the prototype kilogram on display at Cité des Sciences et de l'Industrie, featuring the protective double glass bell.

The International Prototype Kilogram was commissioned by the General Conference on Weights and Measures (CGPM) under the authority of the Metre Convention (1875), and is in the custody of the International Bureau of Weights and Measures (BIPM) who hold it on behalf of the CGPM. The IPK is rarely used or handled. Copies of the IPK kept by national metrology laboratories around the world were compared with the IPK in 1889, 1948, and 1989 to provide traceability of measurements of mass anywhere in the world back to the IPK.

The kilogram was the last SI unit that was directly defined by an artefact rather than a fundamental physical property that could be independently reproduced in different laboratories. Three other base units (cd, A, mol) and 17 derived units (N, Pa, J, W, C, V, F, Ω, S, Wb, T, H, kat, Gy, Sv, lm, lx) in the SI system are defined in relation to the kilogram, and thus its stability is important. The definitions of only eight other named SI units did not depend on the kilogram: those of temperature (K, °C), time and frequency (s, Hz, Bq), length (m), and angle (rad, sr).

Replacement of the International Prototype Kilogram

Main article: 2019 redefinition of SI base units

After the International Prototype Kilogram had been found to vary in mass over time relative to its reproductions, the International Committee for Weights and Measures (CIPM) recommended in 2005 that the kilogram be redefined in terms of a fundamental constant of nature. At its 2011 meeting, the CGPM agreed in principle that the kilogram should be redefined in terms of the Planck constant, h. The decision was originally deferred until 2014; in 2014 it was deferred again until the next meeting. CIPM had proposed revised definitions of the SI base units, for consideration at the 26th CGPM. The formal vote, which took place on 16 November 2018, approved the change.

Other units

Most other traditional units of weight and mass, in use around the world, have been redefined in terms of the kilogram. For example, the avoirdupois (or international) pound, used in both the imperial and US customary systems, is defined as 0.453 592 37 kg.

Name and terminology

The kilogram is the only base SI unit with an SI prefix (kilo) as part of its name. The word kilogramme or kilogram is derived from the French kilogramme, which itself was a learned coinage, prefixing the Greek stem of χίλιοι khilioi "a thousand" to gramma, a Late Latin term for "a small weight", itself from Greek γράμμα. The word kilogramme was written into French law in 1795, in the Decree of 18 Germinal, which revised the older system of units introduced by the French National Convention in 1793, where the gravet had been defined as weight (poids) of a cubic centimetre of water, equal to 1/1000 of a grave. In the decree of 1795, the term gramme thus replaced gravet, and kilogramme replaced grave.

The French spelling was adopted in Great Britain when the word was used for the first time in English in 1795, with the spelling kilogram being adopted in the United States. In the United Kingdom both spellings are used, with "kilogram" having become by far the more common. UK law regulating the units to be used when trading by weight or measure does not prevent the use of either spelling.

In the 19th century the French word kilo, a shortening of kilogramme, was imported into the English language where it has been used to mean both kilogram and kilometre. While kilo is acceptable in many generalist texts, for example The Economist, its use is typically considered inappropriate in certain applications including scientific, technical and legal writing, where authors should adhere strictly to SI nomenclature. When the United States Congress gave the metric system legal status in 1866, it permitted the use of the word kilo as an alternative to the word kilogram, but in 1990 revoked the status of the word kilo.

During the 19th century, the standard system of metric units was the centimetre–gram–second system of units, treating the gram as the fundamental unit of mass and the kilogram simply as a derived unit. In 1901, however, following the discoveries by James Clerk Maxwell to the effect that electric measurements could not be explained in terms of the three fundamental units of length, mass and time, Giovanni Giorgi proposed a new standard system that would include a fourth fundamental unit to measure quantities in electromagnetism. In 1935 this was adopted by the IEC as the Giorgi system, now also known as MKS system, and in 1946 the CIPM approved a proposal to adopt the ampere as the electromagnetic unit of the "MKSA system". In 1948 the CGPM commissioned the CIPM "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention". This led to the launch of SI in 1960 and the subsequent publication of the "SI Brochure", which stated that "It is not permissible to use abbreviations for unit symbols or unit names ...". The CGS and MKS systems co-existed during much of the early-to-mid 20th century, but as a result of the decision to adopt the "Giorgi system" as the international system of units in 1960, the kilogram is now the SI base unit for mass, while the definition of the gram is derived from that of the kilogram.

