The metre ( British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

noun , "measure"), symbol m, is the primary unit of

length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Inter ...

in the International System of Units (SI), though its prefixed forms are also used relatively frequently. The metre was originally defined in 1793 as one ten-millionth of the distance from the

equator The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can a ...

to the

North Pole The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where the Earth's axis of rotation meets its surface. It is called the True North Pole to distinguish from the Ma ...

along a

great circle In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Any arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry ...

, so the

Earth's circumference Earth's circumference is the distance around Earth. Measured around the Equator, it is . Measured around the poles, the circumference is . Measurement of Earth's circumference has been important to navigation since ancient times. The first kno ...

is approximately km. In 1799, the metre was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of

krypton-86 There are 34 known isotopes of krypton (36Kr) with atomic mass numbers from 69 through 102. Naturally occurring krypton is made of five stable isotopes and one () which is slightly radioactive with an extremely long half-life, plus traces of radi ...

. The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of

proper length Proper length or rest length is the length of an object in the object's rest frame. The measurement of lengths is more complicated in the theory of relativity than in classical mechanics. In classical mechanics, lengths are measured based on ...

. From 1983 until 2019, the metre was formally defined as the length of the path travelled by light in a vacuum in of a

second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ea ...

. After the

2019 redefinition of the SI base units In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144t ...

, this definition was rephrased to include the definition of a second in terms of the caesium frequency .

Spelling

''Metre'' is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use ''meter.'' Other

West Germanic languages The West Germanic languages constitute the largest of the three branches of the Germanic family of languages (the others being the North Germanic and the extinct East Germanic languages). The West Germanic branch is classically subdivided into ...

, such as German and Dutch, and

North Germanic languages The North Germanic languages make up one of the three branches of the Germanic languages—a sub-family of the Indo-European languages—along with the West Germanic languages and the extinct East Germanic languages. The language group is also r ...

, such as Danish, Norwegian, and Swedish, likewise spell the word ''Meter'' or ''meter''. Measuring devices (such as

ammeter An ammeter (abbreviation of ''Ampere meter'') is an instrument used to measure the current in a circuit. Electric currents are measured in amperes (A), hence the name. For direct measurement, the ammeter is connected in series with the circuit ...

speedometer A speedometer or speed meter is a gauge that measures and displays the instantaneous speed of a vehicle. Now universally fitted to motor vehicles, they started to be available as options in the early 20th century, and as standard equipment ...

) are spelled "-meter" in all variants of English. The suffix "-meter" has the same Greek origin as the unit of length.

Etymology

The etymological roots of ''metre'' can be traced to the Greek verb () (to measure, count or compare) and noun () (a measure), which were used for physical measurement, for poetic metre and by extension for moderation or avoiding extremism (as in "be measured in your response"). This range of uses is also found in Latin (), French (), English and other languages. The Greek word is derived from the Proto-Indo-European root '' *meh₁-'' 'to measure'. The motto () in the seal of the

International Bureau of Weights and Measures The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry ...

(BIPM), which was a saying of the Greek statesman and philosopher

Pittacus of Mytilene Pittacus (; grc-gre, Πιττακός; 640 – 568 BC) was an ancient Mytilenean military general and one of the Seven Sages of Greece. Biography Pittacus was a native of Mytilene and son of Hyrradius. He became a Mytilenaean general who, with ...

and may be translated as "Use measure!", thus calls for both measurement and moderation. The use of the word ''metre'' (for the French unit ) in English began at least as early as 1797.

Oxford English Dictionary The ''Oxford English Dictionary'' (''OED'') is the first and foundational historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a co ...

, Clarendon Press 2nd ed.1989, vol.IX p.697 col.3.

History of definition

Pendulum or meridian

In 1671,

Jean Picard Jean Picard (21 July 1620 – 12 July 1682) was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand. He is principally notable for his accurate measure of the size of the Earth, ba ...

measured the length of a "

seconds pendulum A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 0.5 Hz. Pendulum A pendulum is a weight suspended from a pivot so that ...

" and proposed a unit of measurement twice that length to be called the universal toise (French: ''Toise universelle''). In 1675,

Tito Livio Burattini Tito Livio Burattini ( pl, Tytus Liwiusz Burattini, 8 March 1617 – 17 November 1681) was an inventor, architect, Egyptologist, scientist, instrument-maker, traveller, engineer, and nobleman, who spent his working life in Poland and Lithuania. ...

suggested the term metre for a unit of length based on a

pendulum A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward th ...

length, but then it was discovered that the length of a seconds pendulum varies from place to place. Since

Eratosthenes Eratosthenes of Cyrene (; grc-gre, Ἐρατοσθένης ; – ) was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was a man of learning, becoming the chief librarian at the Library of Alexan ...

, geographers had used

meridian arc In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length. The purpose of measuring meridian arcs is to d ...

s to assess the size of the Earth, which in 1669,

determined to have a radius of

toise A toise (; symbol: T) is a unit of measure for length, area and volume originating in pre-revolutionary France. In North America, it was used in colonial French establishments in early New France, French Louisiana (''Louisiane''), Acadia (''Acad ...

s, treated as a simple sphere. In the 18th century,

geodesy Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure ( geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equiv ...

grew in importance as a means of empirically demonstrating the theory of gravity, which

Émilie du Châtelet Gabrielle Émilie Le Tonnelier de Breteuil, Marquise du Châtelet (; 17 December 1706 – 10 September 1749) was a French natural philosopher and mathematician from the early 1730s until her death due to complications during childbirth in 1749. ...

promoted in France in combination with

Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathe ...

mathematical work, and because the radius of the Earth was the unit to which all celestial distances were to be referred.

