# kilogram

Shown above is a computer-generated image of the International Prototype Kilogram (“IPK”). The IPK is the kilogram. It sits next to an inch-based ruler for scale. The IPK is made of a platinum-iridium alloy and is stored in a vault at the BIPM in Sèvres, France. For other kilogram-related images, see Links to photographs, below.
The kilogram or kilogramme (symbol: kg) is the SI base unit of mass. The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one liter of water. It is the only SI base unit with an SI prefix as part of its name. It is also the only SI unit that is still defined in relation to an artifact rather than to a fundamental physical property that can be reproduced in different laboratories.

While the weight of objects is often given in kilograms, the kilogram is, in the strict scientific sense, a unit of mass. The equivalent unit of weight is the non-SI kilogram-force. Similarly, the avoirdupois pound, used in both the Imperial system and U.S. customary units, is a unit of mass and its related unit of weight is the pound-force. The avoirdupois pound is defined as exactly 0.453 592 37 kg, making one kilogram approximately equal to 2.205 avoirdupois pounds.

Many units in the SI system are defined relative to the kilogram so its stability is important. After the International Prototype Kilogram had been found to vary in mass over time, the International Committee for Weights and Measures (known by the initials CIPM) recommended in 2005 that the kilogram be redefined in terms of fundamental constants of nature.[1]

## The nature of mass

The kilogram is a unit of mass, the measurement of which corresponds to the general, everyday notion of how “heavy” something is. However, mass is actually an inertial property; that is, the tendency of an object to remain at constant velocity unless acted upon by an outside force. An object with a mass of one kilogram will accelerate at one meter/second² (about one-tenth the acceleration of Earth’s gravity) when acted upon (pushed by) a force of one newton (symbol: N).

While the weight of matter is entirely dependent upon the strength of gravity, the mass of matter is constant (assuming it is not traveling at a relativistic speed with respect to an observer). Accordingly, for astronauts in microgravity, no effort is required to hold objects off the cabin floor since such objects naturally hover; they are “weightless.” However, since objects in microgravity still retain their mass, an astronaut must exert one hundred times more effort to accelerate a 100-kilogram object at the same rate as for a 1-kilogram object. See also Mass vs. weight below.

## SI multiples

Because SI prefixes may not be concatenated (united serially) within the name or symbol for a unit of measure, SI prefixes are used with the gram, not the kilogram, which already has a prefix as part of its name.[2] For instance, one-millionth of a kilogram is 1 mg (one milligram), not 1 µkg (one microkilogram).
Multiple Name Symbol Multiple Name Symbol
100gramg
101decagramdag10–1decigramdg
102hectogramhg10–2centigramcg
103kilogramkg10–3milligrammg
106megagramMg10–6microgramg
109gigagramGg10–9nanogramng
1012teragramTg10–12picogrampg
1015petagramPg10–15femtogramfg
1018exagramEg10–18attogramag
1021zettagramZg10–21zeptogramzg
1024yottagramYg10–24yoctogramyg

• When the Greek lowercase “µ” (mu) in the symbol of microgram is typographically unavailable, it is occasionally—although not properly—replaced by Latin lowercase “u”.
• The microgram is often abbreviated “mcg”, particularly in pharmaceutical and nutritional supplement labeling, to avoid confusion since the “µ” prefix is not well recognized outside of technical disciplines.[3] Note however, that the abbreviation “mcg”, is also the symbol for an obsolete CGS unit of measure known as the “millicentigram,” which is equal to 10 µg.
• The unit name “megagram” is rarely used, and even then, typically only in technical fields in contexts where especially rigorous consistency with the units of measure is desired. For most purposes, the term “tonne,” or “metric ton” is instead used.

## History

#### Early definitions

See also Grave (mass) for more on the history of the kilogram.

On 7 April 1795, the gram was decreed in France to be equal to “the absolute weight of a volume of pure water equal to a cube of one hundredth of a meter, and to the temperature of the melting ice.”[4] The regulation of trade and commerce required a practical reference standard in addition to the definition based on fundamental physical properties. Accordingly, a provisional kilogram standard was made as a single-piece, metallic reference standard one thousand times more massive than the gram.

In addition to this provisional kilogram standard, work was commissioned to determine precisely how massive a cubic decimeter (now defined as one liter) of water is. Although the decreed definition of the kilogram specified water at 0 °C — a highly stable temperature point — the scientists chose to redefine the standard and perform their measurements at the most stable density point: the temperature at which water reaches maximum density, which was measured at the time as 4 °C.[5] They concluded that one cubic decimeter of water at its maximum density was equal to 99.92072% of the mass of the provisional kilogram made earlier that year.[6] Four years later in 1799, an all-platinum prototype kilogram, the Kilogramme des Archive (Kilogram of the Archives), was fabricated with the objective that it would equal, as close as was scientifically feasible for the day, the mass of a cubic decimeter of water at 4 °C. The kilogram was defined to be equal to the mass of the Kilogram of the Archives and this standard stood for the next ninety years.