Mass and weight

Measurement of weight – gravitational attraction of the measurand causes a distortion of the spring

Measurement of mass – the gravitational force on the measurand is balanced against the gravitational force on the weights.

See also: Mass versus weight

The kilogram is a unit of mass, a property corresponding to the common perception of how "heavy" an object is. Mass is an inertial property; that is, it is related to the tendency of an object at rest to remain at rest, or if in motion to remain in motion at a constant velocity, unless acted upon by a force.

While the weight of an object is dependent on the strength of the local gravitational field, the mass of an object is independent of gravity, as mass is a measure of the quantity of matter. Accordingly, for astronauts in microgravity, no effort is required to hold objects off the cabin floor; they are "weightless". However, since objects in microgravity still retain their mass and inertia, an astronaut must exert ten times as much force to accelerate a 10‑kilogram object at the same rate as a 1‑kilogram object.

Because at any given point on Earth the weight of an object is proportional to its mass, the mass of an object in kilograms is usually measured by comparing its weight to the weight of a standard mass, whose mass is known in kilograms, using a device called a weighing scale. The ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses.

2019 redefinition based on fundamental constants

The SI system after the 2019 redefinition: the kilogram is now fixed in terms of the second, the speed of light and the Planck constant, and the ampere no longer depends on the kilogram

Main articles: 2019 redefinition of SI base units and CODATA 2018

In the following subsections, wherever numeric equalities are shown in concise form—such as 1.85487(14)×10¹³—the two digits between the parentheses denote the uncertainty at one standard deviation (1σ, the 68% confidence level) in the two least significant digits of the significand.

The International Committee for Weights and Measures (CIPM) approved a redefinition of the SI base units in November 2018 that defines the kilogram by defining the Planck constant to be exactly 6.62607015×10⁻³⁴ kg⋅m²⋅s⁻¹. This approach effectively defines the kilogram in terms of the second and the metre, and took effect on 20 May 2019.

History of redefinition

Prior to the redefinition the kilogram, and several other SI units based on the kilogram, were defined by a man-made metal artefact: the Kilogramme des Archives from 1799 to 1889, and the International Prototype Kilogram from 1889 onward.

In 1960, the metre, previously similarly having been defined with reference to a single platinum-iridium bar with two marks on it, was redefined in terms of an invariant physical constant (the wavelength of a particular emission of light emitted by krypton, and later the speed of light) so that the standard can be independently reproduced in different laboratories by following a written specification.

At the 94th Meeting of the International Committee for Weights and Measures (CIPM) in 2005, it was recommended that the same be done with the kilogram.

In October 2010, the CIPM voted to submit a resolution for consideration at the General Conference on Weights and Measures (CGPM), to "take note of an intention" that the kilogram be defined in terms of the Planck constant, h (which has dimensions of energy times time) together with other physical constants. This resolution was accepted by the 24th conference of the CGPM in October 2011 and further discussed at the 25th conference in 2014. Although the Committee recognised that significant progress had been made, they concluded that the data did not yet appear sufficiently robust to adopt the revised definition, and that work should continue to enable the adoption at the 26th meeting, scheduled for 2018. Such a definition would theoretically permit any apparatus that was capable of delineating the kilogram in terms of the Planck constant to be used as long as it possessed sufficient precision, accuracy and stability. The Kibble balance (discussed below) is one way do this.

As part of this project, a variety of very different technologies and approaches were considered and explored over many years. They too are covered below. Some of these now-abandoned approaches were based on equipment and procedures that would have enabled the reproducible production of new, kilogram-mass prototypes on demand (albeit with extraordinary effort) using measurement techniques and material properties that are ultimately based on, or traceable to, physical constants. Others were based on devices that measured either the acceleration or weight of hand-tuned kilogram test masses and which expressed their magnitudes in electrical terms via special components that permit traceability to physical constants. All approaches depend on converting a weight measurement to a mass, and therefore require the precise measurement of the strength of gravity in laboratories. All approaches would have precisely fixed one or more constants of nature at a defined value.