Meridional definition

As a result of the Lumières and during the

French Revolution The French Revolution ( ) was a period of radical political and societal change in France that began with the Estates General of 1789 and ended with the formation of the French Consulate in November 1799. Many of its ideas are consid ...

, the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at ...

charged a commission with determining a single scale for all measures. On 7 October 1790 that commission advised the adoption of a decimal system, and on 19 March 1791 advised the adoption of the term ''mètre'' ("measure"), a basic unit of length, which they defined as equal to one ten-millionth of the quarter meridian, the distance between the

and the

Equator The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can a ...

along the

meridian Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to Science * Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon * ...

through Paris. On 26 March 1791, the French National Constituent Assembly adopted the proposal. The

commissioned an expedition led by

Jean Baptiste Joseph Delambre Jean Baptiste Joseph, chevalier Delambre (19 September 1749 – 19 August 1822) was a French mathematician, astronomer, historian of astronomy, and geodesist. He was also director of the Paris Observatory, and author of well-known books on ...

and Pierre Méchain, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in

Dunkerque Dunkirk (french: Dunkerque ; vls, label= French Flemish, Duunkerke; nl, Duinkerke(n) ; , ;) is a commune in the department of Nord in northern France.Montjuïc castle in

Barcelona Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ci ...

at the

longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek l ...

of the Paris Panthéon (see meridian arc of Delambre and Méchain). The expedition was fictionalised in Denis Guedj, ''Le Mètre du Monde''. Ken Alder wrote factually about the expedition in ''The Measure of All Things: the seven year odyssey and hidden error that transformed the world''. This portion of the

Paris meridian The Paris meridian is a meridian line running through the Paris Observatory in Paris, France – now longitude 2°20′14.02500″ East. It was a long-standing rival to the Greenwich meridian as the prime meridian of the world. The "Paris meridi ...

was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator. From 1801 to 1812 France adopted this definition of the metre as its official unit of length based on results from this expedition combined with those of the Geodesic Mission to Peru. The latter was related by Larrie D. Ferreiro in ''Measure of the Earth: The Enlightenment Expedition that Reshaped Our World''. In the 19th century, geodesy underwent a revolution through advances in mathematics as well as improvements in the instruments and methods of observation, for instance accounting for individual bias in terms of the personal equation. The application of the

least squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the r ...

method to

measurements demonstrated the importance of the

scientific method The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article history of scientific ...

in geodesy. On the other hand, the invention of the

telegraph Telegraphy is the long-distance transmission of messages where the sender uses symbolic codes, known to the recipient, rather than a physical exchange of an object bearing the message. Thus flag semaphore is a method of telegraphy, whereas ...

made it possible to measure

parallel Parallel is a geometric term of location which may refer to: Computing * Parallel algorithm * Parallel computing * Parallel metaheuristic * Parallel (software), a UNIX utility for running programs in parallel * Parallel Sysplex, a cluster of I ...

arcs, and the improvement of the reversible pendulum gave rise to the study of the Earth's

gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phen ...

. A more accurate determination of the

Figure of the Earth Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A sphere is a well-known historical approxima ...

would soon result from the measurement of the Struve Geodetic Arc (1816–1855) and would have given another value for the definition of this standard of length. This did not invalidate the metre but highlighted that progress in science would allow better measurement of Earth's size and shape. In 1832,

Carl Friedrich Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

studied the

Earth's magnetic field Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic ...

and proposed adding the

to the basic units of the metre and the

kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...

in the form of the CGS system (

centimetre 330px, Different lengths as in respect to the Electromagnetic spectrum, measured by the Metre and its deriveds scales. The Microwave are in-between 1 meter to 1 millimeter. A centimetre (international spelling) or centimeter (American spellin ...

gram The gram (originally gramme; SI unit symbol g) is a unit of mass in the International System of Units (SI) equal to one one thousandth of a kilogram. Originally defined as of 1795 as "the absolute weight of a volume of pure water equal to ...

, second). In 1836, he founded the ''Magnetischer Verein'', the first international scientific association, in collaboration with

Alexander von Humboldt Friedrich Wilhelm Heinrich Alexander von Humboldt (14 September 17696 May 1859) was a German polymath, geographer, naturalist, explorer, and proponent of Romantic philosophy and science. He was the younger brother of the Prussian minister ...

and Wilhelm Edouard Weber. The coordination of the observation of geophysical phenomena such as the Earth's magnetic field, lightning and

gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the str ...

in different points of the globe stimulated the creation of the first international scientific associations. The foundation of the ''Magnetischer Verein'' would be followed by that of the Central European Arc Measurement (German: ''Mitteleuropaïsche Gradmessung'') on the initiative of

Johann Jacob Baeyer Johann Jacob Baeyer (born 5 November 1794 in Berlin Berlin ( , ) is the capital and List of cities in Germany by population, largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's List o ...

in 1863, and by that of the International Meteorological Organisation whose second president, the Swiss meteorologist and physicist, Heinrich von Wild would represent Russia at the

International Committee for Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established ...

(CIPM).