#### International Prototype Kilogram

Since 1889, the SI system defines the magnitude of the kilogram to be equal to the mass of the International Prototype Kilogram — often referred to in the professional metrology world as the “IPK”. The IPK comprises an alloy of 90% platinum and 10% iridium (by weight) and is machined into a right-circular cylinder (height = diameter) of 39.17 mm to minimize its surface area.[7] The IPK and six of its official copies (its “sister copies”) are stored in an environmentally monitored vault in the basement of the BIPM’s House of Breteuil in Sèvres on the outskirts of Paris (see Links to photographs, below for images). Three independently controlled keys are required to open the vault. Official copies of the IPK were made available to other nations to serve as their national standards. These are compared to the IPK roughly every 40 years.

The IPK is one of three cylinders made in 1879. In 1883, it was found to be indistinguishable from the mass of the Kilogram of the Archives made eighty-four years prior, and was formally ratified as the kilogram by the 1st CGPM in 1889.[7] Modern measurements of the density of purified water that has a carefully controlled isotopic composition (known as Vienna Standard Mean Ocean Water) show that a cubic decimeter (one liter) of water at its point of maximum density, 3.984 °C, has a mass that is 25.05 parts per million less than the kilogram.[8] This small, 25 ppm difference, and the fact that the mass of the IPK was indistinguishable from the mass of the Kilogram of the Archives, speak volumes of the scientists’ skills over 208 years ago when making their measurements of water’s properties and in manufacturing the Kilogram of the Archives.

## Stability of the International Prototype Kilogram

By definition, the error in the measured value of the IPK’s mass is exactly zero; the IPK is the kilogram. However, any changes in the IPK’s mass over time can be deduced by comparing its mass to that of its official copies stored throughout the world, a process called “periodic verification.” For instance, the U.S. owns three kilogram replicas, two of which, K4 and K20, are from the original batch of 40 replicas of the IPK delivered in 1884. The K20 replica was designated as the primary national standard of mass for the U.S. Both of these, as well as those from other nations, are periodically returned to the BIPM for verification.[9]

Note that the masses of the replicas are not precisely equal to that of the IPK; their masses are calibrated and documented as offset values. For instance, K20, the U.S.’s primary standard, originally had an official mass of 1 kg – 39 µg in 1889; that is to say, K20 was 39 µg less than the IPK. A verification performed in 1948 showed a mass of 1 kg – 19 µg. The latest verification performed in 1999 shows a mass identical to its original 1889 value. The mass of K4, the U.S.’s check standard, as of 1999 was officially calibrated as 1 kg – 116 µg. However, it was 41 µg more massive (in comparison to the IPK) in 1889.

Since the IPK and its replicas are stored in air (albeit under two or more nested bell jars), they adsorb atmospheric contamination onto their surfaces and gain mass. Accordingly, they are cleaned in preparation for periodic verifications—a process the BIPM developed between 1939 and 1946 known as “the BIPM cleaning method” that includes steam cleaning, lightly rubbing with chemical-soaked chamois, and allowing the prototypes to settle for 7–10 days. Cleaning the prototypes removes between 5 and 60 µg of contamination depending largely on the time elapsed since the last cleaning. Further, a second cleaning can remove up to 10 µg more. After cleaning—even when they are stored in their bell jars—the IPK and its replicas immediately begin gaining mass again. The BIPM even developed a model of this gain and concluded that it averaged 1.11 µg per month for the first 3 months after cleaning and then decreased to an average of about 1 µg per year thereafter. Since check standards like K4 are not cleaned for routine calibrations of other mass standards—a precaution to minimize the potential for wear and handling damage—the BIPM’s model has been used as an “after cleaning” correction factor.

Because the first forty official copies are made of precisely the same alloy as the IPK and are stored under similar conditions, periodic verifications using a large number of replicas—especially the national primary standards, which are rarely used—can convincingly demonstrate the stability of the IPK. What has become clear after the third periodic verification performed between 1988 and 1992 is that the mass of the IPK lost perhaps 50 µg over the last century, and possibly significantly more, in comparison to its official copies.[10][11] The answer as to why this might be the case has proved elusive for physicists who have dedicated their careers to the SI unit of mass. No plausible mechanism has been proposed to explain either a steady decrease in the mass of the IPK, or an increase in that of its six sister copies and the others dispersed throughout the world.[12] Further, the IPK exhibits an instability of about 30 µg over a period of about a month in its after-cleaned mass.[13] The precise reason for this instability is not fully understood but is thought to entail surface effects: microscopic differences in their polished surfaces, unintentional differences in the cleaning process, and/or differences in the precise nature of the contamination. What is known is the past assumption that the cleaning process reliably restores the prototypes to their original value is false and the BIPM’s after-cleaning correction factor is useful only for long-term trends. Scientists are seeing far greater variability in the prototypes than previously believed. Further, there is no technical means available to know whether or not the entire worldwide ensemble of prototypes suffer from even greater long-term trends upwards or downwards because their mass “relative to an invariant of nature is unknown at a level below 1000 µg over a period of 100 or even 50 years.”[10]

The relative change in mass and the instability in the IPK has prompted research into improved methods to obtain a smooth surface finish using diamond-turning on newly manufactured replicas and has intensified the search for a new definition of the kilogram. See Proposed future definitions, below.[14]

## Importance of the kilogram

As the SI system of measurement is currently defined and structured, the stability of the kilogram is crucial since it effectively underpins the entire system. For instance, the newton—the SI unit of force—is defined as the force necessary to accelerate the kilogram by one meter per second². Accordingly, if the mass of the IPK were to change slightly, so too must the newton by a proportional degree so the acceleration remains at precisely one meter/second². In turn, the pascal—the unit of pressure—is defined in terms of the newton. This chain of dependency follows to all the electrical units. For instance, the joule, which is the electrical and mechanical unit of energy, is defined as the energy expended when a force of one newton acts through one meter. The ampere too is defined relative to the kilogram. With two of the primary units of electricity thus defined in terms of the kilogram, so too follow all the rest, including the watt, volt, ohm, coulomb, farad, and weber.