Kibble balance

The NIST's Kibble balance is a project of the US government to develop an "electronic kilogram". The vacuum chamber dome, which lowers over the entire apparatus, is visible at top.

Main article: Kibble balance

The Kibble balance (known as a "watt balance" before 2016) is essentially a single-pan weighing scale that measures the electric power necessary to oppose the weight of a kilogram test mass as it is pulled by Earth's gravity. It is a variation of an ampere balance, with an extra calibration step that eliminates the effect of geometry. The electric potential in the Kibble balance is delineated by a Josephson voltage standard, which allows voltage to be linked to an invariant constant of nature with extremely high precision and stability. Its circuit resistance is calibrated against a quantum Hall effect resistance standard.

The Kibble balance requires extremely precise measurement of the local gravitational acceleration g in the laboratory, using a gravimeter. For instance when the elevation of the centre of the gravimeter differs from that of the nearby test mass in the Kibble balance, the NIST compensates for Earth's gravity gradient of 309 μGal per metre, which affects the weight of a one-kilogram test mass by about 316 μg/m.

In April 2007, the NIST's implementation of the Kibble balance demonstrated a combined relative standard uncertainty (CRSU) of 36 μg. The UK's National Physical Laboratory's Kibble balance demonstrated a CRSU of 70.3 μg in 2007. That Kibble balance was disassembled and shipped in 2009 to Canada's Institute for National Measurement Standards (part of the National Research Council), where research and development with the device could continue.

The local gravitational acceleration g is measured with exceptional precision with the help of a laser interferometer. The laser's pattern of interference fringes—the dark and light bands above—blooms at an ever-faster rate as a free-falling corner reflector drops inside an absolute gravimeter. The pattern's frequency sweep is timed by an atomic clock.

Gravity and the nature of the Kibble balance, which oscillates test masses up and down against the local gravitational acceleration g, are exploited so that mechanical power is compared against electrical power, which is the square of voltage divided by electrical resistance. However, g varies significantly—by nearly 1%—depending on where on the Earth's surface the measurement is made (see Earth's gravity). There are also slight seasonal variations in g at a location due to changes in underground water tables, and larger semimonthly and diurnal changes due to tidal distortions in the Earth's shape caused by the Moon and the Sun. Although g would not be a term in the definition of the kilogram, it would be crucial in the process of measurement of the kilogram when relating energy to power. Accordingly, g must be measured with at least as much precision and accuracy as are the other terms, so measurements of g must also be traceable to fundamental constants of nature. For the most precise work in mass metrology, g is measured using dropping-mass absolute gravimeters that contain an iodine-stabilised helium–neon laser interferometer. The fringe-signal, frequency-sweep output from the interferometer is measured with a rubidium atomic clock. Since this type of dropping-mass gravimeter derives its accuracy and stability from the constancy of the speed of light as well as the innate properties of helium, neon, and rubidium atoms, the 'gravity' term in the delineation of an all-electronic kilogram is also measured in terms of invariants of nature—and with very high precision. For instance, in the basement of the NIST's Gaithersburg facility in 2009, when measuring the gravity acting upon Pt‑10Ir test masses (which are denser, smaller, and have a slightly lower center of gravity inside the Kibble balance than stainless steel masses), the measured value was typically within 8 ppb of 9.80101644 m/s².

