Metric system

Short description: Decimal-based systems of measurement

A kilogram mass and three metric measuring devices: a tape measure in centimetres, a thermometer in degrees Celsius, and a multimeter that measures potential in volts, current in amperes and resistance in ohms.

The metric system is a system of measurement that standardises a set of base units and a nomenclature for describing relatively large and small quantities using decimal-based multiplicative unit prefixes. Though the rules governing the metric system have changed over time, the modern definition, the International System of Units (SI), defines the metric prefixes and seven base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).[1]

An SI derived unit is a named combination of base units, such as the hertz (cycles per second), newton (kg⋅m/s2), and tesla (1 kg⋅s−2⋅A−1). In the case of degrees Celsius, it is a shifted scale derived from the kelvin. Certain units have been officially accepted for use with the SI. Some of these are decimalised, like the litre and electronvolt, and are considered "metric". Others, like the astronomical unit are not. Ancient non-metric but SI-accepted multiples of time, minute and hour, are base 60 (sexagesimal). Similarly, the angular measure degree and submultiples, arcminute, and arcsecond, are also sexagesimal and SI-accepted.

The SI system derives from the older metre-kilogram-second (MKS) system of units, though the definitions of the base units have evolved over time. Today, all base units are defined by physical constants – not by prototypes in the form of physical objects, as they were in the past.

Other metric system variants include the centimetre–gram–second system of units, the metre–tonne–second system of units, and the gravitational metric system. Each has unaffiliated metric units. Some of these systems are still used in limited contexts.

## Contents

* 1 Adoption
* 2 Multiplicative prefixes
* 3 Base units
* 4 Attributes
* 4.1 Ease of learning and use
* 4.2 Extensibility
* 4.3 Realisation
* 4.4 Base and derived unit structure
* 4.5 Decimal ratios
* 4.6 Coherence
* 4.7 Rationalisation
* 5 Everyday notions
* 5.1 Time
* 5.2 Length
* 5.3 Mass
* 5.4 Temperature
* 5.5 Length, mass, volume relationship
* 5.6 Relationship between candela and watt
* 5.7 Relationship between watt, volt and ampere
* 5.8 Mole and mass relationship
* 6 History
* 6.1 17th & 18th centuries
* 6.2 19th century
* 6.3 20th century
* 6.4 Current
* 7 See also
* 8 References
* 9 External links

## Adoption

Units in everyday use by country as of 2019

The SI system has been adopted as the official system of weights and measures by most countries in the world.

A notable outlier is the United States (US). Although it uses the system in some contexts, the US has resisted full adoption, and continues to use different measurement systems.[2]

Adopting the metric system is known as metrication.

## Multiplicative prefixes

Main article: Metric prefix

In the SI system and generally in older metric systems, multiples and fractions of a unit can be described via a prefix on a unit name that implies a decimal (base-10), multiplicative factor. The only exceptions are for the SI-accepted units of time (minute and hour) and angle (degree, arcminute, arcsecond) which, based on ancient convention, use base-60 multipliers.[3]

Metric prefixes in everyday use

Text  | Symbol  | Factor  | Power
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
v * d * e

The prefix kilo, for example, implies a factor of 1000 (103), and the prefix milli implies a factor of 1/1000 (10−3). Thus, a kilometre is a thousand metres, and a milligram is one thousandth of a gram. These relations can be written symbolically as:[4]

1 km = 1000 m

1 mg = 0.001 g

## Base units

The decimalised system is based on the metre, which had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the International System of Units (SI) in the mid-20th century, under the oversight of an international standards body.

The historical evolution of metric systems has resulted in the recognition of several principles. A set of independent dimensions of nature is selected, in terms of which all natural quantities can be expressed, called base quantities. For each of these dimensions, a representative quantity is defined as a base unit of measure. The definition of base units has increasingly been realised in terms of fundamental natural phenomena, in preference to copies of physical artefacts. A unit derived from the base units is used for expressing quantities of dimensions that can be derived from the base dimensions of the system—e.g., the square metre is the derived unit for area, which is derived from length. These derived units are coherent, which means that they involve only products of powers of the base units, without any further factors. For any given quantity whose unit has a name and symbol, an extended set of smaller and larger units is defined that are related by factors of powers of ten. The unit of time should be the second; the unit of length should be either the metre or a decimal multiple of it; and the unit of mass should be the gram or a decimal multiple of it.

Metric systems have evolved since the 1790s, as science and technology have evolved, in providing a single universal measuring system. Before and in addition to the SI, other metric systems include: the MKS system of units and the MKSA systems, which are the direct forerunners of the SI; the centimetre–gram–second (CGS) system and its subtypes, the CGS electrostatic (cgs-esu) system, the CGS electromagnetic (cgs-emu) system, and their still-popular blend, the Gaussian system; the metre–tonne–second (MTS) system; and the gravitational metric systems, which can be based on either the metre or the centimetre, and either the gram, gram-force, kilogram or kilogram-force.

