Kilogram

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

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, 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.

The avoirdupois pound, the unit of mass in both the Imperial system and U.S. customary units, is defined as exactly 0.453 592 37 kg, which is to say, one kilogram is approximately equal to 2.205 avoirdupois pounds.

While the weight of objects are often given in kilograms, the kilogram is, in the strict scientific sense, a unit of mass. The equivalent unit of weight is the kilogram-force, which is a deprecated unit. Similarly, ever since the 1893 redefinition of the pound in terms of the kilogram, the pound too is a measure of mass and its related unit of weight is the pound-force.

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 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 an object off the cabin floor since such objects naturally hover. However, since objects in microgravity still retain their mass, an astronaut must exert one hundred times more effort to accelerate a 100-kilogram object to the same velocity as a 1-kilogram object. See also Mass vs. weight below.

SI multiples

Because multiple 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. For instance, one-millionth of a kilogram is 1 mg (one milligram), not 1 µkg (one microkilogram). The most common prefixed forms of gram are shown in bold text in the table below.

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

• 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 full unit name ‘microgram’ is often abbreviated as ‘mcg’, particularly in pharmaceutical and nutritional supplement labeling. Further, 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 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.” 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 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. 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. Four years later in 1799, an all-platinum standard, the “Kilogramme des Archives,” was fabricated with the objective that it would equal, as close as was scientifically feasible for the day, to the mass of cubic decimeter of water at 4 °C. The kilogram was defined to be equal to the mass of the Kilogramme des 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. The IPK and six of its official 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. 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 Kilogramme des Archives made eighty-four years prior, and formally ratified as the kilogram by the 1st CGPM in 1889. 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. Given this small, 25 ppm difference, and the fact that the mass of the IPK was indistinguishable from the mass of the Kilogramme des Archives, speaks volumes of the scientists’ skills in 1795–1799 when making their measurements of water’s properties and in manufacturing the Kilogramme des 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.

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, had an official mass of 1 kg – 0.039 mg in 1889. A verification performed in 1948 showed a mass of 1 kg – 0.019 mg. 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, is today officially calibrated as 1 kg – 0.116 mg. However, it was 0.041 mg more massive (in comparison to the IPK) in 1889.

Since the IPK and its copies are stored in air (albeit under two or more nested bell jars), they adsorb atmospheric contamination onto their surface and gain mass. Accordingly, they are cleaned in preparation for periodic verifications, a process that includes steam cleaning and lightly rubbing with chemical-soaked chamois. Cleaning the official copies of the IPK can easily remove 0.020 mg of contamination. After cleaning—even when they are stored in their bell jars—the IPK and its replicas gain an average of 1.11 µg per month for the first 3 months after cleaning. Thereafter, the rate of change in their mass decreases to an average of about 1 µg per year. In fact, since the check standards are not cleaned every time they are routinely used for calibrations, the BIPM developed a model of mass gain vs. time after a cleaning so an “after cleaning” correction factor may be applied.

Because the 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 and its copies. What has become clear, particularly since the modern and extremely sensitive NBS-2 and FB-2 balances have become available, is that the IPK and its copies have demonstrated a long-term instability—drifts—in the after-cleaned mass of 30 µg over the last century. The reason for this instability is unknown, but what is known is that the assumption that the cleaning process restores the mass standards to their original mass is false. It is conjectured that the instability could involve subtle, microscopic differences in their polished surfaces in combination with unintentional differences in the cleaning process as well as the precise nature of the contamination.

Following a number of print articles, including the 2003, #26 issue of Der Spiegel, it was widely—but incorrectly—believed by the general public that the IPK lost 50 µg over the last century. The issue is not one of loss (although that could be occurring too), but rather, is one of instability. Although the IPK and its official copies might be losing mass due to the cleaning process, there would be no possible way to detect this if they were all losing mass at roughly equal rates. The concern with the IPK and its copies is that there is a fugitive variable causing long-term instability in the measured values after the mass standards have been very carefully cleaned and there is no way to know if this instability is a harbinger of even greater, long-term trends upwards or downwards. The instability in the IPK and its copies 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.

Mass vs. weight

The distinction between the two

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 remain 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, “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 (see Tire code), 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 deprecated 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 force

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). Kilograms are converted to newtons by multiplying by 9.8, 9.81, or 9.80665. Note that the highest-precision figure 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”

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. 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. 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 mass standards, 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.” 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.” This is because the density of lead is greater and displaces less air.

