Metric system

The metric system is an internationally recognised decimalised system of measurement. It is in widespread use, and where it is adopted, it is the only or most common system of weights and measures (see metrication). It is now known as the International System of Units (SI). It is used to measure everyday things such as the mass of a sack of flour, the height of a person, the speed of a car, and the volume of fuel in its tank. It is also used in science, industry and trade.

In its modern form, it consists of a set of base units including metre for length, kilogram for mass, second for time and ampere for electrical current, and a few others, which together with their derived units, can measure any physical quantity. Metric system may also refer to other systems of related base and derived units defined before the middle of the 20th century, some of which are still in limited use today.

The metric system was designed to have properties that make it easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units. It is also a coherent system, which means that its units do not introduce conversion factors not already present in equations relating quantities. It has a property called rationalisation that eliminates certain constants of proportionality in equations of physics.

The units of the metric system, originally taken from observable features of nature, are now defined by phenomena such as the microwave frequency of a caesium atomic clock which accurately measures seconds. One unit, the kilogram, remains defined in terms of a man-made artefact, but scientists recently voted to change the definition to one based on Planck's constant via a Kibble balance. The new definition is expected to be formally propagated on 20 May 2019.

While there are numerous named derived units of the metric system, such as watt and lumen, other common quantities such as velocity and acceleration do not have their own unit, but are defined in terms of existing base and derived units such as metres per second for velocity.

Though other currently or formerly widespread systems of weights and measures continue to exist, such as the British imperial system and the US customary system of weights and measures, in those systems most or all of the units are now defined in terms of the metric system, such as the US foot which is now a defined decimal fraction of a metre.

The metric system is also extensible, and new base and derived units are defined as needed in fields such as radiology and chemistry. The most recent derived unit, the katal, for catalytic activity, was added in 1999. Recent changes are directed toward defining base units in terms of invariant constants of physics to provide more precise realisations of units for advances in science and industry.

FourMetricInstruments
Four metric measuring devices: a tape measure in centimetres, a thermometer in degrees Celsius, a kilogram weight and a multimeter that measures volts, amperes and ohms

Units

Base units

The modern metric system consists of four electromechanical base units representing seven fundamental dimensions of measure: length, mass, time, electromagnetism, thermodynamic temperature, luminous intensity, and quantity of substance. The units are:

Together they are sufficient for measuring any known quantity,[1] without reference to further quantities or phenomena.

The metre, ampere, candela, and mole are all defined in terms of other base units. For example, the speed of light is defined as 299,792,458 metres per second, and the metre is derived from that constant and the definition of a second. As a result, in dimensional analysis, they remain wholly separate concepts.

Derived units with special names

There are currently 22 derived units with special names in the metric system, these are defined in terms of the base units or other named derived units.

Eight of these units are electromagnetic quantities:

  • volt, a unit of electrical potential
  • ohm, a unit of electrical resistance
  • tesla, a unit of magnetic flux density
  • weber, a unit of magnetic flux
  • farad, a unit of electrical capacitance
  • henry, a unit of electrical inductance
  • siemens, a unit of electrical conductance (the inverse of ohm)
  • coulomb, a unit of electrical charge

Four of these units are mechanical quantities:

  • watt, a unit of mechanical or electrical power
  • newton, a unit of mechanical force
  • joule, a unit of mechanical, electrical or thermodynamic energy
  • pascal, a unit of pressure

Five units represent measures of electromagnetic radiation and radioactivity:

  • becquerel, a unit of radioactive decay
  • sievert, a unit of absorbed ionising radiation
  • gray, a unit of ionising radiation
  • lux, a unit of luminous flux
  • lumen, a unit of luminous intensity

Two units are measures of circular arcs and spherical surfaces:

Three units are miscellaneous:

  • degree Celsius, a unit of thermodynamic temperature
  • katal, a unit of catalytic activity (enzymatic)
  • hertz, a unit of cycles per second (inverse of second)

Auxiliary and accessory units

Although SI, as published by the CGPM, should, in theory, meet all the requirements of commerce, science, and technology, certain customary units of measure have acquired established positions within the world community. In order that such units are used consistently around the world, the CGPM catalogued such units in Tables 6 to 9 of the SI brochure. These categories are:[2]

  • Non-SI units accepted for use with the International System of Units (Table 6). This list includes the hour and minute, the angular measures (Degree, Minute and second of arc), and the historic [non-coherent] metric units, the litre, tonne, and hectare (originally agreed by the CGPM in 1879)
  • Non-SI units whose values in SI units must be obtained experimentally (Table 7). This list includes various units of measure used in atomic and nuclear physics and in astronomy such as the dalton, the electron mass, the electron volt, the astronomical unit, the solar mass, and a number of other units of measure that are well-established, but dependent on experimentally-determined physical quantities.
  • Other non-SI units (Table 8). This list catalogues a number of units of measure that have been used internationally in certain well-defined spheres including the bar for pressure, the ångström for atomic physics, the nautical mile and the knot in navigation.
  • Non-SI units associated with the CGS and the CGS-Gaussian system of units (Table 9). This table catalogues a number of units of measure based on the CGS system and dating from the nineteenth century. They appear frequently in the literature, but their continued use is discouraged by the CGPM.