## Attributes

### Ease of learning and use

The metric system is intended to be 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 a coherent system with derived units built from base units using logical rather than empirical relationships and with multiples and submultiples of both units based on decimal factors and identified by a common set of prefixes.[5]: 15–18

### Extensibility

The metric system is extensible since the governing body reviews, modifies and extends it needs arise. For example, the katal, a derived unit for catalytic activity equivalent to one mole per second (1 mol/s), was added in 1999.[6]

### Realisation

See also: Physics:Realisation (metrology)

The base units used in a measurement system must be realisable. To that end, the definition of each SI base unit is accompanied by a mise en pratique (practical realisation) that describes at least one way that the unit can be measured.[7] 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.[8]

The metre was originally defined to be one ten millionth of the distance between the North Pole and the Equator through Paris.[9]

In 1791 the commission originally defined the metre based on the size of the earth, equal to one ten-millionth of the distance from the equator to the North Pole. In the SI, the standard metre is now defined as exactly ⁠+1/299,792,458⁠ of the distance that light travels in a second.[10][11] The metre can be realised by measuring the length that a light wave travels in a given time, or equivalently by measuring the wavelength of light of a known frequency.[12]

The kilogram was originally defined as the mass of one cubic decimetre of water at 4 °C, standardised as the mass of a man-made artefact of platinum–iridium held in a laboratory in France, which was used until a new definition was introduced 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 were subject to periodic validation by comparison to the original, called the IPK. It became apparent that either the IPK or the replicas or both were deteriorating, and are no longer comparable: they had diverged by 50 μg since fabrication, so figuratively, the accuracy of the kilogram was no better than 5 parts in a hundred million or a relative accuracy of 5×10−8. The revision of the SI replaced the IPK with an exact definition of the Planck constant as expressed in SI units, which defines the kilogram in terms of fundamental constants.[13][14][15]

### Base and derived unit structure

Main article: Base unit (measurement)

See also: SI derived unit

A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. A base unit is a unit adopted for expressing a base quantity. A derived unit is used for expressing any other quantity, and is a product of powers of base units. For example, in the modern metric system, length has the unit metre and time has the unit second, and speed has the derived unit metre per second.[5]: 15 Density, or mass per unit volume, has the unit kilogram per cubic metre.[5]: 434

### Decimal ratios

A significant characteristic of the metric system is its use of decimal multiples – powers of 10. For example, a length that is significantly longer or shorter than 1 metre can be represented in units that are a power of 10 or 1000 metres. This differs from many older systems in which the ratio of different units varied. For example, 12 inches is one foot, but the larger unit in the same system, the mile is not a power of 12 feet. It is 5,280 feet – which is hard to remember for many.[5]: 17

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]: 222–223 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.[4]

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

For the most part, the metric prefixes are used uniformly for SI base, derived and accepted units. A notable exception is that for a large measure of seconds, the non-SI units of minute, hour and day are customary instead. Units of duration longer than a day are problematic since both month and year have varying number of days. Sub-second measures are often indicated via submultiple prefixes. For example, millisecond.[4]

### Coherence

Main article: Coherence (units of measurement)

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 has been defined, other relationships in physics that use this set of 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.[20]

### Rationalisation

Maxwell's equations of electromagnetism contained a factor of 1/(4π) 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 made equations more awkward than necessary, and so Oliver Heaviside suggested adjusting the system of units to remove it.[21]

## Everyday notions

The basic units of the metric system have always represented commonplace quantities or relationships in nature, even with modern refinements of definition and methodology. In cases where laboratory precision may not be required or available, or where approximations are good enough, the commonplace notions may suffice.

### Time

The second is readily determined from the Earth's rotation period. Unlike other units, time multiples are not decimal. A second is ⁠1/60⁠ of a minute, which is ⁠1/60⁠ of an hour, which is ⁠1/24⁠ of a day, so a second is ⁠1/86400⁠ of a day.

### Length

The length of the equator is close to 40000000 m (more precisely 40075014.2 m).[22] In fact, the dimensions of our planet were used by the French Academy in the original definition of the metre.[23] A dining tabletop is typically about 0.75 metres high.[24] A very tall human is about 2 metres tall.[25]

### Mass

A 1-euro coin weighs 7.5 g;[26] a Sacagawea US 1-dollar coin weighs 8.1 g;[27] a UK 50-pence coin weighs 8.0 g.[28]

### Temperature

In everyday use, Celsius is more commonly used than Kelvin, however a temperature difference of one Kelvin is the same as one degree Celsius and that is defined as ⁠1/100⁠ of the temperature differential between the freezing and boiling points of water at sea level. A temperature in Kelvin is the temperature in Celsius plus about 273. Human body temperature is about 37 °C or 310 K.

### Length, mass, volume relationship

The mass of a litre of cold water is 1 kilogram. 1 millilitre of water occupies 1 cubic centimetre and weighs 1 gram.

### Relationship between candela and watt

Candela is about the luminous intensity of a moderately bright candle, or 1 candle power. A 60 Watt tungsten-filament incandescent light bulb has a luminous intensity of about 800 lumens[29] which is radiated equally in all directions (i.e. 4π steradians), thus is equal to Iv = ⁠800 lm/4π sr⁠ ≈ 64 cd.

### Relationship between watt, volt and ampere

A 60 W incandescent light bulb consumes 0.5 A at 120 V (US mains voltage). A 60 W bulb rated at 230 V (European mains voltage) consumes 0.26 A at this voltage. This is evident from the formula P = I V.

