Metre

This article is about the unit of length. For other uses of "metre" or "meter", see meter (disambiguation).

Metre
Unit system	SI base unit
Unit of	Length
Symbol	m
Unit conversions
1 m in ...	... is equal to ...
nm	1 0003 (1 000 000 000 nm)
μm	1 0002 (1 000 000 μm)
mm	1 0001 (1 000 mm)
km	1 000−1 (0.001 km)
Mm	1 000−2 (0.000 001 Mm)
in	≈ 39.3701

The metre, or meter (American spelling), (from the Greek noun μέτρον, "measure") is the base unit of length in the International System of Units (SI). The SI unit symbol is m. The metre is defined as the distance travelled by light in a specific fraction – about one three-hundred millionth – of a second.

The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1889, it was redefined in terms of a prototype metre bar (the actual bar used was subsequently changed twice). In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted.

In 1959, the imperial inch was re-defined as 0.0254 metres (2.54 centimetres or 25.4 millimetres). One metre is about ​3 ³⁄₈ inches longer than a yard, i.e. about ​39 ³⁄₈ inches.

Spelling

Metre is the standard spelling of the metric unit for length in all English-speaking nations except the USA, which uses meter.

Measuring devices (such as ammeter, speedometer) are spelled "-meter" in all countries. The word "meter", signifying any such device, has the same derivation as the word "metre", denoting the unit of length.

Etymology

The etymological roots of metre can be traced to the Greek verb μετρέω (metreo) (to measure, count or compare) and noun μέτρον (metron) (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 (metior, mensura), French (mètre, mesure), English and other languages. The motto ΜΕΤΡΩ ΧΡΩ (metro chro) in the seal of the International Bureau of Weights and Measures (BIMP), which was a saying of the Greek statesman and philosopher Pittacus of Mytilene and may be translated as "Use measure!", thus calls for both measurement and moderation.

History of definition

Main article: History of the metre

In 1668 the English cleric and philosopher John Wilkins proposed in an essay a decimal-based unit of length, the universal measure or standard. In 1670 Gabriel Mouton, Bishop of Lyon, also suggested a universal length standard with decimal multiples and divisions, to be based on a one-minute angle of the Earth's meridian arc or (as the Earth's circumference was not easy to measure) on a pendulum with a one-second period. In 1675, the Italian scientist Tito Livio Burattini, in his work Misura Universale, used the phrase metro cattolico ("universal measure"), derived from the Greek μέτρον καθολικόν (métron katholikón), to denote the standard unit of length derived from a pendulum. As a result of the French Revolution, the French Academy of Sciences 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 distance between the North Pole and the Equator, In 1793, the French National Convention adopted the proposal; this use of metre in English began at least as early as 1797.

Belfry, Dunkirk—the northern end of the meridian arc

Fortress of Montjuïc—the southerly end of the meridian arc

Creating the metre-alloy in 1874 at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville and Debray

Pendular

In 1668, Wilkins proposed using Christopher Wren's suggestion of defining the metre using a pendulum with a length which produced a half-period of one second, known as a 'seconds pendulum'. Christiaan Huygens had observed that length to be 38 Rijnland inches or 39.26 English inches. This is the equivalent of what is now known to be 997 mm. No official action was taken regarding this suggestion.

Meridional

In the 18th century, there were two approaches to the definition of the standard unit of length. One favoured Wilkins approach: to define the metre in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the metre as one ten-millionth (1/10 000 000) of the length of a quadrant along the Earth's meridian; that is, the distance from the Equator to the North Pole. This means that the quadrant (a section/distance ​¹⁄₄ of the Earth's circumference) would have been defined as exactly 10 000 000 metres (10 000 km) at that time, with the total circumference of the Earth defined as 40 000 000 metres (40 000 km). In 1791, the French Academy of Sciences selected the meridional definition over the pendular definition because the force of gravity varies slightly over the surface of the Earth, which affects the period of a pendulum.

To establish a universally accepted foundation for the definition of the metre, more accurate measurements of this meridian were needed. The French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in Dunkerque and Montjuïc castle in Barcelona to estimate the length of the meridian arc through Dunkerque. This portion of the meridian, assumed to be the same length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator. The problem with this approach is that the exact shape of the Earth is not a simple mathematical shape, such as a sphere or oblate spheroid, at the level of precision required for defining a standard of length. The irregular and particular shape of the Earth smoothed to sea level is called a geoid, which literally means "Earth-shaped", but does not correspond to the actual shape of the earth, but rather is a mathematical model of its shape. Despite these issues, in 1793 France adopted this definition of the metre as its official unit of length based on provisional results from this expedition.

Prototype metre bar

In the 1870s and in light of modern precision, a series of international conferences was held to devise new metric standards. The Metre Convention (Convention du Mètre) of 1875 mandated the establishment of a permanent International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sèvres, 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 created such a bar in 1889 at the first General Conference on Weights and Measures (CGPM: Conférence Générale des Poids et Mesures), establishing the International Prototype Metre as the distance between two lines on a standard bar composed of an alloy of 90% platinum and 10% iridium, measured at the melting point of ice.