The SI symbols for the metric units are intended to be identical, regardless of the language used[3] but unit names are ordinary nouns and use the character set and follow the grammatical rules of the language concerned. For example, the SI unit symbol for kilometre is "km" everywhere in the world, even though the local language word for the unit name may vary. Language variants for the kilometre unit name include: chilometro (Italian), Kilometer (German),[Note 1] kilometer (Dutch), kilomètre (French), χιλιόμετρο (Greek), quilómetro/quilômetro (Portuguese), kilómetro (Spanish) and километр (Russian).[4][5]

Variations are also found with the spelling of unit names in countries using the same language, including differences in American English and British spelling. For example, meter and liter are used in the United States whereas metre and litre are used in other English-speaking countries. In addition, the official US spelling for the rarely used SI prefix for ten is deka. In American English the term metric ton is the normal usage whereas in other varieties of English tonne is common. Gram is also sometimes spelled gramme in English-speaking countries other than the United States, though this older usage is declining.[6]

In SI, which is a coherent system, the unit of power is the "watt", which is defined as "one joule per second".[7] In the US customary system of measurement, which is non-coherent, the unit of power is the "horsepower", which is defined as "550 foot-pounds per second" (the pound in this context being the pound-force).[8] Similarly, neither the US gallon nor the imperial gallon is one cubic foot or one cubic yard— the US gallon is 231 cubic inches and the imperial gallon is 277.42 cubic inches.[9]

The concept of coherence was only introduced into the metric system in the third quarter of the 19th century;[10] in its original form the metric system was non-coherent—in particular the litre was 0.001 m3 and the are (from which the hectare derives) was 100 m2. However the units of mass and length were related to each other through the physical properties of water, the gram having been designed as being the mass of one cubic centimetre of water at its freezing point.[11]

Realisation of units

Kilometre definition
The metre was originally defined to be one ten millionth of the distance between the North Pole and the Equator through Paris.[12]

The base units used in the metric system must be realisable. Each of the definitions of the base units in SI is accompanied by a defined mise en pratique [practical realisation] that describes in detail at least one way in which the base unit can be measured.[13] Where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to realise a standard without reliance on an artefact held by another country. In practice, such realisation is done under the auspices of a mutual acceptance arrangement (MAA).[14]

The standard metre is defined as exactly 1/299,792,458 of the distance that light travels in a second. The realisation of the metre depends in turn on precise realisation of the second. There are both astronomical observation methods and laboratory measurement methods that are used to realise units of the standard metre. Because the speed of light is now exactly defined in terms of the metre, more precise measurement of the speed of light does not result in a more accurate figure for its velocity in standard units, but rather a more accurate definition of the metre. The accuracy of the measured speed of light is considered to be within 1 m/s, and the realisation of the metre is within about 3 parts in 1,000,000,000, or an order of 10−9 parts.

The kilogram is defined by the mass of a man-made artefact of platinum-iridium held in a laboratory in France, until the new definition takes place in May 2019. Replicas made in 1879 at the time of the artefact's fabrication and distributed to signatories of the Metre Convention serve as de facto standards of mass in those countries. Additional replicas have been fabricated since as additional countries have joined the convention. The replicas are subject to periodic validation by comparison to the original, called the IPK. It has become apparent that either the IPK or the replicas or both are deteriorating, and are no longer comparable: they have diverged by 50 μg since fabrication, so figuratively, the accuracy of the kilogram is no better than 5 parts in a hundred million or within an order of 10−8 parts. The accepted redefinition of SI base units replaces the IPK with an exact definition of Planck's constant, which defines the kilogram in terms of the second and metre.

Properties as a system

Although the metric system has changed and developed since its inception, its basic concepts have hardly changed. Designed for transnational use, it consisted of a basic set of units of measurement, now known as base units. Derived units were built up from the base units using logical rather than empirical relationships while multiples and submultiples of both base and derived units were decimal-based and identified by a standard set of prefixes.

Units based on the natural world

Like most units of measure, the units of the metric system were based on perceptual quantities of the natural world. But they also had definitions in terms of stable relationships in that world: a metre was defined not by the span of a man's arms like a toise, but on a quantitative measure of the earth. A kilogram was defined by a volume of water, whose linear dimensions were fractions of the unit of length. The earth was not easy to measure, nor was it uniformly shaped, but the principle that units of measure were to be based on quantitative relationships among invariant facets of the physical world was established. The units of the metric system today still adhere to that principle, but the relationships used are based on the physics of nature, rather than its sensory dimensions.