### Mole and mass relationship

A mole of a substance has a mass that is its molecular mass expressed in units of grams. The mass of a mole of carbon is 12.0 g, and the mass of a mole of table salt is 58.4 g.

Since all gases have the same volume per mole at a given temperature and pressure far from their points of liquefaction and solidification (see Perfect gas), and air is about ⁠1/5⁠ oxygen (molecular mass 32) and ⁠4/5⁠ nitrogen (molecular mass 28), the density of any near-perfect gas relative to air can be obtained to a good approximation by dividing its molecular mass by 29 (because ⁠4/5⁠ × 28 + ⁠1/5⁠ × 32 = 28.8 ≈ 29). For example, carbon monoxide (molecular mass 28) has almost the same density as air.

## History

The metric system was the result of multiple attempts at standardisation of weights and measures over many centuries, as earlier (Chinese, Egyptian, Greek, Roman, and other) systems of weights and measures interacted with one another through global trade.

### 17th & 18th centuries

Around 1665–1670, Gabriel Mouton, a priest of the Collegiate Church of St Paul in Lyon, France, suggested that the many different systems of units then in use in France should be replaced by a single all-embracing decimal system. He proposed that linear measurements would be based on a natural standard of length, namely the length of one minute of arc of the largest circle that could be drawn round the Earth, and which he proposed to call one milliare. Mouton suggested that the unit of mass should be based on the unit of length, and on the mass density of water. While Mouton's contribution is sometimes overlooked, these ideas were clearly the basis over 120 years later, when the metric system was devised and standardised in France.[30]: 140–142 During the final days of France's Ancien régime (1775-1788) and the early days of the French Revolution (1789–99), the first metric system was devised by chemists Antoine and Anne-Marie Lavoisier for the benefit of the Ferme générale in return for financial support of Antoine Lavoisier's research.

Following the model established by Mouton, Lavoisier's unit of length, the metre, was based on the dimensions of the Earth, and the unit of mass, the kilogram, was based on the mass of 1 litre of water (the volume of water which occupies 1 cubic decimetre of space, using the same unit of length).[30]: 140–142

Pavillon de Breteuil, Saint-Cloud, France, the home of the metric system's Mètre des Archives and Kilogramme des Archives since 1875

The backwardness of the Ancien Régime left France with a need to reform its numerous systems of various local weights and measures. In 1790, Charles Maurice de Talleyrand-Périgord proposed Lavoisier's system based on natural units to the French National Assembly, without reference to the prior work of Mouton and Lavoisier. The aim was global adoption of the metric system. With the United Kingdom not responding to requests to collaborate in the development of the system, the French Academy of Sciences established a commission to implement this new standard alone, and in 1799, the new system was launched in France.[30]: 145–149

A number of different metric systems have since been developed, 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  Measure  | SI/MKS  | CGS | MTS

|
|
|

distance | metre
(m)  | centimetre
(cm)  | metre
(m)
mass | kilogram
(kg)  | gram
(g)  | tonne
(t)
time | second
(s)  | second
(s)  | second
(s)
velocity | m/s  | cm/s  | m/s
acceleration | m/s2 | gal
(Gal) | m/s2
force | newton (N) | dyne
(dyn)  | sthene
(sn)
pressure | pascal (Pa) | barye
(Ba)  | pièze
(pz)
energy | joule
(J)  | erg
(erg)  | kilojoule
(kJ)
power | watt
(W)  | erg/s
(erg/s)  | kilowatt
(kW)
viscosity | Pa⋅s  | poise
(P)  | pz⋅s

### 19th century

In 1832, Gauss used the astronomical second as a base unit in defining the gravitation of the Earth, and together with the milligram and millimetre, this became the first system of mechanical units. He showed that the strength of a magnet could also be quantified in terms of these units, by measuring the oscillations of a magnetised needle and finding the quantity of "magnetic fluid" that produces an acceleration of one unit when applied to a unit mass.[31][32] The centimetre–gram–second system of units (CGS) was the first coherent metric system, having been developed in the 1860s and promoted by James Clerk Maxwell and Lord Kelvin. In 1874, this system was formally promoted by the British Association for the Advancement of Science (BAAS).[33] 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 Association also recognised two sets of units for electrical and magnetic properties – the electrostatic set of units and the electromagnetic set of units.[34]

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, in the International System of Electrical and Magnetic Units.[35] During the same period in which the CGS system was being extended to include electromagnetism, other systems were developed, distinguished by their choice of coherent base unit, including the Practical System of Electric Units, or QES (quad–eleventhgram–second) system. Here, the base units are the quad, equal to 107 m (approximately a quadrant of the Earth's circumference), the eleventhgram, equal to 10−11 g, and the second. These were chosen so that the corresponding electrical units of potential difference, current and resistance had a convenient magnitude.[36]: 268 [37]: 17

### 20th century

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.[38][21]

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.[39][40] 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 Masseneinheit (TME), mug or metric slug.[41] 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).[42]

### Current

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.[20] 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 modelled on those from the older CGS system, but scaled to be coherent with MKSA units. Two additional base units – the kelvin, which is equivalent to degree Celsius for change in thermodynamic temperature but set so that 0 K is absolute zero, and the candela, which is roughly equivalent to the international candle unit of illumination – were introduced. Later, another base unit, the mole, a unit of amount of substance equivalent to the Avogadro number number of specified molecules, was added along with several other derived units.[43]