International prototype metre bar

In 1816,

Ferdinand Rudolph Hassler Ferdinand Rudolph Hassler (October 6, 1770 – November 20, 1843) was a Swiss-American surveyor who is considered the forefather of both the National Oceanic and Atmospheric Administration (NOAA) and the National Institute of Standards and Techno ...

was appointed first Superintendent of the Survey of the Coast. Trained in geodesy in Switzerland, France and Germany, Hassler had brought a standard metre made in Paris to the United States in 1805. He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements, used only one bar calibrated on the metre and optical contact. Thus the metre became the unit of length for

in the United States. Since 1830, Hassler was also head of the Bureau of Weights and Measures which became a part of the Coast Survey. He compared various units of length used in the United States at that time and measured coefficients of expansion to assess temperature effects on the measurements. In 1841,

Friedrich Wilhelm Bessel Friedrich Wilhelm Bessel (; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist, and geodesist. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method ...

, taking into account errors which had been recognized by Louis Puissant in the French meridian arc comprising the arc measurement of Delambre and Méchain which had been extended southward by

François Arago Dominique François Jean Arago ( ca, Domènec Francesc Joan Aragó), known simply as François Arago (; Catalan: ''Francesc Aragó'', ; 26 February 17862 October 1853), was a French mathematician, physicist, astronomer, freemason, supporter of ...

and Jean-Baptiste Biot, recalculated the

flattening Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surf ...

of the

Earth ellipsoid An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximatio ...

making use of nine more arc measurements, namely Peruan, Prussian, first East-Indian, second East-Indian, English, Hannover, Danish, Russian and Swedish covering almost 50 degrees of

latitude In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pole ...

, and stated that the Earth quadrant used for determining the length of the metre was nothing more than a rather imprecise conversion factor between the

and the metre. Regarding the precision of the conversion from the

to the metre, both units of measurement were then defined by primary

standard Standard may refer to: Symbols * Colours, standards and guidons, kinds of military signs * Standard (emblem), a type of a large symbol or emblem used for identification Norms, conventions or requirements * Standard (metrology), an object ...

s, and unique artifacts made of different

alloy An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductilit ...

s with distinct coefficients of expansion were the legal basis of units of length. A wrought iron ruler, the Toise of Peru, also called ''Toise de l'Académie'', was the French primary standard of the toise, and the metre was officially defined by the ''Mètre des Archives'' made of platinum. Besides the latter, another platinum and twelve iron standards of the metre were made in 1799. One of them became known as the ''Committee Meter'' in the United States and served as standard of length in the Coast Survey until 1890. According to geodesists, these standards were secondary standards deduced from the Toise of Peru. In Europe, surveyors continued to use measuring instruments calibrated on the Toise of Peru. Among these, the toise of Bessel and the apparatus of Borda were respectively the main references for geodesy in

Prussia Prussia, , Old Prussian: ''Prūsa'' or ''Prūsija'' was a German state on the southeast coast of the Baltic Sea. It formed the German Empire under Prussian rule when it united the German states in 1871. It was ''de facto'' dissolved by an ...

and in France. A French scientific instrument maker, Jean Nicolas Fortin, had made two direct copies of the Toise of Peru, the first for

Friedrich Georg Wilhelm von Struve Friedrich Georg Wilhelm von Struve (russian: link=no, Василий Яковлевич Струве, trans. ''Vasily Yakovlevich Struve''; 15 April 1793 – ) was a Baltic German astronomer and geodesist from the famous Struve family. He is be ...

in 1821 and a second for

Friedrich Bessel Friedrich Wilhelm Bessel (; 22 July 1784 – 17 March 1846) was a German astronomer, mathematician, physicist, and geodesist. He was the first astronomer who determined reliable values for the distance from the sun to another star by the method ...

in 1823. On the subject of the theoretical definition of the metre, it had been inaccessible and misleading at the time of Delambre and Mechain arc measurement, as the

geoid The geoid () is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is exte ...

is a ball, which on the whole can be assimilated to an oblate spheroid, but which in detail differs from it so as to prohibit any generalization and any extrapolation. As early as 1861, after Friedrich von Schubert showed that the different meridians were not of equal length, Elie Ritter, a mathematician from

Geneva Geneva ( ; french: Genève ) frp, Genèva ; german: link=no, Genf ; it, Ginevra ; rm, Genevra is the second-most populous city in Switzerland (after Zürich) and the most populous city of Romandy, the French-speaking part of Switzerland. Situa ...

, deduced from a computation based on eleven meridian arcs covering 86 degrees that the meridian equation differed from that of the ellipse: the meridian was swelled about the 45th degree of latitude by a layer whose thickness was difficult to estimate because of the uncertainty of the latitude of some stations, in particular that of

Montjuïc Montjuïc () is a hill in Barcelona, Catalonia, Spain. Etymology Montjuïc translates to "Jewish Mountain" from medieval Latin and Catalan, and remains of a medieval Jewish cemetery have been found there. Some sources suggest that Montjuïc ...

in the French meridian arc. By measuring the latitude of two stations in

, Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation. We know now that, in addition to other errors in the survey of Delambre and Méchain, an unfavourable

vertical deflection The vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anom ...

gave an inaccurate determination of Barcelona's

, a metre "too short" compared to a more general definition taken from the average of a large number of arcs. Nevertheless

's use of the metre in coastal survey contributed to the introduction of the Metric Act of 1866 allowing the use of the metre in the United States, and also played an important role in the choice of the metre as international scientific unit of length and the proposal by the European Arc Measurement (German: ''Europäische Gradmessung'') to “establish a European international bureau for weights and measures”. However, in 1866, the most important concern was that the Toise of Peru, the standard of the toise constructed in 1735 for the

French Geodesic Mission to the Equator The French Geodesic Mission to the Equator (french: Expédition géodésique française en Équateur, also called the French Geodesic Mission to Peru and the Spanish-French Geodesic Mission) was an 18th-century expedition to what is now Ecuador c ...