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.

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

Atom-counting approaches

• One Avogadro approach attempts to define the kilogram as a fixed number of silicon atoms of the same isotope. Silicon is the element of choice because the process of creating ultra-pure monocrystalline silicon is well-known (because of its use in the semiconductor industry). As a practical realization the monocrystaline rod would be cut and polished into a sphere, the weight of which would be measured using three different approaches in development by several different institutes. The sizes of the best spheres would be measured by interferometry. As the crystalline structure of the monocrystal is known, the number of atoms in this one kilogram could be estimated.
• The ion accumulation approach involves accumulation of gold atoms and measuring the electrical current required to neutralise them.

Fundamental-constant approaches

In a similar manner that the metre was redefined to fix the speed of light to an exact value of 299,792,458 m/s, there are proposals to redefine the kilogram in such a way to fix other physical constants of nature to exact values.

• Planck's constant: The Watt balance uses the current balance that was formerly used to define the ampere to relate the kilogram to a value for Planck's constant, based on the definitions of the volt and the ohm. Using the Watt balance, a possible definition for the kilogram would be: The kilogram is the mass of a body at rest whose equivalent energy corresponds to a frequency of exactly (299,792,458²/66,260,693) × 10⁴¹ Hz.

This would have the effect of defining Planck's constant to be h = 6.626 0693 × 10^–34 J s (from the 2002 CODATA value for Planck's constant of 6.626 0693(11) × 10^–34 J•s).

• Avogadro constant: The kilogram is the mass of exactly (6.022 1415 × 10²³/0.012) unbound carbon-12 atoms at rest and in their ground state.

This would have the effect of defining Avogadro's number to be N_A = 6.022 1415 × 10²³ elementary entities per mole and, consequently, a simpler and concise definition for the mole (from the 2002 CODATA value for the Avogadro constant of 6.022 1415(10) × 10²³ mol^-1).

• Electron mass: The kilogram is the base unit of mass, equal to 1,097,769,238,499,215,084,016,780,676,223 electron mass units.

This would have the effect of defining the electron mass to be m_e = 9.109 3826 × 10^–31 kg (from the 2002 CODATA value for the electron mass of 9.109 3826(16) × 10^–31 kg).

• Elementary charge: The kilogram is the mass which would be accelerated at precisely 2 × 10^–7 m/s² if 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 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 careful characterization of the gravity at any given laboratory, this definition specifies the kilogram in terms of true acceleration of a mass.

CIPM Recommendation 1 (CI-2005)

CIPM Recommendation 1 (CI-2005): Preparative steps towards new definitions of the kilogram, the ampere, the kelvin and the mole in terms of fundamental constants

The International Committee for Weights and Measures (CIPM),

• Approve in principle the preparation of new definitions and practical realizations of the kilogram, the ampere and the kelvin so that if the results of experimental measurements over the next few years are indeed acceptable, all having been agreed with the various Consultative Committees and other relevant bodies, the CIPM can prepare proposals to be put to Member States of the Metre Convention in time for possible adoption by the 24th CGPM in 2011;
• Give consideration to the possibility of redefining, at the same time, the mole in terms of a fixed value of the Avogadro constant;
• Prepare a Draft Resolution that may be put to the 23rd CGPM in 2007 to alert Member States to these activities;

See also

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

• Metric system
• Mass
• National Institute of Standards and Technology (NIST)
• Newton
• SI base units
• SI derived units
• Standard gravity
• Tonne (metric ton)
• Weight

External links

• The U.K.’s National Physical Laboratory: FAQs on the kilogram and alternatives to the IPK
• NIST: Hysteresis and Related Error Mechanisms in the NIST Watt Balance Experiment (888 kB PDF, here)
• The U.K.’s National Physical Laboratory: More on the Avogadro project
• International Bureau of Weights and Measures (BIPM) home page
• NZZ Folio: What a kilogram really weighs.
• New Scientist: World's most sensitive scales weigh a zeptogram

Links to photographs

• BIPM: The IPK in three nested bell jars
• NIST: K20, the US National Prototype Kilogram
• BIPM: Steam cleaning a 1 kg prototype before a mass comparison
• BIPM: The IPK and six of its official copies in their vault
• NIST: The Rueprecht Balance, Austrian-made, precision balance 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. Also used by NIST and Sandia National Laboratories’ Primary Standards Laboratory