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 atom (krypton-86 being a stable isotope of an inert gas that occurs in undetectable or trace amounts naturally), and the standard metre artefact from 1889 was retired.[5]: 16

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. All the base units except the second are now defined in terms of exact and invariant constants of physics or mathematics, barring those parts of their definitions which are dependent on the second itself. As a consequence, the speed of light has now become an exactly defined constant, and defines the metre as ​1⁄299,792,458 of the distance light travels in a second. The kilogram was defined by a cylinder of platinum-iridium alloy until a new definition in terms of natural physical constants was adopted in 2019. As of 2022, the range of decimal prefixes has been extended to those for 1030 (quetta–) and 10−30 (quecto–).[44]

## See also

* Binary prefix - Prefix indicating a power of two
* Electrostatic units
* History of measurement
* ISO 31
* ISO/IEC 80000
* List of metric units - Class of units of measurement
* Metrology - Science of measurement and its application
* Outline of metrology and measurement - Topical index of English Wikipedia articles about metrology and measurement
* Preferred metric sizes - Metricated industry standards
* Unified Code for Units of Measure - System of codes for unambiguously representing measurement units

## References

1. ↑ "The International System of Units (SI), 9th Edition". Bureau International des Poids et Mesures. 2019. https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf.
2. ↑ Gullberg, Jan (1997). "2.4 Decimal Position System". Mathematics from the Birth of Numbers. New York and London: W. W. Norton and Company. p. 52. ISBN 978-0-393-04002-9.
3. ↑ "Non-SI units accepted for use with SI". 26 July 2018. https://metricsystem.net/non-si-units/accepted-for-use-with-si/.
4. ↑ 4.0 4.1 4.2 International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), pp. 121,122, ISBN 92-822-2213-6, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf
5. ↑ 5.0 5.1 5.2 5.3 5.4 Urone, Peter Paul; Hinrichs, Roger; Dirks, Kim; Sharma, Manjula (2020). College Physics. OpenStax. ISBN 978-1-947172-01-2. https://openstax.org/details/books/college-physics. Retrieved 2 July 2023.
6. ↑ Dybkær, René (2002-03-01). "The Tortuous Road to the Adoption of katal for the Expression of Catalytic Activity by the General Conference on Weights and Measures". Clinical Chemistry 48 (3): 586–590. doi:10.1093/clinchem/48.3.586. ISSN 0009-9147. PMID 11861460.
7. ↑ "What is a mise en pratique?". BIPM. 2011. http://www.bipm.org/en/si/new_si/mise-en-pratique.html.
8. ↑ "OIML Mutual Acceptance Arrangement (MAA)". International Organization of Legal Metrology. http://www.oiml.org/maa/.
9. ↑ Alder, Ken (2002). The Measure of all Things—The Seven-Year-Odyssey That Transformed the World. London: Abacus. ISBN 978-0-349-11507-8.
10. ↑ "17th General Conference on Weights and Measures (1983), Resolution 1.". https://www.bipm.org/en/committees/cg/cgpm/17-1983/resolution-1.
11. ↑ "Mise en pratique for the definition of the metre in the SI". 20 May 2019. https://www.bipm.org/documents/20126/41489670/SI-App2-metre.pdf/0e011055-9736-d293-5e56-b8b1b267fd68?version=1.8&t=1637238031486&download=false.
12. ↑ Lewis, A. (4 July 2019). "1983 realisation of the metre definition". Varenna Summer School. National Physical Laboratory. p. 15. https://static.sif.it/SIF/resources/public/files/va2019/Lewis2.pdf. Retrieved 10 July 2023.
13. ↑ "The Latest: Landmark Change to Kilogram Approved". Associated Press. 16 November 2018. https://apnews.com/e6991383703e4ad5a9570d97b0e57822.
14. ↑ "Mise en pratique for the definition of the kilogram in the SI". 7 July 2021. https://www.bipm.org/documents/20126/41489673/SI-App2-kilogram.pdf/5881b6b5-668d-5d2b-f12a-0ef8ca437176?version=1.9&t=1637237674882&download=false.
15. ↑ Resnick, Brian (20 May 2019). "The new kilogram just debuted. It's a massive achievement.". Vox. https://www.vox.com/science-and-health/2019/5/17/18627757/kilogram-redefined-world-metrology-day-explained.
16. ↑ McGreevy, Thomas (1997). Cunningham, Peter. ed. The Basis of Measurement: Volume 2—Metrication and Current Practice. Chippenham: Picton Publishing. ISBN 978-0-948251-84-9.
17. ↑ Brewster, D. (1830). The Edinburgh Encyclopædia. p. 494. https://archive.org/details/edinburghencyclo07brew.
18. ↑ 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) (3rd ed.), International Bureau of Weights and Measures (BIPM) on behalf of the Joint Committee for Guides in Metrology, 1.12, http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf, retrieved 12 April 2012