Base and derived unit structure

The metric system base units were originally adopted because they represented fundamental orthogonal dimensions of measurement corresponding to how we perceive nature: a spatial dimension, a time dimension, one for the effect of gravitation, and later, a more subtle one for the dimension of an "invisible substance" known as electricity or more generally, electromagnetism. One and only one unit in each of these dimensions was defined, unlike older systems where multiple perceptual quantities with the same dimension were prevalent, like inches, feet and yards or ounces, pounds and tons. Units for other quantities like area and volume, which are also spacial dimensional quantities, were derived from the fundamental ones by logical relationships, so that a unit of square area for example, was the unit of length squared.

Many derived units were already in use before and during the time the metric system evolved, because they represented convenient abstractions of whatever base units were defined for the system, especially in the sciences. So analogous units were scaled in terms of the metric units, and their names adopted into the system. Many of these were associated with electromagnetism. Other perceptual units, like volume, which were not defined in terms of base units, were incorporated into the system with definitions in the metric base units, so that the system remained simple. It grew in number of units, but the system retained a uniform structure.

Decimal ratios

Some customary systems of weights and measures had duodecimal ratios, which meant quantities were conveniently divisible by 2, 3, 4, and 6. But it was difficult to do arithmetic with things like ​14 pound or ​13 foot. There was no system of notation for successive fractions: for example, ​13 of ​13 of a foot was not an inch or any other unit. But the system of counting in decimal ratios did have notation, and the system had the algebraic property of multiplicative closure: a fraction of a fraction, or a multiple of a fraction was a quantity in the system, like ​110 of ​110 which is ​1100. So a decimal radix became the ratio between unit sizes of the metric system.

Prefixes for multiples and submultiples

In the metric system, multiples and submultiples of units follow a decimal pattern.[Note 2]

Metric prefixes in everyday use
Text Symbol Factor Power
yotta Y 1000000000000000000000000 1024
zetta Z 1000000000000000000000 1021
exa E 1000000000000000000 1018
peta P 1000000000000000 1015
tera T 1000000000000 1012
giga G 1000000000 109
mega M 1000000 106
kilo k 1000 103
hecto h 100 102
deca da 10 101
(none) (none) 1 100
deci d 0.1 10−1
centi c 0.01 10−2
milli m 0.001 10−3
micro μ 0.000001 10−6
nano n 0.000000001 10−9
pico p 0.000000000001 10−12
femto f 0.000000000000001 10−15
atto a 0.000000000000000001 10−18
zepto z 0.000000000000000000001 10−21
yocto y 0.000000000000000000000001 10−24

A common set of decimal-based prefixes that have the effect of multiplication or division by an integer power of ten can be applied to units that are themselves too large or too small for practical use. The concept of using consistent classical (Latin or Greek) names for the prefixes was first proposed in a report by the French Revolutionary Commission on Weights and Measures in May 1793.[12]:89–96 The prefix kilo, for example, is used to multiply the unit by 1000, and the prefix milli is to indicate a one-thousandth part of the unit. Thus the kilogram and kilometre are a thousand grams and metres respectively, and a milligram and millimetre are one thousandth of a gram and metre respectively. These relations can be written symbolically as:[15]

In the early days, multipliers that were positive powers of ten were given Greek-derived prefixes such as kilo- and mega-, and those that were negative powers of ten were given Latin-derived prefixes such as centi- and milli-. However, 1935 extensions to the prefix system did not follow this convention: the prefixes nano- and micro-, for example have Greek roots.[16] During the 19th century the prefix myria-, derived from the Greek word μύριοι (mýrioi), was used as a multiplier for 10000.[17]

When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated below.[15]

1 mm2 (square millimetre) = (1 mm)2  = (0.001 m)2  = 0.000001 m2
1 km2 (square kilometre = (1 km)2 = (1000 m)2 = 1000000 m2
1 mm3 (cubic millimetre) = (1 mm)3 = (0.001 m)3 = 0.000000001 m3
1 km3 (cubic kilometre) = (1 km)3 = (1000 m)3 = 1000000000 m3

Prefixes are not usually used to indicate multiples of a second greater than 1; the non-SI units of minute, hour and day are used instead. On the other hand, prefixes are used for multiples of the non-SI unit of volume, the litre (l, L) such as millilitres (ml).[15]

Coherence

James Clerk Maxwell
James Clerk Maxwell played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.