, might be so much damaged that comparison with it would be worthless, while Bessel had questioned the accuracy of copies of this standard belonging to Altona and Koenigsberg Observatories, which he had compared to each other about 1840. Indeed when the primary Imperial

yard The yard (symbol: yd) is an English unit of length in both the British imperial and US customary systems of measurement equalling 3 feet or 36 inches. Since 1959 it has been by international agreement standardized as exactl ...

standard was partially destroyed in 1834, a new standard of reference had been constructed using copies of the "Standard Yard, 1760" instead of the pendulum's length as provided for in the Weights and Measures Act of 1824. In 1864,

Urbain Le Verrier Urbain Jean Joseph Le Verrier FRS (FOR) H FRSE (; 11 March 1811 – 23 September 1877) was a French astronomer and mathematician who specialized in celestial mechanics and is best known for predicting the existence and position of Neptune usi ...

refused to join the first general conference of the Central European Arc Measurement because the French geodetic works had to be verified. Appareil Ibáñez

In 1866, at the meeting of the Permanent Commission of the association in

Neuchâtel Neuchâtel (, , ; german: Neuenburg) is the capital of the Swiss canton of Neuchâtel, situated on the shoreline of Lake Neuchâtel. Since the fusion in 2021 of the municipalities of Neuchâtel, Corcelles-Cormondrèche, Peseux, and Valangin, ...

, Antoine Yvon Villarceau announced that he had checked eight points of the French arc. He confirmed that the metre was too short. It then became urgent to undertake a complete revision of the meridian arc. Moreover, while the extension of the French meridian arc to the Balearic Islands (1803–1807) had seemed to confirm the length of the metre, this survey had not been secured by any baseline in Spain. For that reason, Carlos Ibáñez e Ibáñez de Ibero's announcement, at this conference, of his 1858 measurement of a baseline in Madridejos was of particular importance. Indeed surveyors determined the size of

triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle m ...

networks by measuring baselines which concordance granted the accuracy of the whole survey. In 1867 at the second general conference of the

International Association of Geodesy ) , merged = , successor = , formation = , founder = , founding_location = , extinction = , merger = , type = scholarly society , tax_id ...

held in Berlin, the question of an international standard unit of length was discussed in order to combine the measurements made in different countries to determine the size and shape of the Earth. The conference recommended the adoption of the metre in replacement of the toise and the creation of an international metre commission, according to the proposal of

, Adolphe Hirsch and Carlos Ibáñez e Ibáñez de Ibero who had devised two geodetic standards calibrated on the metre for the map of Spain. Ibáñez adopted the system which

used for the United States Survey of the Coast, consisting of a single standard with lines marked on the bar and microscopic measurements. Regarding the two methods by which the effect of temperature was taken into account, Ibáñez used both the bimetallic rulers, in platinum and brass, which he first employed for the central baseline of Spain, and the simple iron ruler with inlaid mercury thermometers which was utilized in Switzerland. These devices, the first of which is referred to as either Brunner apparatus or Spanish Standard, were constructed in France by Jean Brunner, then his sons. Measurement traceability between the toise and the metre was ensured by comparison of the Spanish Standard with the standard devised by Borda and

Lavoisier Antoine-Laurent de Lavoisier ( , ; ; 26 August 17438 May 1794),
CNRS (

connecting

Dunkirk Dunkirk (french: Dunkerque ; vls, label= French Flemish, Duunkerke; nl, Duinkerke(n) ; , ;) is a commune in the department of Nord in northern France.Barcelona Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ci ...

. Hassler's metrological and geodetic work also had a favourable response in Russia. In 1869, the Saint Petersburg Academy of Sciences sent to the

a report drafted by Otto Wilhelm von Struve, Heinrich von Wild and

Moritz von Jacobi Moritz Hermann or Boris Semyonovich (von) Jacobi (russian: Борис Семёнович Якоби; 21 September 1801, Potsdam – 10 March 1874, Saint Petersburg) was a Prussian and Russian Imperial engineer and physicist of Jewish descent. J ...

inviting his French counterpart to undertake joint action to ensure the universal use of the

metric system 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 Interna ...

in all scientific work. Metre alloy

In the 1870s and in light of modern precision, a series of international conferences was held to devise new metric standards. When a conflict broke out regarding the presence of impurities in the metre-alloy of 1874, a member of the Preparatory Committee since 1870 and Spanish representative at the Paris Conference in 1875, Carlos Ibáñez e Ibáñez de Ibero intervened with the

to rally France to the project to create an

equipped with the scientific means necessary to redefine the units of the

according to the progress of sciences. The

Metre Convention The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Braz ...

(''Convention du Mètre'') of 1875 mandated the establishment of a permanent

(BIPM: ') to be located in

Sèvres Sèvres (, ) is a commune in the southwestern suburbs of Paris, France. It is located from the centre of Paris, in the Hauts-de-Seine department, Île-de-France region. The commune, which had a population of 23,251 as of 2018, is known for ...