The virtue of electronic realisations like the Kibble balance is that the definition and dissemination of the kilogram no longer depends upon the stability of kilogram prototypes, which must be very carefully handled and stored. It frees physicists from the need to rely on assumptions about the stability of those prototypes. Instead, hand-tuned, close-approximation mass standards can simply be weighed and documented as being equal to one kilogram plus an offset value. With the Kibble balance, while the kilogram is delineated in electrical and gravity terms, all of which are traceable to invariants of nature; it is defined in a manner that is directly traceable to three fundamental constants of nature. The Planck constant defines the kilogram in terms of the second and the metre. By fixing the Planck constant, the definition of the kilogram depends in addition only on the definitions of the second and the metre. The definition of the second depends on a single defined physical constant: the ground state hyperfine splitting frequency of the caesium 133 atom Δν(¹³³Cs)_hfs. The metre depends on the second and on an additional defined physical constant: the speed of light c. With the kilogram redefined in this manner, physical objects such as the IPK are no longer be part of the definition, but instead become transfer standards.

Scales like the Kibble balance also permit more flexibility in choosing materials with especially desirable properties for mass standards. For instance, Pt‑10Ir could continue to be used so that the specific gravity of newly produced mass standards would be the same as existing national primary and check standards (≈21.55 g/ml). This would reduce the relative uncertainty when making mass comparisons in air. Alternatively, entirely different materials and constructions could be explored with the objective of producing mass standards with greater stability. For instance, osmium-iridium alloys could be investigated if platinum's propensity to absorb hydrogen (due to catalysis of VOCs and hydrocarbon-based cleaning solvents) and atmospheric mercury proved to be sources of instability. Also, vapor-deposited, protective ceramic coatings like nitrides could be investigated for their suitability for chemically isolating these new alloys.

The challenge with Kibble balances is not only in reducing their uncertainty, but also in making them truly practical realisations of the kilogram. Nearly every aspect of Kibble balances and their support equipment requires such extraordinarily precise and accurate, state-of-the-art technology that—unlike a device like an atomic clock—few countries would currently choose to fund their operation. For instance, the NIST's Kibble balance used four resistance standards in 2007, each of which was rotated through the Kibble balance every two to six weeks after being calibrated in a different part of NIST headquarters facility in Gaithersburg, Maryland. It was found that simply moving the resistance standards down the hall to the Kibble balance after calibration altered their values 10 ppb (equivalent to 10 μg) or more. Present-day technology is insufficient to permit stable operation of Kibble balances between even biannual calibrations. When the new definition takes effect, it is likely there will only be a few—at most—Kibble balances initially operating in the world.

Alternative approaches to redefining the kilogram

Several alternative approaches to redefining the kilogram that were fundamentally different from the Kibble balance were explored to varying degrees, with some abandoned. The Avogadro project, in particular, was important for the 2018 redefinition decision because it provided an accurate measurement of the Planck constant that was consistent with and independent of the Kibble balance method. The alternative approaches included:

Atom-counting approaches

Avogadro project

Achim Leistner at the Australian Centre for Precision Optics (ACPO) is holding a 1 kg, single-crystal silicon sphere for the Avogadro project. These spheres are among the roundest man-made objects in the world. If the best of these spheres were scaled to the size of Earth, its high point—a continent-size area—would rise to a maximum elevation of 2.4 metres above "sea level".

Another Avogadro constant-based approach, known as the International Avogadro Coordination's Avogadro project, would define and delineate the kilogram as a 93.6 mm diameter sphere of silicon atoms. Silicon was chosen because a commercial infrastructure with mature processes for creating defect-free, ultra-pure monocrystalline silicon already exists to service the semiconductor industry. To make a practical realisation of the kilogram, a silicon boule (a rod-like, single-crystal ingot) would be produced. Its isotopic composition would be measured with a mass spectrometer to determine its average relative atomic mass. The boule would be cut, ground, and polished into spheres. The size of a select sphere would be measured using optical interferometry to an uncertainty of about 0.3 nm on the radius—roughly a single atomic layer. The precise lattice spacing between the atoms in its crystal structure (≈ 192 pm) would be measured using a scanning X-ray interferometer. This permits its atomic spacing to be determined with an uncertainty of only three parts per billion. With the size of the sphere, its average atomic mass, and its atomic spacing known, the required sphere diameter can be calculated with sufficient precision and low uncertainty to enable it to be finish-polished to a target mass of one kilogram.