Clearly, having the magnitude of many of the units comprising the SI system of measurement ultimately defined by the mass of a 128-year-old, golf ball-size piece of metal is a tenuous state of affairs. The quality of the IPK must be fanatically protected in order to preserve the integrity of the SI system. Fortunately, definitions of the SI units are quite different from their practical realizations. For instance, the meter is defined as the distance light travels in a vacuum during a time interval of 1/299,792,458 of a second. However, the meter’s practical realization typically takes the form of a helium-neon laser, and the meter’s length is delineated—not defined—as 1,579,800.298 728 wavelengths of light from this laser. Note that the redefinition of the meter in terms of a duration of one second reduced the uncertainty in the wavelength of the laser light. Now suppose that the official measurement of the second was found to have drifted a few parts per billion (it’s actually exquisitely stable). There would be no automatic effect on many of the SI units of measurement because, as with the meter, the duration of the second is often abstracted through other physical principles underlying their practical realizations. Scientists performing meter calibrations would simply continue to measure out the same number of laser wavelengths until an agreement was reached to do otherwise. The same is true with regard to the real-world dependency on the kilogram: if the mass of the IPK was found to have changed slightly, there would be no automatic effect upon the other units of measure because their practical realizations provide an insulating layer of abstraction. Any discrepancy would eventually have to be reconciled though because the virtue of the SI system is its precise mathematical and logical harmony amongst its units. If the IPK’s value was found to have changed, one quick fix would be to simply redefine the kilogram as being equal to the IPK plus an offset value, similarly to what is currently done with its replicas; e.g., “the kilogram is equal to the mass of the IPK + 42 µg.?

The long-term solution is to liberate the SI system’s dependency on the IPK by developing a practical realization of the kilogram that can be reproduced in different laboratories by following a written specification. The units of measure in such a practical realization would have their magnitudes precisely defined and expressed in terms of fundamental physical constants. While major portions of the SI system would still be based upon the kilogram, the kilogram would in turn be based upon invariant, universal constants of nature. While this is a worthwhile objective and much work towards that end is ongoing, no alternative to date has achieved the uncertainty of a few parts in 108 (~30 µg) required to compete with the IPK. The most promising contender, an implementation of the watt balance by the National Institute of Standards and Technology (NIST), as of late 2007 was approaching the level where scientists could resolve a difference of about 25 µg. See Proposed future definitions below.

## Mass vs. weight

#### The distinction between the two

Matter’s mass, not its weight, strongly influences many familiar kinetic properties.
As stated above in The nature of mass, the kilogram is a unit of mass, which is an inertial property. Inertia is the property one senses when they rest a bowling ball on a level, smooth surface and forcefully push on it horizontally to accelerate it. This is quite distinct from “weight,” which is the downwards gravitational force of the bowling ball that one must counter when holding it off the floor. Unless relativistic effects apply, mass is an unchanging, universal property of matter that is unaffected by gravity. Weight on the other hand, is a property of matter that is entirely dependent upon the strength of gravity. For instance, an astronaut’s weight on the Moon is one-sixth of that on the Earth whereas his mass has changed little during the trip. Consequently, wherever the physics of recoil kinetics (mass, velocity, inertia, inelastic and elastic collisions) dominate and the influence of gravity is a negligible factor, the behavior of objects remains consistent even where gravity is relatively weak. For instance, billiard balls on a billiards table would scatter and recoil with the same speeds and energies after a break shot on the Moon as on Earth; they would however, drop into the pockets much slower.

In scientific and engineering contexts, the terms “mass” and “weight” are rigidly defined as separate measures in order to enforce clarity and precision. In everyday use, given that all masses on Earth have weight and this relationship is usually highly proportional,[15] “weight” often serves to describe both properties, its meaning being dependent upon context. For example, the “net weight” of retail products in the U.S., which may be given in both pounds and kilograms, refers to mass (see also Pound: Use in commerce). Conversely, the “load index” rating on automobile tires, which specifies the maximum structural load for a tire in kilograms, actually refers to weight; that is, the force due to gravity.

#### The unit of weight: kilogram-force

When an object's weight (its gravitational force) is expressed in kilograms, the unit of measure is not a true kilogram; it is the kilogram-force (kgf or kg-f), also known as the kilopond (kp), which is a non-SI unit of force that is typically used as a unit of weight. All objects on Earth are subject to a gravitational acceleration of approximately 9.8 m/s². The CGPM (also known as the “General Conference on Weights and Measures”) fixed the value of standard gravity at precisely 9.80665 m/s² so that disciplines such as metrology would have a standard value for converting units of defined mass into defined forces and pressures. In fact, the kilogram-force is defined as precisely 9.80665 newtons. As a practical matter, gravitational acceleration (symbol: g) varies slightly with latitude, elevation and subsurface density; these variations are typically only a few tenths of a percent. See also Gravimetry.