, France. This new organisation was to construct and preserve a prototype metre bar, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation distributed such bars in 1889 at the first

General Conference on Weights and Measures The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established ...

(CGPM: '), establishing the ''

International Prototype Metre The history of the metre starts with the Scientific Revolution that is considered to have begun with Nicolaus Copernicus's publication of '' De revolutionibus orbium coelestium'' in 1543. Increasingly accurate measurements were required, and ...

'' as the distance between two lines on a standard bar composed of an alloy of 90%

platinum Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver". Pla ...

and 10%

iridium Iridium is a chemical element with the symbol Ir and atomic number 77. A very hard, brittle, silvery-white transition metal of the platinum group, it is considered the second-densest naturally occurring metal (after osmium) with a density o ...

, measured at the melting point of ice. National Institute of Standards and Technology 2003; Historical context of the SI: Unit of length (meter) US National Length Meter

The comparison of the new prototypes of the metre with each other and with the Committee metre (French: '' Mètre des Archives'') involved the development of special measuring equipment and the definition of a reproducible temperature scale. The BIPM's thermometry work led to the discovery of special alloys of iron-nickel, in particular

invar Invar, also known generically as FeNi36 (64FeNi in the US), is a nickel–iron alloy notable for its uniquely low coefficient of thermal expansion (CTE or α). The name ''Invar'' comes from the word ''invariable'', referring to its relative la ...

, for which its director, the Swiss physicist Charles-Edouard Guillaume, was granted the Nobel Prize for physics in 1920. Repsold

As Carlos Ibáñez e Ibáñez de Ibero stated, the progress of

metrology Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in Fran ...

combined with those of

gravimetry Gravimetry is the measurement of the strength of a gravitational field. Gravimetry may be used when either the magnitude of a gravitational field or the properties of matter responsible for its creation are of interest. Units of measurement Gr ...

through improvement of

Kater's pendulum A Kater's pendulum is a reversible free swinging pendulum invented by British physicist and army captain Henry Kater in 1817 for use as a gravimeter instrument to measure the local acceleration of gravity. Its advantage is that, unlike previou ...

led to a new era of

. If precision metrology had needed the help of geodesy, the latter could not continue to prosper without the help of metrology. It was then necessary to define a single unit to express all the measurements of terrestrial arcs and all determinations of the

force of gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...

by the mean of pendulum. Metrology had to create a common unit, adopted and respected by all civilized nations. Moreover, at that time,

statistician A statistician is a person who works with theoretical or applied statistics. The profession exists in both the private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, and statisticians may ...

s knew that scientific observations are marred by two distinct types of errors, constant errors on the one hand, and fortuitous errors, on the other hand. The effects of the latters can be mitigated by the

least-squares The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the res ...

method. Constant or regular errors on the contrary must be carefully avoided, because they arise from one or more causes that constantly act in the same way and have the effect of always altering the result of the experiment in the same direction. They therefore deprive of any value the observations that they impinge. However, the distinction between systematic and random errors is far from being as sharp as one might think at first assessment. In reality, there are no or very few random errors. As science progresses, the causes of certain errors are sought out, studied, their laws discovered. These errors pass from the class of random errors into that of systematic errors. The ability of the observer consists in discovering the greatest possible number of systematic errors in order to be able, once he has become acquainted with their laws, to free his results from them using a method or appropriate corrections. For metrology the matter of expansibility was fundamental; as a matter of fact the temperature measuring

error An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. The etymology derives from the Latin term 'errare', meaning 'to stray'. In statistics ...

related to the length measurement in proportion to the expansibility of the standard and the constantly renewed efforts of metrologists to protect their measuring instruments against the interfering influence of temperature revealed clearly the importance they attached to the expansion-induced errors. It was thus crucial to compare at controlled temperatures with great precision and to the same unit all the standards for measuring geodetic baselines and all the pendulum rods. Only when this series of metrological comparisons would be finished with a probable error of a thousandth of a millimetre would geodesy be able to link the works of the different nations with one another, and then proclaim the result of the measurement of the Globe. As the

figure of the Earth Figure of the Earth is a term of art in geodesy that refers to the size and shape used to model Earth. The size and shape it refers to depend on context, including the precision needed for the model. A sphere is a well-known historical approxima ...

could be inferred from variations of the

length with

, the

United States Coast Survey United may refer to: Places * United, Pennsylvania, an unincorporated community * United, West Virginia, an unincorporated community Arts and entertainment Films * ''United'' (2003 film), a Norwegian film * ''United'' (2011 film), a BBC Two f ...

instructed

Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for ...

in the spring of 1875 to proceed to Europe for the purpose of making pendulum experiments to chief initial stations for operations of this sort, in order to bring the determinations of the forces of gravity in America into communication with those of other parts of the world; and also for the purpose of making a careful study of the methods of pursuing these researches in the different countries of Europe. In 1886 the association of geodesy changed name for the International Geodetic Association, which Carlos Ibáñez e Ibáñez de Ibero presided up to his death in 1891. During this period the International Geodetic Association (German: ''Internationale Erdmessung'') gained worldwide importance with the joining of United States,

Mexico Mexico (Spanish: México), officially the United Mexican States, is a country in the southern portion of North America. It is bordered to the north by the United States; to the south and west by the Pacific Ocean; to the southeast by Gua ...