Experiments are being performed on the Avogadro Project's silicon spheres to determine whether their masses are most stable when stored in a vacuum, a partial vacuum, or ambient pressure. However, no technical means currently exist to prove a long-term stability any better than that of the IPK's, because the most sensitive and accurate measurements of mass are made with dual-pan balances like the BIPM's FB‑2 flexure-strip balance (see § External links, below). Balances can only compare the mass of a silicon sphere to that of a reference mass. Given the latest understanding of the lack of long-term mass stability with the IPK and its replicas, there is no known, perfectly stable mass artefact to compare against. Single-pan scales, which measure weight relative to an invariant of nature, are not precise to the necessary long-term uncertainty of 10–20 parts per billion. Another issue to be overcome is that silicon oxidises and forms a thin layer (equivalent to 5–20 silicon atoms deep) of silicon dioxide (quartz) and silicon monoxide. This layer slightly increases the mass of the sphere, an effect that must be accounted for when polishing the sphere to its finished size. Oxidation is not an issue with platinum and iridium, both of which are noble metals that are roughly as cathodic as oxygen and therefore don't oxidise unless coaxed to do so in the laboratory. The presence of the thin oxide layer on a silicon-sphere mass prototype places additional restrictions on the procedures that might be suitable to clean it to avoid changing the layer's thickness or oxide stoichiometry.

All silicon-based approaches would fix the Avogadro constant but vary in the details of the definition of the kilogram. One approach would use silicon with all three of its natural isotopes present. About 7.78% of silicon comprises the two heavier isotopes: ²⁹Si and ³⁰Si. As described in § Carbon-12 below, this method would define the magnitude of the kilogram in terms of a certain number of ¹²C atoms by fixing the Avogadro constant; the silicon sphere would be the practical realisation. This approach could accurately delineate the magnitude of the kilogram because the masses of the three silicon nuclides relative to ¹²C are known with great precision (relative uncertainties of 1 ppb or better). An alternative method for creating a silicon sphere-based kilogram proposes to use isotopic separation techniques to enrich the silicon until it is nearly pure ²⁸Si, which has a relative atomic mass of 27.9769265325(19). With this approach, the Avogadro constant would not only be fixed, but so too would the atomic mass of ²⁸Si. As such, the definition of the kilogram would be decoupled from ¹²C and the kilogram would instead be defined as ​¹⁰⁰⁰⁄_{27.9769265325} ⋅ 6.02214179×10²³ atoms of ²⁸Si (≈ 35.74374043 fixed moles of ²⁸Si atoms). Physicists could elect to define the kilogram in terms of ²⁸Si even when kilogram prototypes are made of natural silicon (all three isotopes present). Even with a kilogram definition based on theoretically pure ²⁸Si, a silicon-sphere prototype made of only nearly pure ²⁸Si would necessarily deviate slightly from the defined number of moles of silicon to compensate for various chemical and isotopic impurities as well as the effect of surface oxides.

Carbon-12

Though not offering a practical realisation, this definition would precisely define the magnitude of the kilogram in terms of a certain number of carbon‑12 atoms. Carbon‑12 (¹²C) is an isotope of carbon. The mole is currently defined as "the quantity of entities (elementary particles like atoms or molecules) equal to the number of atoms in 12 grams of carbon‑12". Thus, the current definition of the mole requires that ​¹⁰⁰⁰⁄₁₂ moles (​83 ¹⁄₃ mol) of ¹²C has a mass of precisely one kilogram. The number of atoms in a mole, a quantity known as the Avogadro constant, is experimentally determined, and the current best estimate of its value is 6.02214076×10²³ entities per mole. This new definition of the kilogram proposed to fix the Avogadro constant at precisely 6.02214X×10²³ mol⁻¹ with the kilogram being defined as "the mass equal to that of ​¹⁰⁰⁰⁄₁₂ ⋅ 6.02214X×10²³ atoms of ¹²C".