19. ↑ Good, Michael. "Some Derivations of E = mc2". http://www.unc.edu/~mgood/research/RestEnergy.pdf.
20. ↑ 20.0 20.1 International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), pp. 111–120, ISBN 92-822-2213-6, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf
21. ↑ 21.0 21.1 Jayson, Joel S. (January 2014). "The Daniell cell, Ohm's law, and the emergence of the International System of Units" (in en). American Journal of Physics 82 (1): 60–65. doi:10.1119/1.4826445. ISSN 0002-9505. Bibcode: 2014AmJPh..82...60J. https://pubs.aip.org/aapt/ajp/article/82/1/60-65/1058039.
22. ↑ Science, Tim Sharp 2017-09-15T15:47:00Z; Astronomy. "How Big Is Earth?". https://www.space.com/17638-how-big-is-earth.html.
23. ↑ "Metre | measurement". https://www.britannica.com/science/metre-measurement.
24. ↑ "Standard Table Sizes". https://www.bassettfurniture.com/blog/standard-table-sizes.aspx.
25. ↑ "The Average Height of NBA Players – From Point Guards to Centers". 9 December 2018. https://www.thehoopsgeek.com/average-nba-height/.
26. ↑ "RUBINGHSCIENCE.ORG / Using Euro coins as weights". http://www.rubinghscience.org/surv/euroweights1.html.
27. ↑ "Coin Specifications | U.S. Mint". 20 September 2016. https://www.usmint.gov/learn/coin-and-medal-programs/coin-specifications.
28. ↑ "Fifty Pence Coin". https://www.royalmint.com/discover/uk-coins/coin-design-and-specifications/fifty-pence-coin/.
29. ↑ "Lumens and the Lighting Facts Label" (in en). https://www.energy.gov/energysaver/save-electricity-and-fuel/lighting-choices-save-you-money/lumens-and-lighting-facts.
30. ↑ 30.0 30.1 30.2 McGreevy, Thomas (1995). Cunningham, Peter. ed. The Basis of Measurement: Volume 1—Historical Aspects. Chippenham: Picton Publishing. ISBN 978-0-948251-82-5.
31. ↑ O'Hara, James Gabriel (1983). "Gauss and the Royal Society: The Reception of His Ideas on Magnetism in Britain (1832-1842)". Notes and Records of the Royal Society of London 38 (1): 17–78. doi:10.1098/rsnr.1983.0002. ISSN 0035-9149. https://www.jstor.org/stable/531344. Retrieved 26 June 2023.
32. ↑ Van Baak, D. A. (October 2013). "Re-creating Gauss's method for non-electrical absolute measurements of magnetic fields and moments" (in en). American Journal of Physics 81 (10): 738–744. doi:10.1119/1.4816806. ISSN 0002-9505. Bibcode: 2013AmJPh..81..738V. https://pubs.aip.org/aapt/ajp/article/81/10/738-744/1057517.
33. ↑ International Bureau of Weights and Measures (2006), The International System of Units (SI) (8th ed.), p. 109, ISBN 92-822-2213-6, http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf
34. ↑ Thomson, William; Joule, James Prescott; Maxwell, James Clerk; Jenkin, Flemming (1873). "First Report – Cambridge 3 October 1862". in Jenkin, Flemming. Reports on the Committee on Standards of Electrical Resistance – Appointed by the British Association for the Advancement of Science. London. pp. 1–3. https://archive.org/stream/reportscommitte00maxwgoog. Retrieved 12 May 2011.
35. ↑ "Historical context of the SI—Unit of electric current (ampere)". The NIST Reference on Constants, Units and Uncertainty. http://physics.nist.gov/cuu/Units/ampere.html.
36. ↑ James Clerk Maxwell (1954), A Treatise on Electricity & Magnetism, 2 (3rd ed.), Dover Publications
37. ↑ Carron, Neal (2015). "Babel of Units. The Evolution of Units Systems in Classical Electromagnetism". arXiv:1506.01951 [physics.hist-ph].
38. ↑ "In the beginning... Giovanni Giorgi". International Electrotechnical Commission. 2011. http://www.iec.ch/about/history/beginning/giovanni_giorgi.htm.
39. ↑ "System of Measurement Units". IEEE Global History Network. Institute of Electrical and Electronics Engineers (IEEE). http://www.ieeeghn.org/wiki/index.php/System_of_Measurement_Units.
40. ↑ "Notions de physique – Systèmes d'unités" (in fr). Hydrelect.info. http://www.hydrelect.info/articles.php?lng=fr&pg=3.
41. ↑ Michon, Gérard P (9 September 2000). "Final Answers". Numericana.com. http://www.numericana.com/answer/units.htm#slug.
42. ↑ "Resolution of the 3rd meeting of the CGPM (1901)". General Conference on Weights and Measures. http://www.bipm.org/en/CGPM/db/3/2/.
43. ↑ IUPAC Gold Book. IUPAC – mole (M03980). International Union of Pure and Applied Chemistry. doi:10.1351/goldbook.M03980. https://goldbook.iupac.org/terms/view/M03980. Retrieved 10 July 2023.
44. ↑ "New SI prefixes clear the way for quettabytes of storage". The Register. 22 November 2022. https://www.theregister.com/2022/11/22/new_si_prefixes_clear_the/.