Chile Chile, officially the Republic of Chile, is a country in the western part of South America. It is the southernmost country in the world, and the closest to Antarctica, occupying a long and narrow strip of land between the Andes to the east ...

Argentina Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country in the southern half of South America. Argentina covers an area of , making it the second-largest country in South America after Brazil, th ...

and Japan. GPS-IIR

Efforts to supplement the various national

surveying Surveying or land surveying is the technique, profession, art, and science of determining the land, terrestrial Two-dimensional space#In geometry, two-dimensional or Three-dimensional space#In Euclidean geometry, three-dimensional positions of ...

systems, which began in the 19th century with the foundation of the '' Mitteleuropäische Gradmessung'', resulted in a series of global

ellipsoid An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a surface that may be defined as the ...

s of the Earth (e.g.,

Helmert Friedrich Robert Helmert (31 July 1843 – 15 June 1917) was a German geodesist and statistician with important contributions to the theory of errors. Career Helmert was born in Freiberg, Kingdom of Saxony. After schooling in Freiberg a ...

1906, Hayford 1910 and 1924) which would later lead to develop the

World Geodetic System The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also descr ...

. Nowadays the practical realisation of the metre is possible everywhere thanks to the

atomic clock An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwee ...

s embedded in

GPS satellites GPS satellite blocks are the various production generations of the Global Positioning System (GPS) used for satellite navigation. The first satellite in the system, Navstar 1, was launched on 22 February 1978. The GPS satellite constellatio ...

Wavelength definition

In 1873,

James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...

suggested that light emitted by an element be used as the standard both for the metre and for the second. These two quantities could then be used to define the unit of mass. In 1893, the standard metre was first measured with an

interferometer Interferometry is a technique which uses the '' interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber ...

by Albert A. Michelson, the inventor of the device and an advocate of using some particular wavelength of light as a standard of length. By 1925,

interferometry Interferometry is a technique which uses the '' interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber o ...

was in regular use at the BIPM. However, the International Prototype Metre remained the standard until 1960, when the eleventh CGPM defined the metre in the new International System of Units (SI) as equal to wavelengths of the orange-

red Red is the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength of approximately 625–740 nanometres. It is a primary color in the RGB color model and a second ...

emission line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...

in the

electromagnetic spectrum The electromagnetic spectrum is the range of frequencies (the spectrum) of electromagnetic radiation and their respective wavelengths and photon energies. The electromagnetic spectrum covers electromagnetic waves with frequencies ranging from ...

of the

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, g ...

in a

vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists ofte ...

Speed of light definition

To further reduce uncertainty, the 17th CGPM in 1983 replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of the

and the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit for ...

: ::The metre is the length of the path travelled by light in vacuum during a time interval of of a second. This definition fixed the speed of light in

at exactly metres per second (≈ or ≈1.079 billion km/hour). An intended by-product of the 17th CGPM's definition was that it enabled scientists to compare lasers accurately using frequency, resulting in wavelengths with one-fifth the uncertainty involved in the direct comparison of wavelengths, because interferometer errors were eliminated. To further facilitate reproducibility from lab to lab, the 17th CGPM also made the iodine-stabilised

helium–neon laser A helium–neon laser or He-Ne laser, is a type of gas laser whose high energetic medium gain medium consists of a mixture of 10:1 ratio of helium and neon at a total pressure of about 1 torr inside of a small electrical discharge. The be ...

"a recommended radiation" for realising the metre. For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, , to be with an estimated relative standard uncertainty (''U'') of .The term "relative standard uncertainty" is explained by NIST on their web site: This uncertainty is currently one limiting factor in laboratory realisations of the metre, and it is several orders of magnitude poorer than that of the second, based upon the caesium fountain

(). Consequently, a realisation of the metre is usually delineated (not defined) today in labs as wavelengths of helium-neon laser light in a vacuum, the error stated being only that of frequency determination. This bracket notation expressing the error is explained in the article on

measurement uncertainty In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by ...

. Practical realisation of the metre is subject to uncertainties in characterising the medium, to various uncertainties of interferometry, and to uncertainties in measuring the frequency of the source. A commonly used medium is air, and the National Institute of Standards and Technology (NIST) has set up an online calculator to convert wavelengths in vacuum to wavelengths in air.The formulas used in the calculator and the documentation behind them are found at The choice is offered to use either th
modified Edlén equation
or th
Ciddor equation
The documentation provide
a discussion of how to choose
between the two possibilities. As described by NIST, in air, the uncertainties in characterising the medium are dominated by errors in measuring temperature and pressure. Errors in the theoretical formulas used are secondary. By implementing a refractive index correction such as this, an approximate realisation of the metre can be implemented in air, for example, using the formulation of the metre as wavelengths of helium–neon laser light in a vacuum, and converting the wavelengths in a vacuum to wavelengths in air. Air is only one possible medium to use in a realisation of the metre, and any partial vacuum can be used, or some inert atmosphere like helium gas, provided the appropriate corrections for refractive index are implemented. The metre is ''defined'' as the path length travelled by light in a given time, and practical laboratory length measurements in metres are determined by counting the number of wavelengths of laser light of one of the standard types that fit into the length, and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement: A more detailed listing of errors can be found in Zagar, 1999, pp. 6–65''ff''. * uncertainty in vacuum wavelength of the source, * uncertainty in the refractive index of the medium, * least count resolution of the interferometer. Of these, the last is peculiar to the interferometer itself. The conversion of a length in wavelengths to a length in metres is based upon the relation :