Since masses are rarely measured to an uncertainty of better than one percent, it is technically just as valid to state that a one-kilogram object on Earth has a weight of one kilogram-force as it is to state that it has a mass of one kilogram. Accordingly, it may correctly be assumed that when someone speaks or writes of a “weight” in kilograms, they are referring to the gravitational load of the kilogram and the proper “kilogram-force” is implied.

#### Converting mass to weight

Unlike laypeople, professionals in virtually all SI-unit-using engineering and scientific disciplines involving accelerations and kinetic energies rigorously maintain the distinctions between mass, force, and weight, as well as their respective units of measure. Engineers in disciplines involving weight loading, such as structural engineering, first convert loads due to objects like concrete and automobiles—which are always tallied in kilograms—to newtons before continuing with their calculations. Primarily, this is because material properties like elastic modulus are quite properly measured and published in terms of newtons and pascals (which is a unit of pressure derived from the newton). Mass in kilograms is converted to weight in newtons by multiplying by 9.8, 9.81, or 9.80665. Note that when converting mass to weight, the highest-precision factor (which is the precise conversion value between kilograms-force and newtons) would likely result in false precision if the final product was expressed to six significant digits since loads in kilograms are rarely known with such accuracy and local gravity is rarely identical to standard gravity.

#### Buoyancy and “conventional mass”

Regardless of the fluid in which an object is immersed (gas or liquid), the buoyancy of an object is proportional to the mass of the fluid it displaces.
The masses of objects are relatively invariant whereas their weights vary slightly with changes in barometric pressure, such as with changes in weather and altitude. This is because objects have volume and therefore have a buoyant effect in air. Buoyancy—a force that counters gravity’s—reduces the weight of all objects immersed in fluids. Further, objects with precisely the same mass but with different densities displace different volumes and therefore have different buoyancies and weights. Normally, the effect of air buoyancy is too small to be of any consequence in normal day-to-day activities.[16] In metrology however, where mass standards are calibrated with extreme accuracy, buoyancy is a significant effect so air density is precisely accounted for during calibration.

Given the extremely high cost of platinum-iridium prototypes, high-quality “working” standards are made of special stainless steel alloys, which occupy greater volume than those made of platinum-iridium. For convenience, a standard value of buoyancy relative to stainless steel was developed for metrology work and this results in the term “conventional mass.”[17] Conventional mass is defined as follows: “For a mass at 20 °C, ‘conventional mass’ is the mass of a reference standard of density 8000 kg/m³ which it balances in air with a density of 1.2 kg/m³.” The effect is a small one, 150 ppm for stainless steel mass standards, but the appropriate corrections are made during the calibration of all precision mass standards so they have the true mass indicated on them. In routine laboratory use however, the reading on a precision scale when a stainless steel standard is placed upon it is actually its conventional mass; that is, its true mass minus buoyancy. Also, any object compared to a stainless steel mass standard has its conventional mass measured; that is, its true mass minus some (usually unknown) degree of buoyancy.

The effect of buoyancy invalidates the standard answer to the childhood riddle of “Which weighs more, a ton of lead or a ton of feathers (or aluminum)?” The standard answer is that they both weigh the same, but the correct answer is “Lead weighs more than aluminum, by 327 grams-force or 3.21 newtons (a difference of 0.0327%).” This is because the density of lead is greater and displaces less air.[18]

#### Types of scales and what they measure

It’s notable at a purely technical level, that whenever someone stands on a balance-beam scale at a doctor’s office, they are really and truly having their mass measured. Excluding buoyancy, which affects all types of scales in fluids, balance-beam scales compare the mass on the platform with those of the sliding counterweights on the beams; gravity serves only as the force-generating mechanism that allows the needle to diverge from the “balanced” (null) point. On scales such as these, gravity can vary in strength without affecting the reading. Conversely, whenever someone steps onto a spring-based or digital load cell-based scale, they are technically having their weight measured notwithstanding that the displayed units of measure are in kilograms. On force-measuring instruments such as these, variations in gravity will affect the reading.

## Proposed future definitions

In the following section, wherever numeric equalities are shown in ‘concise form’ — such as 1.854 87(14) × 1043 — the two digits between the parentheses denotes the uncertainty (the standard deviation at 68.27% confidence level) in the two least significant digits of the mantissa.

The kilogram is the only SI unit that is still defined in relation to an artifact. Note that the meter was also once defined as an artifact (a single platinum-iridium bar with two marks on it). However, it was eventually redefined in terms of invariant, fundamental constants of nature that are delineated via practical realizations (apparatus) that can be reproduced in different laboratories by following a written specification. Today, physicists are investigating various approaches to do the same with the kilogram. Some of the approaches are fundamentally very different from each other. Some are based upon equipment and procedures that enable 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, fundamental constants. Others are essentially devices that measure either the acceleration or weight of hand-tuned, kilogram test masses and which express their magnitudes in electrical terms via special components that permit traceability to fundamental constants. Measuring the weight of test masses requires the precise measurement of the strength of gravity in laboratories. All approaches but one, the Avogadro Project, would precisely fix one or more constants of nature at a defined value. These different approaches are as follows:

#### Atom-counting approaches

An Avogadro constant-based approach, known as the Avogadro project, attempts to define and delineate the kilogram as a quantity 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 realization 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 atomic mass. The rod would be cut, ground, and polished into spheres. The size of a select sphere would be measured using optical interferometry. The precise lattice spacing between the atoms in its crystal structure (≈192 pm) would be measured using a scanning X-ray interferometer. Amazingly, this permits its atomic spacing to be determined with an uncertainty of only three parts in a billion. With the size of the sphere, its average atomic mass, and the atomic spacing known, the required number of atoms in the sphere could be calculated with sufficient precision and uncertainty to enable it to be ground down to the desired quantity of atoms (mass).