However, it was later determined that the first prototype metre bar was short by about 200 micrometres because of miscalculation of the flattening of the Earth, making the prototype about 0.02% shorter than the original proposed definition of the metre. Regardless, this length became the standard. The original international prototype of the metre is still kept at the BIPM under the conditions specified in 1889.

Number of wavelengths of red-orange emission line of krypton-86

In 1893, the standard metre was first measured with an interferometer 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 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 1 650 763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum.

Distance travelled by light in a specified time

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 second and the speed of light:

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.

This definition fixed the speed of light in vacuum at exactly 299792458 metres per second (≈300 000 km/s). 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 recommended radiation" for realising the metre. For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, λ_HeNe, to be 632.99121258 nm with an estimated relative standard uncertainty (U) of 2.1×10⁻¹¹. 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 atomic clock (U = 5×10⁻¹⁶). Consequently, a realisation of the metre is usually delineated (not defined) today in labs as 1579800.762042(33) 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.

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. 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 1579800.762042(33) wavelengths of helium-neon laser light in vacuum, and converting the wavelengths in a vacuum to wavelengths in air. Of course, 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:

• 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{c}{n f} \$

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

Timeline

Closeup of National Prototype Metre Bar No. 27, made in 1889 by the International Bureau of Weights and Measures (BIPM) and given to the United States, which served as the standard for defining all units of length in the US from 1893 to 1960

• 8 May 1790 – The French National Assembly decides that the length of the new metre would be equal to the length of a pendulum with a half-period of one second.
• 30 March 1791 – The French National Assembly accepts the proposal by the French Academy of Sciences that the new definition for the metre be equal to one ten-millionth of the length of a quadrant along the Earth's meridian through Paris, that is the distance from the equator to the north pole.
• 1795 – Provisional metre bar constructed of brass. Based on Bessel's ellipsoid and legally equal to 443.44 lines on the toise du Pérou (a standard French unit of length from 1747).
• 10 December 1799 – The French National Assembly specifies the platinum metre bar, constructed on 23 June 1799 and deposited in the National Archives, as the final standard. Legally equal to 443.296 lines on the toise du Pérou.
• 28 September 1889 – The 1st General Conference on Weights and Measures (CGPM) defines the metre as the distance between two lines on a standard bar of an alloy of platinum with 10% iridium, measured at the melting point of ice.
• 6 October 1927 – The 7th CGPM redefines the metre as the distance, at 0 °C (273 K), between the axes of the two central lines marked on the prototype bar of platinum-iridium, this bar being subject to one standard atmosphere of pressure and supported on two cylinders of at least 10 mm (1 cm) diameter, symmetrically placed in the same horizontal plane at a distance of 571 mm (57.1 cm) from each other.
• 14 October 1960 – The 11th CGPM defines the metre as 1650763.73 wavelengths in a vacuum of the radiation corresponding to the transition between the 2p¹⁰ and 5d⁵ quantum levels of the krypton-86 atom.
• 21 October 1983 – The 17th CGPM defines the metre as the length of the path travelled by light in a vacuum during a time interval of 1/299 792 458 of a second.
• 2002 – The International Committee for Weights and Measures (CIPM) considers the metre to be a unit of proper length and thus recommends this definition be restricted to "lengths ℓ which are sufficiently short for the effects predicted by general relativity to be negligible with respect to the uncertainties of realisation".

Definitions of the metre since 1795

Basis of definition	Date	Absolute uncertainty	Relative uncertainty
1/10 000 000 part of the quadrant along the meridian, measurement by Delambre and Méchain (443.296 lines)	1795	500–100 μm	10−4
First prototype [[Metre des Archives]] platinum bar standard	1799	50–10 μm	10−5
Platinum-iridium bar at melting point of ice (1st CGPM)	1889	0.2–0.1 µm (200-100 nm)	10−7
Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM)	1927	n.a.	n.a.
Hyperfine atomic transition; 1650763.73 wavelengths of light from a specified transition in krypton-86 (11th CGPM)	1960	4 nm	4x10−9
Length of the path travelled by light in a vacuum in 1/299 792 458 of a second (17th CGPM)	1983	0.1 nm	10−10

SI prefixed forms of metre

SI prefixes are often employed to denote decimal multiples and submultiples of the metre, as shown in the table below. As indicated in the table, some are commonly used, while others are not. Long distances are usually expressed in km, astronomical units (149.6 Gm), light-years (10 Pm), or parsecs (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 (occasionally) millimicron are often used instead of micrometre (μm) and nanometre (nm), but this practice is officially discouraged.

SI multiples for metre (m)

Submultiples				Multiples
Value	SI symbol	Name		Value	SI symbol	Name
10−1 m	dm	decimetre		101 m	dam	decametre
10−2 m	cm	centimetre		102 m	hm	hectometre
10−3 m	mm	millimetre		103 m	km	kilometre
10−6 m	µm	micrometre		106 m	Mm	megametre
10−9 m	nm	nanometre		109 m	Gm	gigametre
10−12 m	pm	picometre		1012 m	Tm	terametre
10−15 m	fm	femtometre		1015 m	Pm	petametre
10−18 m	am	attometre		1018 m	Em	exametre
10−21 m	zm	zeptometre		1021 m	Zm	zettametre
10−24 m	ym	yoctometre		1024 m	Ym	yottametre
Common prefixed units are in bold face.