Each variant of the metric system has a degree of coherence—the derived units are directly related to the base units without the need for intermediate conversion factors.[18] For example, in a coherent system the units of force, energy and power are chosen so that the equations

force = mass × acceleration
energy = force × distance
energy = power × time

hold without the introduction of unit conversion factors. Once a set of coherent units have been defined, other relationships in physics that use those units will automatically be true. Therefore, Einstein's mass–energy equation, E = mc2, does not require extraneous constants when expressed in coherent units.[19]

The CGS system had two units of energy, the erg that was related to mechanics and the calorie that was related to thermal energy; so only one of them (the erg) could bear a coherent relationship to the base units. Coherence was a design aim of SI, which resulted in only one unit of energy being defined – the joule.[7]

Rationalisation

Maxwell's equations of electromagnetism contained a factor relating to steradians, representative of the fact that electric charges and magnetic fields may be considered to emanate from a point and propagate equally in all directions, i.e. spherically. This factor appeared awkwardly in many equations of physics dealing with the dimensionality of electromagnetism and sometimes other things.

International System of Units

The International System of Units is the modern metric system. It is based on the Metre-Kilogram-Second-Ampere (MKSA) system of units from early in the 20th century. It also includes numerous coherent derived units for common quantities like power (watt) and irradience (lumen). Electrical units were taken from the International system then in use. Other units like those for energy (joule) were modeled on those from the older CGS system, but scaled to be coherent with MKSA units. Two additional base units, degree Kelvin equivalent to degree Centigrade for thermodynamic temperature, and candela, roughly equivalent to the international candle unit of illumination, were introduced. Later, another base unit, the mole, a unit of mass equivalent to Avogadro's number of specified molecules, was added along with several other derived units.

The system was promulgated by the General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM) in 1960. At that time, the metre was redefined in terms of the wavelength of a spectral line of the krypton-86[Note 3] atom, and the standard metre artefact from 1889 was retired.

Today, the International system of units consists of 7 base units and innumerable coherent derived units including 22 with special names. The last new derived unit, the katal for catalytic activity, was added in 1999. Some of the base units are now realised in terms of invariant constants of physics. As a consequence, the speed of light has now become an exactly defined constant, and defines the metre as ​1299,792,458 of the distance light travels in a second. The kilogram remains defined by a man-made artefact of platinum-iridium, and it is deteriorating. The range of decimal prefixes has been extended to those for 1024, yotta, and 10−24, yocto, which are unfamiliar because nothing in our everyday lives is that big or that small.

The International System of Units has been adopted as the official system of weights and measures by all nations in the world except for Myanmar, Liberia, and the United States, while the United States is the only industrialised country where the metric system is not the predominant system of units. There are 192 countries that predominantly use the metric system and 3 that do not.

Historical variants

A number of variants of the metric system evolved, all using the Mètre des Archives and Kilogramme des Archives (or their descendants) as their base units, but differing in the definitions of the various derived units.

Variants of the metric system
Quantity CGS MKS MTS
distance, displacement,
length, height, etc.
(d, x, l, h, etc.)
centimetre (cm) metre (m) metre
mass (m) gram (g) kilogram (kg) tonne (t)
time (t) second (s) second second
speed, velocity (v, v) cm/s m/s m/s
acceleration (a) gal (Gal) m/s2 m/s2
force (F) dyne (dyn) newton (N) sthene (sn)
pressure (P or p) barye (Ba) pascal (Pa) pièze (pz)
energy (E, Q, W) erg (erg) joule (J) kilojoule (kJ)
power (P) erg/s watt (W) kilowatt (kW)
viscosity (μ) poise (P) Pa⋅s pz⋅s

Gaussian second and the first mechanical system of units

In 1832, Gauss used the astronomical second as a base unit in defining the gravitation of the earth, and together with the gram and millimetre, became the first system of mechanical units.

The EMU, ESU and Gaussian systems of electrical units

Several systems of electrical units were defined following discovery of Ohm's law in 1824.

Centimetre–gram–second systems

The centimetre–gram–second system of units (CGS) was the first coherent metric system, having been developed in the 1860s and promoted by Maxwell and Thomson. In 1874, this system was formally promoted by the British Association for the Advancement of Science (BAAS).[20] The system's characteristics are that density is expressed in g/cm3, force expressed in dynes and mechanical energy in ergs. Thermal energy was defined in calories, one calorie being the energy required to raise the temperature of one gram of water from 15.5 °C to 16.5 °C. The meeting also recognised two sets of units for electrical and magnetic properties – the electrostatic set of units and the electromagnetic set of units.[21]

International system of electrical units

The CGS units of electricity were cumbersome to work with. This was remedied at the 1893 International Electrical Congress held in Chicago by defining the "international" ampere and ohm using definitions based on the metre, kilogram and second.[22]

MKS and MKSA systems

In 1901, Giovanni Giorgi showed that by adding an electrical unit as a fourth base unit, the various anomalies in electromagnetic systems could be resolved. The metre–kilogram–second–coulomb (MKSC) and metre–kilogram–second–ampere (MKSA) systems are examples of such systems.[23]

The International System of Units (Système international d'unités or SI) is the current international standard metric system and is also the system most widely used around the world. It is an extension of Giorgi's MKSA system—its base units are the metre, kilogram, second, ampere, kelvin, candela and mole.[7] The MKS (Metre, Kilogram, Second) system came into existence in 1889, when artefacts for the metre and kilogram were fabricated according to the convention of the Metre. Early in the 20th century, an unspecified electrical unit was added, and the system was called MKSX. When it became apparent that the unit would be the ampere, the system was referred to as the MKSA system, and was the direct predecessor of the SI.