Experiments are planned for the Avogadro Project’s silicon sphere to determine whether its mass is most stable when stored in a vacuum, a partial vacuum, or ambient pressure. However, no technical means currently exist to prove a stability any better than that of the IPK’s because the most sensitive and accurate measurements of mass are made with balances like the BIPM’s FB-2 flexure-strip balance (see Links to photographs 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 relative stability between the IPK and its replicas, there is no known, perfectly stable mass artifact to compare against. Scales capable of measuring mass relative to an invariant of nature at the 30-parts-per-billion level of uncertainty of the IPK do not yet exist. Another issue to be overcome is that silicon oxidizes and forms a thin layer of silicon dioxide (common glass). This layer slightly increases the mass of the sphere and its effect must be accounted for when grinding the sphere to its finish dimension. 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 oxidize unless coaxed to do so in the laboratory. The presence of a thin glass layer on a silicon-sphere mass prototype places additional restrictions on the procedures that might be suitable to clean it.
##### Ion accumulation
Another Avogadro-based approach, ion accumulation, would define and delineate the kilogram by creating metal mass artifacts. It would do so by accumulating of gold or bismuth ions (atoms stripped of an electron) and counting them by measuring the electrical current required to neutralize the ions. Gold and bismuth are used because, unlike most other elements, they each have only one naturally occurring isotope.

With a gold-based definition of the kilogram for instance, the definition of the mole would be changed from one based on a carbon-12 to the quantity of atoms as are in 196.966 569 g of gold (from the current value of 196.966 569(4) grams) and the kilogram would be defined as “the mass equal to that of precisely 1000/196.966569 moles (≅5.077 003 7021 moles) of gold atoms.?

Ion-accumulation techniques, while a relatively new field of study, have advanced rapidly. In 2003, experiments with gold at a current of only 10 µa demonstrated a relative uncertainty of 1.5%. Yet, 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 part in 106.[19]

The difficulty with ion-accumulation-based standards is in obtaining truly practical mass artifacts. Gold, while dense and a noble metal (resistant to oxidation and the formation of other compounds), is extremely soft so mass artifacts would require extraordinary care to avoid wear. Bismuth, while an inexpensive metal for experiments, would not produce stable artifacts because it readily oxidizes and forms other chemical compounds. Iridium and platinum are composed of two and six isotopes respectively and this places an upper limit on relative uncertainty.
##### Carbon-12
Though not offering a practical realization, this definition would precisely define the magnitude of the kilogram in terms of a certain number of carbon-12 atoms. The mole is currently defined as “the quantity of ‘entities’ (elementary particles like atoms or molecules) as there are atoms in 12 grams of carbon-12.” Thus, the current definition of the mole requires that 1000/12 (83⅓) moles of C-12 has a mass of precisely one kilogram. The number of atoms in a mole, a quantity known as the Avogadro constant, is an experimentally determined value that is currently measured as being 6.022 141 79(30) × 1023 atoms (2006 CODATA value). This new definition of the kilogram proposes to fix the Avogadro constant at precisely 6.022 141 79 × 1023 and the kilogram would be defined as “the mass equal to that of 83⅓ × 6.022 141 79 × 1023 atoms of carbon-12.?

Currently, the uncertainty in the Avogadro constant is determined by the uncertainty in the measured mass of carbon-12 atoms (a relative standard uncertainty of 50 parts per billion at this time). By fixing the Avogadro constant, the practical effect of this proposal would be that the precise magnitude of the kilogram would be subject to future refinement as improved measurements of the mass of carbon-12 atoms become available. Electronic realizations of the kilogram would be recalibrated as required. In an electronic definition of the kilogram, the mole would remain decoupled from the kilogram and could continue to be defined in terms of 12 grams of carbon-12. In that case, 83⅓ moles of carbon-12 would—by definition—continue to have a mass of precisely one kilogram and the Avogadro constant would continue to have uncertainty in its precise value.

A variation on a carbon-12-based definition proposes to define the Avogadro constant as being precisely 84,446,8863 (≅6.022 140 98 × 1023) atoms. An imaginary realization of a 12-gram mass prototype would be a cube of carbon-12 atoms measuring precisely 84,446,886 atoms across on a side. With this proposal, the kilogram would be defined as “the mass equal to 84,446,8863 × 83⅓ atoms of carbon-12.” The value 84,446,886 was chosen because it has a special property; its cube (the proposed new value for the Avogadro constant) is evenly divisible by twelve. Thus with this definition of the kilogram, there would be an integer number of atoms in one gram of carbon-12: 50,184,508,190,229,061,679,538 atoms.[20]

#### Electronic approaches

##### Watt balance
The watt balance is essentially an ampere balance with an extra calibration step that nulls the effect of geometry. The electrical current in the watt balance is delineated by a Josephson voltage standard, which allows voltages to be linked to an invariant constant of nature with extremely high precision and stability, and the circuit resistance is calibrated against a quantum Hall resistance standard. The watt balance requires exquisitely precise measurement of gravity in a laboratory (see “FG-5 absolute gravimeter” in Links to photographs below) and compares this acceleration to the electrical power necessary to counter it. For instance, the gravity gradient of 3.1 µGal/cm (3 parts in 109) is accounted for when the elevation of the center of the gravimeter differs from that of the nearby test mass. As of late 2007, the NIST's implementation of the watt balance was approaching the level where scientists could resolve a difference of about 25 µg. Ultimately, the watt balance would define the kilogram in terms of the Planck constant, which is a measure that relates the energy of photons to their frequency.

