Metric system

Metre-based systems of measurement

For a topical guide, see Outline of the metric system.

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 succeeded the decimalised system based on the metre that 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. Adopting the metric system is known as metrication.

The historical evolution of metric systems has resulted in the recognition of several principles. Each of the fundamental dimensions of nature is expressed by a single base unit of measure. The definition of base units has increasingly been realised from natural principles, rather than by copies of physical artefacts. For quantities derived from the fundamental base units of the system, units derived from the base units are used—e.g., the square metre is the derived unit for area, a quantity derived from length. These derived units are coherent, which means that they involve only products of powers of the base units, without empirical factors. For any given quantity whose unit has a special 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, some other examples of metric systems are the following: 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(-force) or the kilogram(-force).

The SI 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.

## Contents

* 1 Background
* 2 Principles
* 2.1 Realisation
* 2.2 Base and derived unit structure
* 2.3 Decimal ratios
* 2.4 Prefixes for multiples and submultiples
* 2.5 Coherence
* 2.6 Rationalisation
* 3 Common metric systems
* 3.1 Gaussian second and the first mechanical system of units
* 3.2 Centimetre–gram–second systems
* 3.3 The EMU, ESU and Gaussian systems of electrical units
* 3.4 International System of Electrical and Magnetic Units
* 3.5 Other early electromagnetic systems of units
* 3.6 MKS and MKSA systems
* 3.7 Metre–tonne–second systems
* 3.8 Gravitational systems
* 3.9 International System of Units
* 4 See also
* 5 Notes
* 6 References
* 7 External links

## Background[edit | edit source]

Main articles: History of the metric system and metrication

Pavillon de Breteuil, Saint-Cloud, France, the home of the metric system since 1875

The French revolution (1789–99) provided an opportunity for the French to reform their unwieldy and archaic system of many local weights and measures. Charles Maurice de Talleyrand championed a new system based on natural units, proposing to the French National Assembly in 1790 that such a system be developed. Talleyrand had ambitions that a new natural and standardised system would be embraced worldwide, and was keen to involve other countries in its development. Great Britain ignored invitations to co-operate, so the French Academy of Sciences decided in 1791 to go it alone and they set up a commission for the purpose. The commission decided that the standard of length should be based on the size of the Earth. They defined that length to be the 'metre' and its length as one ten-millionth of the length of an Earth quadrant, the length of the meridian arc on the Earth's surface from the equator to the north pole. In 1799, after the arc measurement had been surveyed, the new system was launched in France.[1]: 145–149

The units of the metric system, originally taken from observable features of nature, are now defined by seven physical constants being given exact numerical values in terms of the units. In the modern form of the International System of Units (SI), the seven base units are: metre for length, kilogram for mass, second for time, ampere for electric current, kelvin for temperature, candela for luminous intensity and mole for amount of substance. These, together with their derived units, can measure any physical quantity. Derived units may have their own unit name, such as the watt (J/s) and lux (cd/m2), or may just be expressed as combinations of base units, such as velocity (m/s) and acceleration (m/s2).[2]

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 metric system is extensible, and new derived units are defined as needed in fields such as radiology and chemistry. For example, the katal, a derived unit for catalytic activity equivalent to one mole per second (1 mol/s), was added in 1999.

## Principles[edit | edit source]

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.

### Realisation[edit | edit source]

See also: Realisation (metrology)

The metre was originally defined to be one ten millionth of the distance between the North Pole and the Equator through Paris.[3]

The base units used in a measurement system must be realisable. Each of the definitions of the base units in the 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.[4] 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.[5]

In the SI, 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 a proportion of 0.3x10−8:1.

The kilogram was originally defined as the mass of one cubic decimetre of water at 4 °C, standardized 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 proportion of 5x10−8:1. The accepted redefinition of SI base units replaced the IPK with an exact definition of the Planck constant, which defines the kilogram in terms of the second and metre.