Metre–tonne–second systems

The metre–tonne–second system of units (MTS) was based on the metre, tonne and second – the unit of force was the sthène and the unit of pressure was the pièze. It was invented in France for industrial use and from 1933 to 1955 was used both in France and in the Soviet Union.[24][25]

Gravitational systems

Gravitational metric systems use the kilogram-force (kilopond) as a base unit of force, with mass measured in a unit known as the hyl, Technische Mass Einheit (TME), mug or metric slug.[26] Although the CGPM passed a resolution in 1901 defining the standard value of acceleration due to gravity to be 980.665 cm/s2, gravitational units are not part of the International System of Units (SI).[27]

Conversion, calculation and symbol confusion incidents

The dual usage of or confusion between metric and non-metric units and confusion of metric symbols have resulted in a number of serious incidents. These include:

  • Due to serious medication errors having resulted from confusion between mg and μg, doses of less than one milligram must be expressed in micrograms written in full (the symbol μg being banned) in the Scottish health service.[28]
  • Flying an overloaded American International Airways aircraft from Miami, Florida to Maiquetia, Venezuela on 26 May 1994. The degree of overloading was consistent with ground crew reading the kilogram markings on the cargo as pounds.[29]
  • In 1999 the Institute for Safe Medication Practices reported that confusion between grains and grams led to a patient receiving phenobarbital 0.5 grams instead of 0.5 grains (0.03 grams) after the practitioner misread the prescription.[30]
  • The Canadian "Gimli Glider" accident in 1983, when a Boeing 767 jet ran out of fuel in mid-flight because of two mistakes made when calculating the fuel supply of Air Canada's first aircraft to use metric measurements: mechanics miscalculated the amount of fuel required by the aircraft as a result of their unfamiliarity with metric units.[31]
  • The root cause of the loss in 1999 of NASA's US$125 million Mars Climate Orbiter was a mismatch of units – the spacecraft engineers calculated the thrust forces required for velocity changes using US customary units (lbf⋅s) whereas the team who built the thrusters were expecting a value in metric units (N⋅s) as per the agreed specification.[32][33]

Conversion table

During its evolution, the metric system has adopted many units of measure. The introduction of SI rationalised both the way in which units of measure were defined and also the list of units in use. These are now catalogued in the official SI Brochure.[7] The table below lists the units of measure in this catalogue and shows the conversion factors connecting them with the equivalent units that were in use on the eve of the adoption of SI.[34][35][36][37]

Quantity Dimension SI unit and symbol Legacy unit and symbol Conversion
factor
Time T second (s) second (s) 1
Length L metre (m) centimetre (cm)
ångström (Å)
0.01
10−10
Mass M kilogram (kg) gram (g) 0.001
Electric current I ampere (A) international ampere
abampere or biot
statampere
1.000022
10.0
3.335641×10−10
Temperature Θ kelvin (K)
degree Celsius (°C)
centigrade (°C) [K] = [°C] + 273.15
1
Luminous intensity J candela (cd) international candle 0.982
Amount of substance N mole (mol) No legacy unit n/a
Area L2 square metre (m2) are (a)[38] 100
Acceleration LT−2 (m⋅s−2) gal (gal) 10−2
Frequency T−1 hertz (Hz) cycles per second 1
Energy L2MT−2 joule (J) erg (erg) 10−7
Power L2MT−3 watt (W) (erg/s)
horsepower (hp)
Pferdestärke (PS)
10−7
745.7
735.5
Force LMT−2 newton (N) dyne (dyn)
sthene (sn)
kilopond (kp)
10−5
103
9.80665
Pressure L−1MT−2 pascal (Pa) barye (Ba)
pieze (pz)
atmosphere (at)
0.1
103
1.01325×105
Electric charge IT coulomb (C) abcoulomb
statcoulomb or franklin
10
3.335641×10−10
Potential difference L2MT−3I−1 volt (V) international volt
abvolt
statvolt
1.00034
10−8
2.997925×102
Capacitance L−2M−1T4I2 farad (F) abfarad
statfarad
109
1.112650×10−12
Inductance L2MT−2I−2 henry (H) abhenry
stathenry
10−9
8.987552×1011
Electric resistance L2MT−3I−2 ohm (Ω) international ohm
abohm
statohm
1.00049
10−9
8.987552×1011
Electric conductance L−2M−1T3I2 siemens (S) international mho (℧)
abmho
statmho
0.99951
109
1.112650×10−12
Magnetic flux L2MT−2I−1 weber (Wb) maxwell (Mx) 10−8
Magnetic flux density MT−2I−1 tesla (T) gauss (G) 10−4
Magnetic field strength IL−1 (A/m) oersted (Oe) 1034π = 79.57747
Dynamic viscosity ML−1T−1 (Pa⋅s) poise (P) 0.1
Kinematic viscosity L2T−1 (m2⋅s−1) stokes (St) 10−4
Luminous flux J lumen (lm) stilb (sb) 104
Illuminance JL−2 lux (lx) phot (ph) 104
[Radioactive] activity T−1 becquerel (Bq) curie (Ci) 3.70×1010
Absorbed [radiation] dose L2T−2 gray (Gy) rad (rad) 0.01
Radiation dose equivalent L2T−2 sievert roentgen equivalent man (rem) 0.01
Catalytic activity NT−1 katal (kat) enzyme unit(U) 1/60μkat