Equivalents in other units

Metric unit expressed in non-SI units					Non-SI unit expressed in metric units
1 metre	≈	1.0936	yard		1 yard	≡	0.9144	metre
1 metre	≈	39.370	inches		1 inch	≡	0.0254	metre
1 centimetre	≈	0.39370	inch		1 inch	≡	2.54	centimetres
1 millimetre	≈	0.039370	inch		1 inch	≡	25.4	millimetres
1 metre	≡	1×1010	ångström		1 ångström	≡	1×10−10	metre
1 nanometre	≡	10	ångström		1 ångström	≡	100	picometres

Within this table, "inch" and "yard" mean "international inch" and "international yard", respectively, though approximate conversions in the left-hand column hold for both international and survey units.

"≈" means "is approximately equal to";

"≡" means "equal by definition" or "is exactly equal to."

One metre is exactly equivalent to 10 000/254 inches and to 10 000/9 144 yards.

A simple mnemonic aid exists to assist with conversion, as three "3"s:

1 metre is nearly equivalent to 3 feet ​3 ³⁄₈ inches. This gives an overestimate of 0.125 mm. However, the practice of memorising such conversion formulas has been discouraged in favour of practice and visualisation of metric units.

The ancient Egyptian cubit was about 0.5 m (surviving rods are 523–529 mm). Scottish and English definitions of the ell (two cubits) were 941 mm (0.941 m) and 1 143 mm (1.143 m), respectively. The ancient Parisian toise (fathom) was slightly shorter than 2 m, and was standardised at exactly 2 m in the mesures usuelles system, such that 1 m was exactly ​¹⁄₂ toise. The Russian versta was 1.0668 km. The Swedish mil was 10.688 km, but was changed to 10 km when Sweden converted to metric units.

See also

• Conversion of units for comparisons with other units
• International System of Units
• Introduction to the metric system
• ISO 1 – standard reference temperature for length measurements
• Length measurement
• Metre Convention
• Metric system
• Metric prefix
• Metrication
• Orders of magnitude (length)
• SI prefix
• Speed of light

References

• 17th General Conference on Weights and Measures. (1983). Resolution 1. International Bureau of Weights and Measures.
• 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, 8:45 a.m.)
• Beers, J.S. & Penzes, W. B. (1992). NIST Length Scale Interferometer Measurement Assurance. (NISTIR 4998). National Institute of Standards and Technology.
• • HTML version. Retrieved 24 August 2008.
• Bureau International des Poids et Mesures. (n.d.). Resolutions of the CGPM (search facility). Retrieved 3 June 2006.
• Bureau International des Poids et Mesures. (n.d.). The BIPM and the evolution of the definition of the metre. Retrieved 3 June 2006.
• Cardarelli, Francois (2003). Encydopaedia of scientific units, weights, and measures: their SI equivalences and origins, Springer-Verlag London Limited, ISBN 1-85233-682-X, page 5, table 2.1, data from Giacomo, P., Du platine a la lumiere, Bull. Bur. Nat. Metrologie, 102 (1995) 5–14.
• Humerfelt, Sigurd. (26 October 2010). How WGS 84 defines Earth. Retrieved 29 April 2011.
• Layer, H.P. (2008). Length—Evolution from Measurement Standard to a Fundamental Constant. Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 18 August 2008.
• Mohr, P., Taylor, B.N., and David B. Newell, D. (28 December 2007). CODATA Recommended Values of the Fundamental Physical Constants: 2006. Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 18 August 2008.
• National Institute of Standards and Technology. (December 2003). The NIST Reference on Constants, Units, and Uncertainty: International System of Units (SI) (web site):
  • SI base units. Retrieved 18 August 2008.
  • Definitions of the SI base units. Retrieved 18 August 2008.
  • Historical context of the SI: Meter. 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.
• National Research Council Canada. (5 February 2010). Maintaining the SI unit of length. Retrieved 4 December 2010.
• Penzes, W. (29 December 2005). Time Line for the Definition of the Meter. Gaithersburg, MD: National Institute of Standards and Technology – Precision Engineering Division. Retrieved 4 December 2010.
• 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.
• Tibo Qorl. (2005) The History of the Meter (Translated by Sibille Rouzaud). Retrieved 18 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.
• Wilkins, J. (c. 2007). An essay towards a real character, and a philosophical language.[Also available without images of original.] Metrication Matters. (Reprinted from title page and pp. 190–194 of original, 1668, London: Royal Society)
• Zagar, B.G. (1999). Laser interferometer displacement sensors in J.G. Webster (ed.). The Measurement, Instrumentation, and Sensors Handbook. CRC Press. isbn=0-8493-8347-1.

Further reading

• Alder, Ken. (2002). The Measure of All Things : The Seven-Year Odyssey and Hidden Error That Transformed the World. Free Press, New York ISBN 0-7432-1675-X

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