### Base and derived unit structure[edit | edit source]

Main article: Base unit (measurement)

See also: SI derived unit

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 inertia, 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 spatial 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 units of the newly established metric system, 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[edit | edit source]

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 1⁄4 pound or 1⁄3 foot. There was no system of notation for successive fractions: for example, 1⁄3 of 1⁄3 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 1⁄10 of 1⁄10 which is 1⁄100. So a decimal radix became the ratio between unit sizes of the metric system.

### Prefixes for multiples and submultiples[edit | edit source]

Main article: Metric prefix

In the metric system, multiples and submultiples of units follow a decimal pattern.[Note 1]

Metric prefixes in everyday use

* v
* t
* e

Prefix  | 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

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.[3]: 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:[6]

1 mg = 0.001 g

1 km = 1000 m

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.[1]: 222–223 During the 19th century the prefix myria-, derived from the Greek word μύριοι (mýrioi), was used as a multiplier for 10000.[7]

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.[6]

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).[6]

### Coherence[edit | edit source]

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.[8] 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.[9]

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.[10]

### Rationalisation[edit | edit source]

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.

##  Common metric systems[edit | edit source]

A number of different metric system have 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  Quantity  | SI/MKS | CGS | MTS

|
|
|

distance, displacement,

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

### Gaussian second and the first mechanical system of units[edit | edit source]

Main article: Gaussian 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.

### Centimetre–gram–second systems[edit | edit source]

Main article: centimetre–gram–second system of units

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).[11] 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.[12]

### The EMU, ESU and Gaussian systems of electrical units[edit | edit source]

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

### International System of Electrical and Magnetic Units[edit | edit source]

Main article: International System of Electrical and Magnetic 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.[13]

### Other early electromagnetic systems of units[edit | edit source]

Further information: History of the metric system § QES

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, was being used.[14]: 268 [15]: 17 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.

### MKS and MKSA systems[edit | edit source]

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.[16]

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.[10] The MKS (metre–kilogram–second) system came into existence in 1889, when artefacts for the metre and kilogram were fabricated according to the Metre Convention. 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[edit | edit source]

Main article: metre–tonne–second system of units

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.[17][18]

### Gravitational systems[edit | edit source]

Main article: Gravitational metric system

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.[19] 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).[20]

### International System of Units[edit | edit source]

Main articles: International System of Units and List of physical quantities

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|

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 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.

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 2] 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. 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. The range of decimal prefixes has been extended to those for 1024 (yotta–) and 10−24 (yocto–).

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. In the United States, the Metric Conversion Act of 1975 declared the metric system to be the "preferred system of weights and measures" but did not suspend use of customary units, and the United States is the only industrialised country where commercial and standards activities do not predominantly use the metric system.[21]

## See also[edit | edit source]

* Binary prefix, used in computer science
* Electrostatic units
* History of measurement
* ISO/IEC 80000, international standard of quantities and their units, superseding ISO 31
* Metric units
* Metrology
* Unified Code for Units of Measure
* International System of Units