The SI Brochure also catalogues certain non-SI units that are widely used with the SI in matters of everyday life or units that are exactly defined values in terms of SI units and are used in particular circumstances to satisfy the needs of commercial, legal, or specialised scientific interests. These units include:[7]

Quantity Dimension Unit and symbol Equivalence
Mass M tonne (t) 1000 kg
Area L2 hectare (ha) 0.01 km2
104 m2
Volume L3 litre (L or l) 0.001 m3
Time T minute (min)
hour (h)
day (d)
60 s
3600 s
86400 s
Pressure L−1MT−2 bar 100 kPa
Plane angle none degree (°)
minute (′)
second (″)
(​π180) rad
(​π10800) rad
(​π648000) rad

See also

Notes

  1. ^ In German all nouns start with an upper-case letter
  2. ^ Non-SI units for time and plane angle measurement, inherited from existing systems, are an exception to the decimal-multiplier rule
  3. ^ A stable isotope of an inert gas that occurs in undetectable or trace amounts naturally

References

  1. ^ Strictly speaking, weak and strong charges may add two base dimensions: see Chyla, W.T. (December 2011). "Evolution of the International Metric System of Units SI" (PDF). Acta Physica Polonica A. 120 (6): 998–1011.
  2. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 124–129, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
  3. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 130, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
  4. ^ "Online Translation—Offering hundreds of dictionaries and translation in more than 800 language pairs". Babylon. Retrieved 5 February 2011.
  5. ^ Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2). (2008), International vocabulary of metrology — Basic and general concepts and associated terms (VIM) (PDF) (3rd ed.), International Bureau of Weights and Measures (BIPM) on behalf of the Joint Committee for Guides in Metrology, p. 9, retrieved 5 March 2011
  6. ^ "Weights and Measures Act 1985 (c. 72)". The UK Statute Law Database. Office of Public Sector Information. Archived from the original on 12 September 2008. Retrieved 26 January 2011. § 92.
  7. ^ a b c d e International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 111–120, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
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External links

Cambodian units of measurement

A number of units of measurement were used in Cambodia to measure length, mass, capacity, etc. Since 1914, the metric system is compulsory in Cambodia.

File size

File size is a measure of how much data a computer file contains or, alternately, how much storage it consumes. Typically, file size is expressed in units of measurement based on the byte. By convention, file size units use either a metric prefix (as in megabyte and gigabyte) or a binary prefix (as in mebibyte and gibibyte).When a file is written to a file system, which is the case in most modern devices, it may consume slightly more disk space than the file requires. This is because the file system rounds the size up to include any unused space left over in the last disk sector used by the file. (A sector is the smallest amount of space addressable by the file system. The size of a disk sectors is several hundred or several thousands bytes.) The wasted space is called slack space or internal fragmentation. Although smaller sector sizes allow for denser use of disk space, they decrease the operational efficiency of the file system.

The maximum file size a file system supports depends not only on the capacity of the file system, but also on the number of bits reserved for the storage of file size information. The maximum file size in the FAT32 file system, for example, is 4,294,967,295 bytes, which is one byte less than four gibibytes.

Kilobyte (KB) (JEDEC), is sometimes referred to unambiguously as kibibyte (KiB)(IEC). Sometimes kB, with lower cased SI-prefix k- for kilo (1000), is used, then always equaling 1000 bytes.

A file system may display all sizes with the metric system with only kB on small files indicating it, while some file systems/operating systems would display sizes in, the traditionally used on computers, binary system for all sizes, e.g. KB, even if hard disk manufacturers may prefer to use the metric system (for e.g. GB = 1,000,000,000 bytes and TB = 1000 GB), to show higher capacity numbers for their products.

File transfers (e.g. "downloads") may use rates of units of bytes (e.g. MB/s) in binary rather than metric system, while networking hardware, such as WiFi, always uses the metric system (Mbits/s, Gbits/s etc.). of units of bits (and it needs to send more than the files themselves, so some overhead needs to be factored in), making superficially similar terms very incompatible.