## External links

* v
* t
* e

French Revolution

* Causes
* Timeline
* Ancien Régime
* Revolution
* Constitutional monarchy
* Republic
* Directory
* Consulate
* Glossary
* Journals
* Museum

Significant civil and political events by year

1788|

* Day of the Tiles (7 Jun 1788)
* Assembly of Vizille (21 Jul 1788)

1789|

* What Is the Third Estate? (Jan 1789)
* Réveillon riots (28 Apr 1789)
* Convocation of the Estates General (5 May 1789)
* Death of the Dauphin (4 June 1789)
* National Assembly (17 Jun – 9 Jul 1790)
* Tennis Court Oath (20 Jun 1789)
* National Constituent Assembly (9 Jul – 30 Sep 1791)
* Storming of the Bastille (14 Jul 1789)
* Great Fear (20 Jul – 5 Aug 1789)
* Abolition of Feudalism (4-11 Aug 1789)
* Declaration of the Rights of Man and of the Citizen (27 Aug 1789)
* Women's March on Versailles (5 Oct 1789)

1790|

* Abolition of the Parlements (Feb–Jul 1790)
* Abolition of the Nobility (19 Jun 1790)
* Civil Constitution of the Clergy (12 Jul 1790)
* Fête de la Fédération (14 Jul 1790)

1791|

* Flight to Varennes (20–21 Jun 1791)
* Champ de Mars massacre (17 Jul 1791)
* Declaration of Pillnitz (27 Aug 1791)
* The Constitution of 1791 (3 Sep 1791)
* National Legislative Assembly (1 Oct 1791 – Sep 1792)

1792|

* France declares war (20 Apr 1792)
* Brunswick Manifesto (25 Jul 1792)
* Paris Commune becomes insurrectionary (Jun 1792)
* 10th of August (10 Aug 1792)
* September Massacres (Sep 1792)
* National Convention (20 Sep 1792 – 26 Oct 1795)
* First republic declared (22 Sep 1792)

1793|

* Execution of Louis XVI (21 Jan 1793)
* Revolutionary Tribunal (9 Mar 1793 – 31 May 1795)
* Reign of Terror (27 Jun 1793 – 27 Jul 1794)
* Committee of Public Safety
* Committee of General Security
* Fall of the Girondists (2 Jun 1793)
* Assassination of Marat (13 Jul 1793)
* Levée en masse (23 Aug 1793)
* The Death of Marat (painting)
* Law of Suspects (17 Sep 1793)
* Marie Antoinette is guillotined (16 Oct 1793)
* Anti-clerical laws (throughout the year)

1794|

* Danton and Desmoulins guillotined (5 Apr 1794)
* Law of 22 Prairial (10 Jun 1794)
* Thermidorian Reaction (27 Jul 1794)
* Robespierre guillotined (28 Jul 1794)
* White Terror (Fall 1794)
* Closing of the Jacobin Club (11 Nov 1794)

1795–6|

* Constitution of the Year III (22 Aug 1795)
* Directoire (1795–99)
* Council of Five Hundred
* Council of Ancients
* 13 Vendémiaire 5 Oct 1795
* Conspiracy of the Equals (May 1796)

1797|

* Coup of 18 Fructidor (4 Sep 1797)
* Second Congress of Rastatt (Dec 1797)

1799|

* Coup of 30 Prairial VII (18 Jun 1799)
* Coup of 18 Brumaire (9 Nov 1799)
* Constitution of the Year VIII (24 Dec 1799)
* Consulate

Revolutionary campaigns

1792|

* Verdun
* Thionville
* Valmy
* Royalist Revolts
* Chouannerie
* Vendée
* Dauphiné
* Lille
* Siege of Mainz
* Jemappes
* Namur [fr; fr; Siège de Namur (1792)]

1793|

* First Coalition
* War in the Vendée
* Battle of Neerwinden)
* Battle of Famars (23 May 1793)
* Expedition to Sardinia (21 Dec 1792 - 25 May 1793)
* Battle of Kaiserslautern
* Siege of Mainz
* Battle of Wattignies
* Battle of Hondschoote
* Siege of Bellegarde
* Battle of Peyrestortes (Pyrenees)
* Siege of Toulon (18 Sep – 18 Dec 1793)
* First Battle of Wissembourg (13 Oct 1793)
* Battle of Truillas (Pyrenees)
* Second Battle of Wissembourg (26–27 Dec 1793)

1794|

* Battle of Villers-en-Cauchies (24 Apr 1794)
* Second Battle of Boulou (Pyrenees) (30 Apr – 1 May 1794)
* Battle of Tourcoing (18 May 1794)
* Battle of Tournay (22 May 1794)
* Battle of Fleurus (26 Jun 1794)
* Chouannerie
* Battle of Aldenhoven (2 Oct 1794)

1795|

* Peace of Basel

1796|

* Battle of Lonato (3–4 Aug 1796)
* Battle of Castiglione (5 Aug 1796)
* Battle of Theiningen
* Battle of Neresheim (11 Aug 1796)
* Battle of Amberg (24 Aug 1796)
* Battle of Würzburg (3 Sep 1796)
* Battle of Rovereto (4 Sep 1796)
* First Battle of Bassano (8 Sep 1796)
* Battle of Emmendingen (19 Oct 1796)
* Battle of Schliengen (26 Oct 1796)
* Second Battle of Bassano (6 Nov 1796)
* Battle of Calliano (6–7 Nov 1796)
* Battle of Arcole (15–17 Nov 1796)
* Ireland expedition (Dec 1796)