The accuracy of the measured value of the Avogadro constant is currently limited by the uncertainty in the value of the Planck constant. That relative standard uncertainty has been 50 parts per billion (ppb) since 2006. By fixing the Avogadro constant, the practical effect of this proposal would be that the uncertainty in the mass of a ¹²C atom—and the magnitude of the kilogram—could be no better than the current 50 ppb uncertainty in the Planck constant. Under this proposal, the magnitude of the kilogram would be subject to future refinement as improved measurements of the value of the Planck constant become available; electronic realisations of the kilogram would be recalibrated as required. Conversely, an electronic definition of the kilogram (see § Electronic approaches, below), which would precisely fix the Planck constant, would continue to allow ​83 ¹⁄₃ moles of ¹²C to have a mass of precisely one kilogram but the number of atoms comprising a mole (the Avogadro constant) would continue to be subject to future refinement.

A variation on a ¹²C-based definition proposes to define the Avogadro constant as being precisely 84446889³ (≈ 6.02214162×10²³) atoms. An imaginary realisation of a 12-gram mass prototype would be a cube of ¹²C atoms measuring precisely 84446889 atoms across on a side. With this proposal, the kilogram would be defined as "the mass equal to 84446889³ × ​83 ¹⁄₃ atoms of ¹²C."

Ion accumulation

Another Avogadro-based approach, ion accumulation, since abandoned, would have defined and delineated the kilogram by precisely creating new metal prototypes on demand. It would have done so by accumulating gold or bismuth ions (atoms stripped of an electron) and counting them by measuring the electric current required to neutralise the ions. Gold (¹⁹⁷Au) and bismuth (²⁰⁹Bi) were chosen because they can be safely handled and have the two highest atomic masses among the mononuclidic elements that are stable (gold) or effectively so (bismuth). See also Table of nuclides.

With a gold-based definition of the kilogram for instance, the relative atomic mass of gold could have been fixed as precisely 196.9665687, from the current value of 196.9665687(6). As with a definition based upon carbon‑12, the Avogadro constant would also have been fixed. The kilogram would then have been defined as "the mass equal to that of precisely ​¹⁰⁰⁰⁄_196.9665687 ⋅ 6.02214179×10²³ atoms of gold" (precisely 3,057,443,620,887,933,963,384,315 atoms of gold or about 5.07700371 fixed moles).

In 2003, German experiments with gold at a current of only 10 μA demonstrated a relative uncertainty of 1.5%. Follow-on experiments using bismuth ions and a current of 30 mA were expected to accumulate a mass of 30 g in six days and to have a relative uncertainty of better than 1 ppm. Ultimately, ion‑accumulation approaches proved to be unsuitable. Measurements required months and the data proved too erratic for the technique to be considered a viable future replacement to the IPK.

Among the many technical challenges of the ion-deposition apparatus was obtaining a sufficiently high ion current (mass deposition rate) while simultaneously decelerating the ions so they could all deposit onto a target electrode embedded in a balance pan. Experiments with gold showed the ions had to be decelerated to very low energies to avoid sputtering effects—a phenomenon whereby ions that had already been counted ricochet off the target electrode or even dislodged atoms that had already been deposited. The deposited mass fraction in the 2003 German experiments only approached very close to 100% at ion energies of less than around 1 eV (< 1 km/s for gold).

If the kilogram had been defined as a precise quantity of gold or bismuth atoms deposited with an electric current, not only would the Avogadro constant and the atomic mass of gold or bismuth have to have been precisely fixed, but also the value of the elementary charge (e), likely to 1.60217X×10⁻¹⁹ C (from the currently recommended value of 1.602176634×10⁻¹⁹ C). Doing so would have effectively defined the ampere as a flow of ​¹⁄_{1.60217X×10⁻¹⁹} electrons per second past a fixed point in an electric circuit. The SI unit of mass would have been fully defined by having precisely fixed the values of the Avogadro constant and elementary charge, and by exploiting the fact that the atomic masses of bismuth and gold atoms are invariant, universal constants of nature.