Gravitational metric system

The gravitational metric system (original French term Système des Méchaniciens) is a non-standard system of units, which does not comply with the International System of Units (SI). It is built on the three base quantities length, time and force with base units metre, second and kilopond respectively. Internationally used abbreviations of the system are MKpS, MKfS or MKS (from French mètre–kilogramme-poids–seconde or mètre–kilogramme-force–seconde).

However, the abbreviation MKS is also used for the MKS system of units, which, like the SI, uses mass in kilogram as a base unit.

Hectare

The hectare (; SI symbol: ha) is an SI accepted metric system unit of area equal to a square with 100-metre sides, or 10,000 m2, and is primarily used in the measurement of land. There are 100 hectares in one square kilometre. An acre is about 0.405 hectare and one hectare contains about 2.47 acres.

In 1795, when the metric system was introduced, the "are" was defined as 100 square metres and the hectare ("hecto-" + "are") was thus 100 "ares" or ​1⁄100 km2 (10,000 square metres). When the metric system was further rationalised in 1960, resulting in the International System of Units (SI), the are was not included as a recognised unit. The hectare, however, remains as a non-SI unit accepted for use with the SI units, mentioned in Section 4.1 of the SI Brochure as a unit whose use is "expected to continue indefinitely".The name was coined in French, from the Latin ārea.

International System of Units

The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the ampere, kelvin, second, metre, kilogram, candela, mole, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.

The base units are derived from invariant constants of nature, such as the speed of light in vacuum and the triple point of water, which can be observed and measured with great accuracy, and one physical artefact. The artefact is the international prototype kilogram, certified in 1889, and consisting of a cylinder of platinum-iridium, which nominally has the same mass as one litre of water at the freezing point. Its stability has been a matter of significant concern, culminating in a revision of the definition of the base units entirely in terms of constants of nature, scheduled to be put into effect on 20 May 2019.Derived units may be defined in terms of base units or other derived units. They are adopted to facilitate measurement of diverse quantities. The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves. The most recent derived unit, the katal, was defined in 1999.

The reliability of the SI depends not only on the precise measurement of standards for the base units in terms of various physical constants of nature, but also on precise definition of those constants. The set of underlying constants is modified as more stable constants are found, or may be more precisely measured. For example, in 1983 the metre was redefined as the distance that light propagates in vacuum in a given fraction of a second, thus making the value of the speed of light in terms of the defined units exact.

The motivation for the development of the SI was the diversity of units that had sprung up within the centimetre–gram–second (CGS) systems (specifically the inconsistency between the systems of electrostatic units and electromagnetic units) and the lack of coordination between the various disciplines that used them. The General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM), which was established by the Metre Convention of 1875, brought together many international organisations to establish the definitions and standards of a new system and standardise the rules for writing and presenting measurements. The system was published in 1960 as a result of an initiative that began in 1948. It is based on the metre–kilogram–second system of units (MKS) rather than any variant of the CGS. Since then, the SI has been adopted by all countries except the United States, Liberia and Myanmar.

Introduction to the metric system

The metric system was developed during the French Revolution to replace the various measures previously used in France. The metre (sometimes spelled "meter" in American English) is the unit of length in the metric system and was originally based on the dimensions of the earth, as far as it could be measured at the time. The litre (also spelled "liter"), is the unit of volume and was defined as one thousandth of a cubic metre. The metric unit of mass is the kilogram and it was defined as the mass of one litre of water. The metric system was, in the words of French philosopher Marquis de Condorcet, "for all people for all time".The metric system has names to cover different ranges of the same measure. Instead of using names based on the context of the measure, the metric system mainly uses names made by adding prefixes, such as kilo- or milli-, as decimal multipliers to the base unit names. Thus, one kilogram is 1000 grams and one kilometre is 1000 metres.

During the nineteenth century the metric system was adopted by both the worldwide scientific community and many countries as the system of measurement. It therefore became truly international. Until 1875 the French government owned the prototype metre and kilogram, but in that year the Convention of the metre was signed and control of the standards relating to mass and length passed on to a trio of inter-government organisations.

In 1960 the metric system was extensively revised to form the International System of Units, abbreviated to SI.

Litre

The litre (international spelling) or liter (American spelling) (symbols L, l or ℓ) is an SI accepted metric system unit of volume equal to 1 cubic decimetre (dm3), 1,000 cubic centimetres (cm3) or 1/1,000 cubic metre. A cubic decimetre (or litre) occupies a volume of 10 cm×10 cm×10 cm (see figure) and is thus equal to one-thousandth of a cubic metre.

The original French metric system used the litre as a base unit. The word litre is derived from an older French unit, the litron, whose name came from Greek — where it was a unit of weight, not volume — via Latin, and which equalled approximately 0.831 litres. The litre was also used in several subsequent versions of the metric system and is accepted for use with the SI, although not an SI unit — the SI unit of volume is the cubic metre (m3). The spelling used by the International Bureau of Weights and Measures is "litre", a spelling which is shared by almost all English-speaking countries. The spelling "liter" is predominantly used in American English.One litre of liquid water has a mass of almost exactly one kilogram, because the kilogram was originally defined in 1795 as the mass of one cubic decimetre of water at the temperature of melting ice. Subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact.