In the watt balance, the Planck constant would be fixed, where h = 6.626 068 96 × 10–34 J·s (from the 2006 CODATA value of 6.626 068 96(33) × 10–34 J·s) and the kilogram would be defined as “the mass of a body at rest whose equivalent energy equals the energy of photons whose frequencies sum to 1.356 392 733 × 1050 Hz.”[21]

The virtue of electronic-based realizations like the watt balance is the kilogram would be liberated from the necessity of fanatically storing and handling kilogram prototypes—as would still be the case with ion-accumulation techniques and silicon spheres. It would free physicists from the need to rely on blind assumptions about the stability of those prototypes, allay fears over the consequences of cleaning them, and break away from the rigidity of definitions that would mandate that each new atom-count-based prototype is the precise embodiment of the kilogram. Instead, hand-tuned, close-approximation mass standards would simply be weighed and documented as being equal to one kilogram plus an offset value. With scales, the kilogram would not only be defined in electrical terms, it would also be delineated in electrical terms. Mass artifacts calibrated in a watt balance would effectively become transfer standards. Further, one additional term in all scale-based realizations—acceleration due to gravity—is currently measured using dropping-mass absolute gravimeters that contain an iodine-stabilized HeNe laser interferometer. The fringe-signal, frequency-sweep output from the interferometer is measured with a rubidium atomic clock. Thus, the “gravity” term in the delineation of an all-electronic kilogram would also be measured relative to invariants of nature.

Scales also permit new flexibility in choosing materials with especially desirable properties for mass standards. For instance, 90Pt–Ir could continue to be used so the specific gravity of newly produced mass standards would be the same as existing national primary and check standards. This would reduce the relative uncertainty when making mass comparisons in air. Alternately, 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 mercury and hydrogen (due to catalysis of VOCs and hydrocarbon-based cleaning solvents) proved to be sources of instability. Also, vapor-deposited, protective ceramic coatings like nitrides could be investigated for their suitability to isolate these new alloys.
##### Ampere-based force
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-meter force between two straight parallel conductors of infinite length, of negligible circular cross section, placed 1 meter apart in vacuum, through which flow a constant current of 1/1.602 176 487 × 10–19 (6,241,509,647,120,417,390) elementary charges per second.?

Effectively, this would define the kilogram as a derivative of the ampere, rather than present relationship, which defines the ampere as a derivative of the kilogram. This redefinition of the kilogram would result from fixing the elementary charge (e) to be precisely 1.602 176 487 × 10–19 coulomb (from the current 2006 CODATA value of 1.602 176 487(40) × 10–19), which effectively defines the coulomb as being the sum of 6,241,509,647,120,417,390 elementary charges. It would necessarily follow that the ampere then becomes an electrical current of this same quantity of elementary charges per second.

The virtue of a practical realization based upon this definition is that unlike the watt balance and other scale-based methods, all of which require the careful characterization 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 realization based upon accelerating masses. Experiments over a period of years in Japan with a superconducting, 30-gram mass supported by diamagnetic levitation never achieved an uncertainty better than 10 parts in 106. Magnetic hysteresis was one of the limiting issues. Other groups are continuing this line of research using different techniques to levitate the mass.[22]

 Inertia International System of Units (SI) International Bureau of Weights and Measures (BIPM) International Committee for Weights and Measures (CIPM) Gal (unit) General Conference on Weights and Measures (CGPM) Gram Grave (orig. name of the kilogram, history of) Gravimetry Kilogram-force