Beyond the slowness of making a new mass standard and the poor reproducibility, there were other intrinsic shortcomings to the ion‑accumulation approach that proved to be formidable obstacles to ion-accumulation-based techniques becoming a practical realisation. The apparatus necessarily required that the deposition chamber have an integral balance system to enable the convenient calibration of a reasonable quantity of transfer standards relative to any single internal ion-deposited prototype. Furthermore, the mass prototypes produced by ion deposition techniques would have been nothing like the freestanding platinum-iridium prototypes currently in use; they would have been deposited onto—and become part of—an electrode imbedded into one pan of a special balance integrated into the device. Moreover, the ion-deposited mass wouldn't have had a hard, highly polished surface that can be vigorously cleaned like those of current prototypes. Gold, while dense and a noble metal (resistant to oxidation and the formation of other compounds), is extremely soft so an internal gold prototype would have to be kept well isolated and scrupulously clean to avoid contamination and the potential of wear from having to remove the contamination. Bismuth, which is an inexpensive metal used in low-temperature solders, slowly oxidises when exposed to room-temperature air and forms other chemical compounds and so would not have produced stable reference masses unless it was continually maintained in a vacuum or inert atmosphere.

Ampere-based force

A magnet floating above a superconductor bathed in liquid nitrogen demonstrates perfect diamagnetic levitation via the Meissner effect. Experiments with an ampere-based definition of the kilogram flipped this arrangement upside-down: an electric field accelerated a superconducting test mass supported by fixed magnets.

This approach would define the kilogram as "the mass which would be accelerated at precisely 2×10⁻⁷ m/s² when subjected to the per-metre force between two straight parallel conductors of infinite length, of negligible circular cross section, placed one metre apart in vacuum, through which flow a constant current of ​¹⁄_{1.60217×10^⁻¹⁹} elementary charges per second".

Effectively, this would define the kilogram as a derivative of the ampere rather than the present relationship, which defines the ampere as a derivative of the kilogram. This redefinition of the kilogram would specify elementary charge (e) as precisely 1.60217×10^⁻¹⁹ coulomb rather than the current recommended value of 1.602176634×10⁻¹⁹ C. It would necessarily follow that the ampere (one coulomb per second) would also become an electric current of this precise quantity of elementary charges per second passing a given point in an electric circuit. The virtue of a practical realisation based upon this definition is that unlike the Kibble balance and other scale-based methods, all of which require the careful characterisation of gravity in the laboratory, this method delineates the magnitude of the kilogram directly in the very terms that define the nature of mass: acceleration due to an applied force. Unfortunately, it is extremely difficult to develop a practical realisation based upon accelerating masses. Experiments over a period of years in Japan with a superconducting, 30 g mass supported by diamagnetic levitation never achieved an uncertainty better than ten parts per million. Magnetic hysteresis was one of the limiting issues. Other groups performed similar research that used different techniques to levitate the mass.

SI multiples

Main article: Orders of magnitude (mass)

Because SI prefixes may not be concatenated (serially linked) within the name or symbol for a unit of measure, SI prefixes are used with the unit gram, not kilogram, which already has a prefix as part of its name. For instance, one-millionth of a kilogram is 1 mg (one milligram), not 1 μkg (one microkilogram).

SI multiples of gram (g)

Submultiples				Multiples
Value	SI symbol	Name		Value	SI symbol	Name
10−1 g	dg	decigram		101 g	dag	decagram
10−2 g	cg	centigram		102 g	hg	hectogram
10−3 g	mg	milligram		103 g	kg	kilogram
10−6 g	µg	microgram		106 g	Mg	megagram (tonne)
10−9 g	ng	nanogram		109 g	Gg	gigagram
10−12 g	pg	picogram		1012 g	Tg	teragram
10−15 g	fg	femtogram		1015 g	Pg	petagram
10−18 g	ag	attogram		1018 g	Eg	exagram
10−21 g	zg	zeptogram		1021 g	Zg	zettagram
10−24 g	yg	yoctogram		1024 g	Yg	yottagram
Common prefixed units are in bold face.