## Notes[edit | edit source]

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

## References[edit | edit source]

1. ^ a b 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.
2. ^ "The International System of Units (SI), 9th Edition" (PDF). Bureau International des Poids et Mesures. 2019.
3. ^ a b Alder, Ken (2002). The Measure of all Things—The Seven-Year-Odyssey That Transformed the World. London: Abacus. ISBN 978-0-349-11507-8.
4. ^ "What is a mise en pratique?". BIPM. 2011. Retrieved 11 March 2011.
5. ^ "OIML Mutual Acceptance Arrangement (MAA)". International Organization of Legal Metrology. Archived from the original on 21 May 2013. Retrieved 23 April 2013.
6. ^ a b c International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), pp. 121, 122, ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
7. ^ Brewster, D (1830). The Edinburgh Encyclopædia. p. 494.
8. ^ 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, 1.12, retrieved 12 April 2012
9. ^ Good, Michael. "Some Derivations of E = mc2" (PDF). Archived from the original (PDF) on 7 November 2011. Retrieved 18 March 2011.
10. ^ a b 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 4 June 2021, retrieved 16 December 2021
11. ^ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 109, ISBN 92-822-2213-6, archived (PDF) from the original on 4 June 2021, retrieved 16 December 2021
12. ^ Thomson, William; Joule, James Prescott; Maxwell, James Clerk; Jenkin, Flemming (1873). "First Report – Cambridge 3 October 1862". In Jenkin, Flemming (ed.). Reports on the Committee on Standards of Electrical Resistance – Appointed by the British Association for the Advancement of Science. London. pp. 1–3. Retrieved 12 May 2011.
13. ^ "Historical context of the SI—Unit of electric current (ampere)". The NIST Reference on Constants, Units and Uncertainty. Retrieved 10 April 2011.
14. ^ James Clerk Maxwell (1954) [1891], A Treatise on Electricity & Magnetism, vol. 2 (3rd ed.), Dover Publications
15. ^ Carron, Neal (2015). "Babel of Units. The Evolution of Units Systems in Classical Electromagnetism". arXiv:1506.01951 [physics.hist-ph].
16. ^ "In the beginning... Giovanni Giorgi". International Electrotechnical Commission. 2011. Archived from the original on 15 May 2011. Retrieved 5 April 2011.
17. ^ "System of Measurement Units". IEEE Global History Network. Institute of Electrical and Electronics Engineers (IEEE). Retrieved 21 March 2011.
18. ^ "Notions de physique – Systèmes d'unités" [Symbols used in physics – units of measure] (in French). Hydrelect.info. Retrieved 21 March 2011.
19. ^ Michon, Gérard P (9 September 2000). "Final Answers". Numericana.com. Retrieved 11 October 2012.
20. ^ "Resolution of the 3rd meeting of the CGPM (1901)". General Conference on Weights and Measures. Retrieved 11 October 2012.
21. ^ "The World Factbook, References - Weights and Measures". Central Intelligence Agency. 2021. Retrieved 11 August 2021.

## External links[edit | edit source]

Wikiversity has learning resources about Using the Metric System

* CBC Radio Archives For Good Measure: Canada Converts to Metric

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French Revolution

* Causes
* Timeline
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* Revolution
* Constitutional monarchy
* Republic
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* Consulate
* Glossary
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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)
* Nationalization of the Church properties (2 Nov 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|

* Insurrection of 12 Germinal, Year III (1 Apr 1795)
* 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)

1798|

* Law of 22 Floréal Year VI (11 May 1798)

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]

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)
* Siege of Luxembourg (22 Nov 1794 - 7 Jun 1795)

1795|

* Siege of Luxembourg (22 Nov 1794 - 7 Jun 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)
* Treaty of Paris (25 Jun 1802)

Military leaders

France|

| 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
* Étienne 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]
* 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

|

Britain|

* Sir Ralph Abercromby
* James Saumarez, 1st Baron de Saumarez
* Edward Pellew, 1st Viscount Exmouth
* Prince Frederick, Duke of York and Albany

Netherlands|

* William V, Prince of Orange

Prussia|

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

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

* Grace Elliott
* Arnaud de La Porte
* Jean-Sifrein Maury
* 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
* 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|

| Figures|

* 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
* Madame de Lamballe
* Madame du Barry
* Louis de Breteuil
* de Chateaubriand
* Jean Chouan
* Loménie de Brienne
* Charles Alexandre de Calonne
* Jacques Necker
* Jean-Jacques Duval d'Eprémesnil
* List of people associated with the French Revolution

|

Factions|

* Jacobin
* Cordeliers
* Panthéon Club
* Social Club

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
* Metric system
* Declaration of the Rights of Man and of the Citizen
* Cult of the Supreme Being
* Cult of Reason
* Temple of Reason
* Sans-culottes
* Phrygian cap
* Women in the French Revolution
* Incroyables and merveilleuses
* Symbolism in the French Revolution
* Historiography of the French Revolution
* Influence of the French Revolution

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