## Notes

1. ^ Proceedings of the 94th meeting (October 2005) of the International Committee for Weights and Measures, (1.1 MB zip file, here)
2. ^ NIST: SI prefixes (link to Web site).
3. ^ The practice of using the abbreviation “mcg” rather than the SI symbol “µg” was formally mandated for medical practitioners in 2004 by the Joint Commission on Accreditation of Healthcare Organizations (JCAHO) in their “Do Not Use” List: Abbreviations, Acronyms, and Symbols because hand-writen expressions of “µg” can be confused with “mg”, resulting in a thousand-fold overdosing. The mandate was also adopted by the Institute for Safe Medication Practices.
4. ^ Decree relating to the weights and measurements
5. ^ Citation: L'Histoire Du Mètre, La Détermination De L'Unité De Poids, link to Web site here.
6. ^ Citation: History of the kilogram
7. ^ New Techniques in the Manufacture of Platinum-Iridium Mass Standards, T. J. Quinn, Platinum Metals Rev., 1986, 30, (2), Pg. 74 – 79
8. ^ Water Structure and Science, Water Properties, Density maximum (and molar volume) at temperature of maximum density, a (by London South Bank University). Link to Web site.
9. ^ Extraordinary care is exercised when transporting prototypes. In 1984, the K4 and K20 replicas were hand-carried in the passenger section of a commercial airliner.
10. ^ Redefinition of the kilogram: a decision whose time has come, Ian M. Mills et al., Metrologia 42 (2005), 71–80
11. ^ The Third Periodic Verification of National Prototypes of the Kilogram (1988–1992), G. Girard, Metrologia 31 (1994) 317–336
12. ^ The SI unit of mass, Richard Davis, Metrologia 40 (2003), 299–305. Note that if the ∆50 µg between the IPK and its replicas was entirely due to wear, the IPK would have to have lost 150 million billion more platinum and iridium atoms over the last century than its replicas. That there would be this much wear, much less a difference of this magnitude, is thought unlikely; 50 µg is roughly the mass of a fingerprint. Many theories have been advanced to explain the data, including one that begins with the observation that the IPK is uniquely stored under three bell jars whereas its six sister copies and the others dispersed throughout the world are stored under only two. This theory is founded on two other facts: that platinum has a strong affinity for mercury, and that atmospheric mercury is significantly more abundant in the atmosphere today than at the time the IPK and its replicas were manufactured. This theory posits that the relative change in mass between the IPK and its replicas is not one of loss at all, and is instead a simple matter that the IPK has gained less than the replicas. This theory is just one of many advanced by the specialists to account for the relative change in mass. To date, each theory has either proven implausible, or there is insufficient data or technical means to either prove or disprove it. Citation: Conjecture why the IPK drifts, R. Steiner, NIST, 11 Sept. 2007.
13. ^ Report to the CGPM, 14th meeting of the Consultative Committee for Units (CCU), April 2001, 2. (ii); General Conference on Weights and Measures, 22nd Meeting, October 2003, which stated “The kilogram is in need of a new definition because the mass of the prototype is known to vary by several parts in 108 over periods of time of the order of a month…” (3.2 MB ZIP file, here).
14. ^ General section citations: Recalibration of the U.S. National Prototype Kilogram, R. S. Davis, Journal of Research of the National Bureau of Standards, 90, No. 4, July–August 1985 (5.5 MB PDF here); and The Kilogram and Measurements of Mass and Force, Z. J. Jabbour et al., J. Res. Natl. Inst. Stand. Technol. 106, 2001, 25–46 (3.5 MB PDF, here)
15. ^ On Earth, masses with densities less than that of air float and have negative weight; that is, they are buoyant. Such masses have weight in a vacuum.
16. ^ For instance, buoyancy’s diminishing effect upon one’s body weight (a relatively low-density object) is 1/860th that of gravity. Variations in barometric pressure rarely affect one’s weight more than ±1 part in 30,000. Assumptions: An air density of 1160 g/m³, an average density of a human body (with collapsed lungs) equal to that of water, and variations in barometric pressure rarely exceeding ±22 torr. Assumptions primary variables: An altitude of 194 meters above mean sea level (the worldwide median altitude of human habitation), an indoor temperature of 23 °C, a dewpoint of 9 °C, and 760 mm–Hg sea level–corrected barometric pressure.
17. ^ International Recommendation OIML R33. See International Organization of Legal Metrology Web site.
18. ^ If true mass in metric tons is measured. If conventional mass is used (no compensations for buoyancy are made), their weights will be identical. Value assumes standard gravity and an air density of 1160 g/m³.
19. ^ General Conference on Weights and Measures, 22nd Meeting, October 2003 (3.2 MB ZIP file, here).
20. ^ Georgia Tech, 21 Sept. 2007 press release: A Better Definition for the Kilogram? Note that the uncertainty in the Avogadro constant narrowed since this proposal was first submitted to American Scientist for publication. The 2006 CODATA value for the Avogadro constant has a relative standard uncertainty of 50 parts per billion and the only cube root values within this uncertainty must fall within the range of 84,446,889.8 ±1.4; that is, there are only three integer cube roots (…89, …90, and …91) in this range and the value 84,446,886 falls outside of it. Unfortunately, none of the three integer values within the range posses the property of their cubes being divisible by twelve; one gram of C-12 could not comprise an integer number of atoms. If the value 84,446,886 was adopted to define the kilogram, many other constants of nature and electrical units would have to be revised an average of about 0.13 part per million. The straightforward adjustment to this approach advanced by the group would instead define the kilogram as “the mass equal to 84,446,8903 × 83⅓ atoms of carbon-12.” This proposed value for the Avogadro constant falls neatly within the measured value (≅6.022 141 84 × 1023 vs. the 2006 CODATA value of 6.022 141 79(30) × 1023) and the proposed definition of the kilogram produces an integer number of atoms in 12 grams of carbon-12, but not for 1 gram nor 1 kilogram.
21. ^ Hysteresis and Related Error Mechanisms in the NIST Watt Balance Experiment, Joshua P. Schwarz et al., Journal of Research of the National Bureau of Standards and Technology, 106, No. 4, July–August 2001 (888 KB PDF here); and On the redefinition of the kilogram, B. N. Taylor et al., Metrologia 36 (1999), 63–64; and the NIST’s Fundamental Physical Constants: “Energy Equivalents” calculator.
22. ^ NIST, Beyond the Kilogram: Redefining the International System of Units; and A Watt Balance On Its Side, R. Steiner, NIST, 24 Sept. 2007.