Luxembourgian units of measurement

Metric System has been compulsory as the system of measurement in Luxembourg since 1820.

Malagasy units of measurement

A number of units of measurement were used in Madagascar to measure length, mass, capacity, etc. The Metric system was introduced in Madagascar in 1897.

Metric prefix

A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. While all metric prefixes in common use today are decadic, historically there have been a number of binary metric prefixes as well. Each prefix has a unique symbol that is prepended to the unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand: one kilogram is equal to one thousand grams. The prefix milli-, likewise, may be added to metre to indicate division by one thousand; one millimetre is equal to one thousandth of a metre.

Decimal multiplicative prefixes have been a feature of all forms of the metric system, with six dating back to the system's introduction in the 1790s. Metric prefixes have even been prepended to non-metric units. The SI prefixes are standardized for use in the International System of Units (SI) by the International Bureau of Weights and Measures (BIPM) in resolutions dating from 1960 to 1991. Since 2009, they have formed part of the International System of Quantities.

Metrication

Metrication or metrification is conversion to the metric system of units of measurement. Worldwide, there has been a long process of independent conversions of countries from various local and traditional systems, beginning in France during the 1790s and spreading widely over the following two centuries, but the metric system has not been fully adopted in all countries and sectors.

Metrication in the United States

Metrication (or metrification) is the process of introducing the International System of Units, also known as SI units or the metric system, to replace a jurisdiction's traditional measuring units. Although U.S. customary units have been defined in terms of metric units since the 19th century, as of 2018 the United States is one of only seven countries, including Myanmar (Burma), Liberia, Palau, the Marshall Islands, the Federated States of Micronesia, and Samoa that have not officially adopted the metric system as the primary means of weights and measures.

The United States has official legislation for metrication; however, conversion was not mandatory and many industries chose not to convert, and unlike other countries, there is no government or major social desire to implement further metrication. The microstates of Federated States of Micronesia, Marshall Islands and Palau, have not metricated due to their close relationship as associated states to the United States.Although customary units are used more often than metric units in the U.S., the SI system is used extensively in some fields such as science, medicine, the military, automobile production and repair, and international affairs. Post 1994 federal law also mandates most packaged consumer goods be labeled in both customary and metric units.

Microgram

In the metric system, a microgram or microgramme (μg; the recommended symbol in the United States when communicating medical information is mcg) is a unit of mass equal to one millionth (1×10−6) of a gram. The unit symbol is μg according to the International System of Units. In μg the prefix symbol for micro- is the Greek letter μ (Mu).

Millimetre

The millimetre (international spelling as used by the International Bureau of Weights and Measures; SI unit symbol mm) or millimeter (American spelling) is a unit of length in the metric system, equal to one thousandth of a metre, which is the SI base unit of length. Therefore, there are one thousand millimetres in a metre. There are ten millimetres in a centimetre.

One millimetre is equal to 1000 micrometres or 1000000 nanometres. A millimetre is equal to exactly ​5⁄127 (approximately 0.039370) of an inch.

Myanmar units of measurement

The traditional Burmese units of measurement are still in everyday use in Myanmar (also known as Burma). According to the CIA Factbook, Myanmar is one of three countries that have not adopted the International System of Units (SI) metric system as their official system of weights and measures. However, in June 2011, the Burmese government's Ministry of Commerce began discussing proposals to reform the measurement system in Burma and adopt the metric system used by most of its trading partners, and in October 2013, Dr. Pwint San, Deputy Minister for Commerce, announced that the country was preparing to adopt the metric system.Most of the nation uses Burmese units only, although Burmese government web pages in English use imperial and metric units inconsistently. For instance, the Ministry of Construction uses miles to describe the length of roads and square feet for the size of houses, but square kilometres for the total land area of new town developments in Yangon City. The Ministry of Agriculture uses acres for land areas. The Ministry of Foreign Affairs uses kilometres (with mile equivalents in parentheses) to describe the dimensions of the country.

Outline of the metric system

The following outline is provided as an overview of and topical guide to the metric system – various loosely related systems of measurement that trace their origin to the decimal system of measurement introduced in France during the French Revolution.

Peruvian units of measurement

A number of units of measurement were used in Peru to measure length, mass, area, etc. The Metric system adopted in 1862 and has been compulsory since 1869 in Peru.

System of measurement

A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement in use include the International System of Units (SI), the modern form of the metric system, the imperial system, and United States customary units.

Uruguayan units of measurement

A number of units of measurement were used in Uruguay to measure quantities. Metric system was optional in Uruguay since 1866, and has been compulsory since 1894.

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