1797|

* Naval Engagement off Brittany (13 Jan 1797)
* Battle of Rivoli (14–15 Jan 1797)
* Battle of the Bay of Cádiz (25 Jan 1797)
* Treaty of Leoben (17 Apr 1797)
* Battle of Neuwied (18 Apr 1797)
* Treaty of Campo Formio (17 Oct 1797)

1798|

* French invasion of Switzerland (28 January – 17 May 1798)
* French Invasion of Egypt (1798–1801)
* Irish Rebellion of 1798 (23 May – 23 Sep 1798)
* Quasi-War (1798–1800)
* Peasants' War (12 Oct – 5 Dec 1798)

1799|

* Second Coalition (1798–1802)
* Siege of Acre (20 Mar – 21 May 1799)
* Battle of Ostrach (20–21 Mar 1799)
* Battle of Stockach (25 Mar 1799)
* Battle of Magnano (5 Apr 1799)
* Battle of Cassano (27 Apr 1799)
* First Battle of Zurich (4–7 Jun 1799)
* Battle of Trebbia (19 Jun 1799)
* Battle of Novi (15 Aug 1799)
* Second Battle of Zurich (25–26 Sep 1799)

1800|

* Battle of Marengo (14 Jun 1800)
* Convention of Alessandria (15 Jun 1800)
* Battle of Hohenlinden (3 Dec 1800)
* League of Armed Neutrality (1800–02)

1801|

* Treaty of Lunéville (9 Feb 1801)
* Treaty of Florence (18 Mar 1801)
* Algeciras campaign (8 Jul 1801)

1802|

* Treaty of Amiens (25 Mar 1802)

Military leaders

French Army|

* Eustache Charles d'Aoust
* Pierre Augereau
* Alexandre de Beauharnais
* Jean-Baptiste Bernadotte
* Louis-Alexandre Berthier
* Jean-Baptiste Bessières
* Guillaume Brune
* Jean François Carteaux
* Jean-Étienne Championnet
* Chapuis de Tourville
* Adam Philippe, Comte de Custine
* Louis-Nicolas Davout
* Louis Desaix
* Jacques François Dugommier
* Thomas-Alexandre Dumas
* Charles François Dumouriez
* Pierre Marie Barthélemy Ferino
* Louis-Charles de Flers
* Paul Grenier
* Emmanuel de Grouchy
* Jacques Maurice Hatry
* Lazare Hoche
* Jean-Baptiste Jourdan
* François Christophe de Kellermann
* Jean-Baptiste Kléber
* Pierre Choderlos de Laclos
* Jean Lannes
* Charles Leclerc
* Claude Lecourbe
* François Joseph Lefebvre
* Jacques MacDonald
* Jean-Antoine Marbot
* Marcellin Marbot
* François Séverin Marceau
* Auguste de Marmont
* André Masséna
* Bon-Adrien Jeannot de Moncey
* Jean Victor Marie Moreau
* Édouard Mortier, Duke of Trévise
* Joachim Murat
* Michel Ney
* Pierre-Jacques Osten [fr; fr]
* Nicolas Oudinot
* Catherine-Dominique de Pérignon
* Jean-Charles Pichegru
* Józef Poniatowski
* Laurent de Gouvion Saint-Cyr
* Barthélemy Louis Joseph Schérer
* Jean-Mathieu-Philibert Sérurier
* Joseph Souham
* Jean-de-Dieu Soult
* Louis-Gabriel Suchet
* Belgrand de Vaubois
* Claude Victor-Perrin, Duc de Belluno

French Navy|

* Charles-Alexandre Linois

Opposition|

|  Austria|

* József Alvinczi
* Archduke Charles, Duke of Teschen
* Count of Clerfayt (Walloon)
* Karl Aloys zu Fürstenberg
* Friedrich Freiherr von Hotze (Swiss)
* Friedrich Adolf, Count von Kalckreuth
* Pál Kray (Hungarian)
* Charles Eugene, Prince of Lambesc (French)
* Maximilian Baillet de Latour (Walloon)
* Karl Mack von Leiberich
* Rudolf Ritter von Otto (Saxon)
* Prince Josias of Saxe-Coburg-Saalfeld
* Peter Vitus von Quosdanovich
* Prince Heinrich XV of Reuss-Plauen
* Johann Mészáros von Szoboszló (Hungarian)
* Karl Philipp Sebottendorf
* Dagobert von Wurmser

|

Kingdom of Great Britain Britain|

* Sir Ralph Abercromby
* Admiral Sir James Saumarez
* Admiral Sir Edward Pellew
* Prince Frederick, Duke of York and Albany

Dutch Republic|

* William V, Prince of Orange

Prussia|

* Charles William Ferdinand, Duke of Brunswick
* Frederick Louis, Prince of Hohenlohe-Ingelfingen

Russian Empire Russia|

* Alexander Korsakov
* Alexander Suvorov

Spain|

* Luis Firmin de Carvajal
* Antonio Ricardos

Other significant figures and factions

Patriotic Society of 1789|

* Jean Sylvain Bailly
* Gilbert du Motier, Marquis de Lafayette
* François Alexandre Frédéric, duc de la Rochefoucauld-Liancourt
* Isaac René Guy le Chapelier
* Honoré Gabriel Riqueti, comte de Mirabeau
* Emmanuel Joseph Sieyès
* Charles Maurice de Talleyrand-Périgord
* Nicolas de Condorcet