## Glossary

• Artifact: A human-made object used as a comparative standard in the measurement of a physical quantity.
• Check standard:
# A standard body’s backup replica of the IPK.
# A secondary kilogram mass standard used for routine calibrations.
• Definition: A formal, specific, and exact specification.
• Delineate: To use physical means to mark a boundary or express the magnitude of an entity.
• Delineation: The physical means used to mark a boundary or express the magnitude of an entity.
• Magnitude: The extent or numeric value of a property
• National prototype: A replica of the IPK possessed by a nation.
• Practical realization: An artifact or readily reproducible apparatus for delineating the magnitude of a unit of measure.
• Primary national standard:
# A replica of the IPK possessed by a nation
# The least used replica of the IPK when a nation possesses more than one.
• Prototype:
# A human-made object that serves as the defining comparative standard in the measurement of a physical quantity.
# A human-made object that serves as the comparative standard in the measurement of a physical quantity.
# The IPK and any of its replicas
• Replica: An official copy of the IPK.
• Transfer standard: An artifact or apparatus that reproduces the magnitude of a unit of measure in a different, usually more practical, form.
KG, Kg or kg may indicate:
• Kilogram, "kg.", the SI base unit of mass
• kilogauss, "kG", unit of magnetic field
• Kampfgeschwader, a unit of command in the former German Luftwaffe

International System of Units (abbreviated SI from the French Le Système international d'unités) is the modern form of the metric system.
The international system (SI) of units defines seven SI base units: physical units defined by an operational definition.

All other physical units can be derived from these base units: these are known as SI derived units. Derivation is by dimensional analysis.
Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic
The litre or liter (see spelling differences) is a unit of volume. There are two official symbols, namely the Latin letter L both in lower and upper case: l and L.
An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple.
weight is a measurement of the gravitational force acting on an object. Near the surface of the Earth, the acceleration due to gravity is approximately constant; this means that an object's weight is roughly proportional to its mass.
The unit kilogram-force (kgf, often just kg) or kilopond (kp) is defined as the force exerted by one kilogram of mass in standard Earth gravity.
The avoirdupois (IPA: /ˌævərdəˈpɔɪz/; French IPA: [avwɑrdypwɑ]
pound or pound-mass (abbreviations: lb, , lbm, or sometimes in the United States: #) is a unit of mass (sometimes called 'weight' in everyday parlance) in a number of different systems, including English units, Imperial units, and United
Imperial units or the Imperial system is a collection of units, first defined in the British Weights and Measures Act of 1824, later refined (until 1959) and reduced.
U.S. customary units, also known in the United States as English units[1] (but see English unit) or standard units, are units of measurement that are currently used in the USA, in some cases alongside units from SI (the International System of Units
A pound or pound-force (abbreviations: lb, lbf, or lbf) is a unit of force. Pound is also the name of a unit of mass. One pound-force is approximately equal to the gravitational force exerted on a mass of one avoirdupois pound on the
The International Committee for Weights and Measures is the English name of the Comité international des poids et mesures (CIPM, sometimes written in English Comité International des Poids et Mesures).
Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic
Inertia is a property of matter by which it remains at rest or in uniform motion in the same straight line unless acted upon by some external force The principle of inertia is one of the fundamental principles of classical physics which are used to describe the motion of matter and
In physics, force is an action or agency that causes a body of mass m to accelerate. It may be experienced as a lift, a push, or a pull. The acceleration of the body is proportional to the vector sum of all forces acting on it (known as net force or resultant force).
acceleration is defined as the rate of change of velocity, or, equivalently, as the second derivative of position. It is thus a vector quantity with dimension length/time². In SI units, acceleration is measured in metres/second² (m·s-²).
The metre (or meter) per second squared is the SI derived unit of acceleration. It is a measure of magnitude and can be a scalar measure or, when associated with a direction, a vector, for example by having sign positive or negative.
The newton (symbol: N) is the SI derived unit of force, named after Sir Isaac Newton in recognition of his work on classical mechanics.

## Definition

A newton
weight is a measurement of the gravitational force acting on an object. Near the surface of the Earth, the acceleration due to gravity is approximately constant; this means that an object's weight is roughly proportional to its mass.
special theory of relativity was proposed in 1905 by Albert Einstein in his article "On the Electrodynamics of Moving Bodies". Some three centuries earlier, Galileo's principle of relativity had stated that all uniform motion was relative, and that there was no absolute and
An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple.
Gram
Unit sign g
Measure Mass
Base Unit Kilogram
Multiple of Base 10−3
System SI, CGS, other
Common usage Commonly used in cooking and food labeling
Examples
centimetre-gram-second system (CGS) is a system of physical units. It is always the same for mechanical units, but there are several variants of electric additions. It was replaced by the MKS, or metre-kilogram-second system, which in turn was replaced by the International
tonne (t) or metric ton (M/T), also referred to as a metric tonne, is a measurement of mass equal to 1,000 kilograms. It is not an SI unit but is accepted for use with the SI.
A grave is a metallic reference standard of one thousand grams that was used for a few years until it was replaced by the kilogram standard in 1799.

Our modern kilogram has its origins in the pre-French Revolution days of France.
Gram
Unit sign g
Measure Mass
Base Unit Kilogram
Multiple of Base 10−3
System SI, CGS, other
Common usage Commonly used in cooking and food labeling
Examples