• The microgram is typically abbreviated "mcg" in pharmaceutical and nutritional supplement labelling, to avoid confusion, since the "μ" prefix is not always well recognised outside of technical disciplines. (The expression "mcg" is also the symbol for an obsolete CGS unit of measure known as the "millicentigram", which is equal to 10 μg.)
• In the United Kingdom, because serious medication errors have been made from the confusion between milligrams and micrograms when micrograms has been abbreviated, the recommendation given in the Scottish Palliative Care Guidelines is that doses of less than one milligram must be expressed in micrograms and that the word microgram must be written in full, and that it is never acceptable to use "mcg" or "μg".
• The hectogram (100 g) is a very commonly used unit in the retail food trade in Italy, usually called an etto, short for ettogrammo, the Italian for hectogram.
• The former standard spelling and abbreviation "deka-" and "dk" produced abbreviations such as "dkm" (dekametre) and "dkg" (dekagram). The abbreviation "dkg" (10 g) is still used in parts of central Europe in retail for some foods such as cheese and meat.
• The unit name megagram is rarely used, and even then typically only in technical fields in contexts where especially rigorous consistency with the SI standard is desired. For most purposes, the name tonne is instead used. The tonne and its symbol, "t", were adopted by the CIPM in 1879. It is a non-SI unit accepted by the BIPM for use with the SI. According to the BIPM, "In English speaking countries this unit is usually called 'metric ton'." The unit name megatonne or megaton (Mt) is often used in general-interest literature on greenhouse gas emissions, whereas the equivalent unit in scientific papers on the subject is often the teragram (Tg).

See also

• 1795 in science
• 1799 in science
• General Conference on Weights and Measures (CGPM)
• Gram
• Grave (orig. name of the kilogram, history of)
• Gravimetry
• Inertia
• International Bureau of Weights and Measures (BIPM)
• International Committee for Weights and Measures (CIPM)
• International System of Units (SI)
• Kibble balance
• Kilogram-force
• Litre
• Mass
• Mass versus weight
• Metric system
• Metric ton
• Milligram per cent
• National Institute of Standards and Technology (NIST)
• Newton
• SI base units
• Standard gravity
• Weight

External links

External images

BIPM: The IPK in three nested bell jars

NIST: K20, the US National Prototype Kilogram resting on an egg crate fluorescent light panel

BIPM: Steam cleaning a 1 kg prototype before a mass comparison

BIPM: The IPK and its six sister copies in their vault

The Age: Silicon sphere for the Avogadro Project

NPL: The NPL's Watt Balance project

NIST: This particular Rueprecht Balance, an Austrian-made precision balance, was used by the NIST from 1945 until 1960

BIPM: The FB‑2 flexure-strip balance, the BIPM's modern precision balance featuring a standard deviation of one ten-billionth of a kilogram (0.1 μg)

BIPM: Mettler HK1000 balance, featuring 1 μg resolution and a 4 kg maximum mass. Also used by NIST and Sandia National Laboratories' Primary Standards Laboratory

Micro-g LaCoste: FG‑5 absolute gravimeter, (diagram), used in national laboratories to measure gravity to 2 μGal accuracy

• NIST Improves Accuracy of 'Watt Balance' Method for Defining the Kilogram
• The UK's National Physical Laboratory (NPL): Are any problems caused by having the kilogram defined in terms of a physical artefact? (FAQ - Mass & Density)
• NPL: NPL Kibble balance
• Metrology in France: Watt balance
• Australian National Measurement Institute: Redefining the kilogram through the Avogadro constant
• International Bureau of Weights and Measures (BIPM): Home page
• NZZ Folio: What a kilogram really weighs
• NPL: What are the differences between mass, weight, force and load?
• BBC: Getting the measure of a kilogram
• NPR: This Kilogram Has A Weight-Loss Problem, an interview with National Institute of Standards and Technology physicist Richard Steiner
• Avogadro and molar Planck constants for the redefinition of the kilogram
• Realization of the awaited definition of the kilogram
• Sample, Ian (November 9, 2018). "In the balance: scientists vote on first change to kilogram in a century". The Guardian. Retrieved November 9, 2018.

Videos

• The BIPM YouTube channel
• "The role of the Planck constant in physics" - presentation at 26th CGPM meeting at Versailles, France, November 2018 when voting on superseding the IPK took place.