\lambda = \frac

which converts the unit of wavelength ''λ'' to metres using ''c'', the speed of light in vacuum in m/s. Here ''n'' is the

refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, o ...

of the medium in which the measurement is made, and ''f'' is the measured frequency of the source. Although conversion from wavelengths to metres introduces an additional error in the overall length due to measurement error in determining the refractive index and the frequency, the measurement of frequency is one of the most accurate measurements available. The CIPM issued a clarification in 2002:

Timeline

Early adoptions of the metre internationally

In France, the metre was adopted as an exclusive measure in 1801 under the

Consulate A consulate is the office of a consul. A type of diplomatic mission, it is usually subordinate to the state's main representation in the capital of that foreign country (host state), usually an embassy (or, only between two Commonwealth count ...

. This continued under the

First French Empire The First French Empire, officially the French Republic, then the French Empire (; Latin: ) after 1809, also known as Napoleonic France, was the empire ruled by Napoleon Bonaparte, who established French hegemony over much of continental Eur ...

until 1812, when

Napoleon Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader who ...

decreed the introduction of the non-decimal ''

mesures usuelles Mesures usuelles (, ''customary measurements'') were a French system of measurement introduced by Napoleon I in 1812 to act as compromise between the metric system and traditional measurements. The system was restricted to use in the retail indus ...

'', which remained in use in France up to 1840 in the reign of Louis Philippe. Meanwhile, the metre was adopted by the Republic of Geneva. After the joining of the

canton of Geneva The Canton of Geneva, officially the Republic and Canton of Geneva (french: link=no, République et canton de Genève; frp, Rèpublica et canton de Geneva; german: Republik und Kanton Genf; it, Repubblica e Cantone di Ginevra; rm, Republica e ...

to Switzerland in 1815, Guillaume Henri Dufour published the first official Swiss map, for which the metre was adopted as the unit of length. Louis Napoléon Bonaparte, a Swiss–French binational officer, was present when a baseline was measured near

Zürich , neighboring_municipalities = Adliswil, Dübendorf, Fällanden, Kilchberg, Maur, Oberengstringen, Opfikon, Regensdorf, Rümlang, Schlieren, Stallikon, Uitikon, Urdorf, Wallisellen, Zollikon , twintowns = Kunming, San Francisco ...

for the Dufour map, which would win the gold medal for a national map at the Exposition Universelle of 1855. Among the scientific instruments calibrated on the metre that were displayed at the Exposition Universelle, was Brunner's apparatus, a geodetic instrument devised for measuring the central baseline of Spain, whose designer, Carlos Ibáñez e Ibáñez de Ibero would represent Spain at the

International Statistical Institute The International Statistical Institute (ISI) is a professional association of statisticians. It was founded in 1885, although there had been international statistical congresses since 1853. The institute has about 4,000 elected members from gov ...

. In 1885, in addition to the Exposition Universelle and the second Statistical Congress held in Paris, an International Association for Obtaining a Uniform Decimal System of Measures, Weights, and Coins was created there. Copies of the Spanish standard were made for Egypt, France and Germany. These standards were compared to each other and with the Borda apparatus, which was the main reference for measuring all geodetic bases in France. In 1869, Napoleon III convened the International Metre Commission, which was to meet in Paris in 1870. The Franco-Prussian War broke out, the

Second French Empire The Second French Empire (; officially the French Empire, ), was the 18-year Imperial Bonapartist regime of Napoleon III from 14 January 1852 to 27 October 1870, between the Second and the Third Republic of France. Historians in the 1930 ...

collapsed, but the metre survived.

Metre adoption dates by country

* France: 1801 - 1812, then 1840, *

Republic of Geneva The Canton of Geneva, officially the Republic and Canton of Geneva (french: link=no, République et canton de Genève; frp, Rèpublica et canton de Geneva; german: Republik und Kanton Genf; it, Repubblica e Cantone di Ginevra; rm, Republica e ...

, Switzerland: 1813, *

Kingdom of the Netherlands , national_anthem = ) , image_map = Kingdom of the Netherlands (orthographic projection).svg , map_width = 250px , image_map2 = File:KonDerNed-10-10-10.png , map_caption2 = Map of the four constituent countries shown to scale , capital = ...

: 1820, * Kingdom of

Belgium Belgium, ; french: Belgique ; german: Belgien officially the Kingdom of Belgium, is a country in Northwestern Europe. The country is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to th ...

: 1830, *

: 1848, *

Kingdom of Sardinia The Kingdom of Sardinia,The name of the state was originally Latin: , or when the kingdom was still considered to include Corsica. In Italian it is , in French , in Sardinian , and in Piedmontese . also referred to as the Kingdom of Savoy-S ...

, Italy: 1850, * Spain: 1852, * Portugal: 1852, *

Colombia Colombia (, ; ), officially the Republic of Colombia, is a country in South America with insular regions in North America—near Nicaragua's Caribbean coast—as well as in the Pacific Ocean. The Colombian mainland is bordered by the Carib ...