Feuillants
and monarchiens

* Madame de Lamballe
* Madame du Barry
* Louis de Breteuil
* Loménie de Brienne
* Charles Alexandre de Calonne
* de Chateaubriand
* Jean Chouan
* Grace Elliott
* Arnaud de La Porte
* Jean-Sifrein Maury
* Jacques Necker
* François-Marie, marquis de Barthélemy
* Guillaume-Mathieu Dumas
* Antoine Barnave
* Lafayette
* Alexandre-Théodore-Victor, comte de Lameth
* Charles Malo François Lameth
* André Chénier
* Jean-François Rewbell
* Camille Jordan
* Madame de Staël
* Boissy d'Anglas
* Jean-Charles Pichegru
* Pierre Paul Royer-Collard
* Bertrand Barère de Vieuzac

Girondins|

* Jacques Pierre Brissot
* Jean-Marie Roland de la Platière
* Madame Roland
* Father Henri Grégoire
* Étienne Clavière
* Marquis de Condorcet
* Charlotte Corday
* Marie Jean Hérault
* Jean Baptiste Treilhard
* Pierre Victurnien Vergniaud
* Jérôme Pétion de Villeneuve
* Jean Debry
* Jean-Jacques Duval d'Eprémesnil
* Olympe de Gouges
* Jean-Baptiste Robert Lindet
* Louis Marie de La Révellière-Lépeaux

The Plain|

* Abbé Sieyès
* de Cambacérès
* Charles-François Lebrun
* Pierre-Joseph Cambon
* Bertrand Barère
* Lazare Nicolas Marguerite Carnot
* Philippe Égalité
* Louis Philippe I
* Mirabeau
* Antoine Christophe Merlin de Thionville
* Jean Joseph Mounier
* Pierre Samuel du Pont de Nemours
* François de Neufchâteau

Montagnards|

* Maximilien Robespierre
* Georges Danton
* Jean-Paul Marat
* Camille Desmoulins
* Louis Antoine de Saint-Just
* Paul Barras
* Louis Philippe I
* Louis Michel le Peletier de Saint-Fargeau
* Jacques-Louis David
* Marquis de Sade
* Georges Couthon
* Roger Ducos
* Jean-Marie Collot d'Herbois
* Jean-Henri Voulland
* Philippe-Antoine Merlin de Douai
* Antoine Quentin Fouquier-Tinville
* Philippe-François-Joseph Le Bas
* Marc-Guillaume Alexis Vadier
* Jean-Pierre-André Amar
* Prieur de la Côte-d'Or
* Prieur de la Marne
* Gilbert Romme
* Jean Bon Saint-André
* Jean-Lambert Tallien
* Pierre Louis Prieur
* Antoine Christophe Saliceti

Hébertists
and Enragés|

* Jacques Hébert
* Jacques-Nicolas Billaud-Varenne
* Pierre Gaspard Chaumette
* Charles-Philippe Ronsin
* Antoine-François Momoro
* François-Nicolas Vincent
* François Chabot
* Jean Baptiste Noël Bouchotte
* Jean-Baptiste-Joseph Gobel
* François Hanriot
* Jacques Roux
* Stanislas-Marie Maillard
* Charles-Philippe Ronsin
* Jean-François Varlet
* Theophile Leclerc
* Claire Lacombe
* Pauline Léon
* Gracchus Babeuf
* Sylvain Maréchal

Others|

* Charles X
* Louis XVI
* Louis XVII
* Louis XVIII
* Louis Antoine, Duke of Enghien
* Louis Henri, Prince of Condé
* Louis Joseph, Prince of Condé
* Marie Antoinette
* Napoléon Bonaparte
* Lucien Bonaparte
* Joseph Bonaparte
* Joseph Fesch
* Empress Joséphine
* Joachim Murat
* Jean Sylvain Bailly
* Jacques-Donatien Le Ray
* Guillaume-Chrétien de Malesherbes
* Talleyrand
* Thérésa Tallien
* Gui-Jean-Baptiste Target
* Catherine Théot
* List of people associated with the French Revolution

Influential thinkers

* Les Lumières
* Beaumarchais
* Edmund Burke
* Anacharsis Cloots
* Charles-Augustin de Coulomb
* Pierre Claude François Daunou
* Diderot
* Benjamin Franklin
* Thomas Jefferson
* Antoine Lavoisier
* Montesquieu
* Thomas Paine
* Jean-Jacques Rousseau
* Abbé Sieyès
* Voltaire
* Mary Wollstonecraft

Cultural impact

* La Marseillaise
* Cockade of France
* Flag of France
* Liberté, égalité, fraternité
* Marianne
* Bastille Day
* Panthéon
* French Republican calendar
* Cult of the Supreme Being
* Cult of Reason
* Temple of Reason
* Sans-culottes
* Metric system
* Phrygian cap
* Women in the French Revolution
* Symbolism in the French Revolution
* Historiography of the French Revolution
* Influence of the French Revolution

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*[MTS]: Metre–tonne–second system of units
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