: 1853, *

Ecuador Ecuador ( ; ; Quechua: ''Ikwayur''; Shuar: ''Ecuador'' or ''Ekuatur''), officially the Republic of Ecuador ( es, República del Ecuador, which literally translates as "Republic of the Equator"; Quechua: ''Ikwadur Ripuwlika''; Shuar: '' ...

: 1856, *

: 1857, *

Brazil Brazil ( pt, Brasil; ), officially the Federative Republic of Brazil (Portuguese: ), is the largest country in both South America and Latin America. At and with over 217 million people, Brazil is the world's fifth-largest country by area an ...

: 1862, *

: 1863, * Italy: 1863, *

German Empire The German Empire (), Herbert Tuttle wrote in September 1881 that the term "Reich" does not literally connote an empire as has been commonly assumed by English-speaking people. The term literally denotes an empire – particularly a hereditar ...

, Germany: 1872, *

Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ci ...

, 1875, * Switzerland: 1877.

SI prefixed forms of metre

SI prefix The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...

es can be used to denote decimal multiples and submultiples of the metre, as shown in the table below. Long distances are usually expressed in km,

astronomical unit The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbit ...

s (149.6 Gm),

light-year A light-year, alternatively spelled light year, is a large unit of length used to express astronomical distances and is equivalent to about 9.46 trillion kilometers (), or 5.88 trillion miles ().One trillion here is taken to be 1012 ...

s (10 Pm), or

parsec The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, ...

s (31 Pm), rather than in Mm, Gm, Tm, Pm, Em, Zm or Ym; "30 cm", "30 m", and "300 m" are more common than "3 dm", "3 dam", and "3 hm", respectively. The terms ''micron'' and ''millimicron'' can be used instead of ''micrometre'' (μm) and ''nanometre'' (nm), but this practice may be discouraged.

Equivalents in other units

Within this table, "inch" and "yard" mean "international inch" and "international yard" respectively, though approximate conversions in the left column hold for both international and survey units. : "≈" means "is approximately equal to"; : "=" means "is exactly equal to". One metre is exactly equivalent to inches and to yards. A simple

mnemonic A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and image ...

aid exists to assist with conversion, as three "3"s: : 1 metre is nearly equivalent to 3

feet The foot ( : feet) is an anatomical structure found in many vertebrates. It is the terminal portion of a limb which bears weight and allows locomotion. In many animals with feet, the foot is a separate organ at the terminal part of the leg ma ...

inches. This gives an overestimate of 0.125mm; however, the practice of memorising such conversion formulas has been discouraged in favour of practice and visualisation of metric units. The ancient Egyptian

cubit The cubit is an ancient unit of length based on the distance from the elbow to the tip of the middle finger. It was primarily associated with the Sumerians, Egyptians, and Israelites. The term ''cubit'' is found in the Bible regarding Noa ...

was about 0.5m (surviving rods are 523–529mm). Scottish and English definitions of the

ell An ell (from Proto-Germanic *''alinō'', cognate with Latin ''ulna'') is a northwestern European unit of measurement, originally understood as a cubit (the combined length of the forearm and extended hand). The word literally means "arm", and ...

(two cubits) were 941mm (0.941m) and 1143mm (1.143m) respectively. The ancient Parisian ''toise'' (fathom) was slightly shorter than 2m and was standardised at exactly 2m in the

system, such that 1m was exactly toise. The Russian

verst A verst (russian: верста, ) is an obsolete Russian unit of length defined as 500 sazhen. This makes a verst equal to . Plurals and variants In the English language, ''verst'' is singular with the normal plural ''versts''. In Russian, the n ...

was 1.0668km. The Swedish mil was 10.688km, but was changed to 10km when Sweden converted to metric units.

Notes

References

* * Astin, A. V. & Karo, H. Arnold, (1959)
''Refinement of values for the yard and the pound''
Washington DC: National Bureau of Standards, republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, Filed, 30 June 1959) * * * * * *

Retrieved 26 May 2010. * National Institute of Standards and Technology. (27 June 2011).
NIST-F1 Cesium Fountain Atomic Clock
'. Author. * National Physical Laboratory. (25 March 2010).
Iodine-Stabilised Lasers
'. Author. * * Republic of the Philippines. (2 December 1978).

'. Author. * Republic of the Philippines. (10 October 1991). '' ttps://www.officialgazette.gov.ph/downloads/1991/10oct/19911010-RA-7160-CCA.pdf Republic Act No. 7160: The Local Government Code of the Philippines'. Author. * Supreme Court of the Philippines (Second Division). (20 January 2010).
G.R. No. 185240
'. Author. * Taylor, B.N. and Thompson, A. (Eds.). (2008a)
''The International System of Units (SI)''
United States version of the English text of the eighth edition (2006) of the International Bureau of Weights and Measures publication ''Le Système International d’ Unités (SI)'' (Special Publication 330). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 18 August 2008. * Taylor, B.N. and Thompson, A. (2008b)
''Guide for the Use of the International System of Units''
(Special Publication 811). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 23 August 2008. * Turner, J. (Deputy Director of the National Institute of Standards and Technology). (16 May 2008
"Interpretation of the International System of Units (the Metric System of Measurement) for the United States"
''Federal Register'' Vol. 73, No. 96, p.28432-3. * Zagar, B.G. (1999)
Laser interferometer displacement sensors
in J.G. Webster (ed.). ''The Measurement, Instrumentation, and Sensors Handbook.'' CRC Press. . {{Authority control SI base units