From Wikipedia, the free encyclopedia
"M^2" redirects here. For other uses, see .
This article needs additional citations for . Please help
by . Unsourced material may be challenged and removed. (January 2015)
Comparison of 1 Square metre with some Imperial and metric units of area
The square metre ( as used by the ) or square meter () is the
of , with symbol m2 (33A1 in ). It is defined as the area of a
whose sides measure exactly one . The square metre is derived from the
of the metre, which itself is defined as the
of the path travelled by
in absolute
interval of 1/299,792,458 of a .
Adding and subtracting
creates multip however, as the unit is squared, the
difference between units doubles from their comparable linear units. For example, a
is one thousand times the length of a metre, but a square kilometre is one million times the area of a square metre.
The square metre may be used with all SI prefixes used with the meter.
Multiplication
Multiplication
square metre ()
square metre ()
square decametre ()
square decimetre
square hectometre ()
square centimetre
square millimetre
square megametre
square micrometre
square gigametre
square nanometre
square terametre
square picometre
square petametre
square femtometre
square exametre
square attometre
square zettametre
square zeptometre
square yottametre
square yoctometre
A square metre is equal to:
10,000 square centimetres (cm2)
0.001 decares (daa)
0.1 deciares (da)
0.000 247 105 381
0.024 710 538
10.763 911
1,550.003 1
(home page)
(SI reference)
: Hidden categories:From Wikipedia, the free encyclopedia
This article is about the unit of length.
For other uses of "metre" or "meter", see .
in Wiktionary, the free dictionary.
The metre,
meter, (from the Greek noun μ?τρον, "measure") is the
of length in the
(SI). The SI
symbol is m. The metre is defined as the distance travelled by light in a specific fraction – about one three-hundred millionths – of a .
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
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.
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 , ) 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.
The etymological roots of metre can be traced to the Greek verb μετρ?ω (metreo) (to measure, count or compare) and noun μ?τρον (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 , which was a saying of the Greek statesman and philosopher
and may be translated as "Use measure!", thus calls for both measurement and moderation.
Main article:
In 1668 the English cleric and philosopher
proposed in an essay a decimal-based unit of length, the universal measure or standard. In 1670 , 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 , in his work Misura Universale, used the phrase metro cattolico ("universal measure"), derived from the Greek
(métron katholikón), to denote the standard unit of length derived from a pendulum. As a result of the , the
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
and the , In 1793, the French
this use of metre in English began at least as early as 1797.
—the northern end of the meridian arc
—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
In 1668, Wilkins proposed using 's suggestion of defining the metre using a
with a length which produced a half- of one , known as a ''.
had observed that length to be 38
or 39.26 . This is the equivalent of what is now known to be 997 mm. No official action was taken regarding this suggestion.
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 the ' that is, the distance from the
to the . This means that the quadrant (a section/distance
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
selected the meridional definition over the pendular definition because the force of
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
and , lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in
to estimate the length of the
through Dunkerque. This portion of the meridian, assumed to be the same length as the , was to serve as the basis for the length of the quarter 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
or , 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 , 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.
In the 1870s and in light of modern precision, a series of international conferences was held to devise new metric standards. The
(Convention du Mètre) of 1875 mandated the establishment of a permanent
(BIPM: Bureau International des Poids et Mesures) to be located in , 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
(CGPM: Conférence Générale des Poids et Mesures), establishing the
as the distance between two lines on a standard bar composed of an alloy of 90%
and 10% , measured at the melting point of ice.
However, it was later determined that the first
was short by about 200 micrometres because of miscalculation of the
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.
In 1893, the standard metre was first measured with an
by , the inventor of the device and an advocate of using some particular
as a standard of length. By 1925,
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
(SI) as equal to 1 650 763.73
of the -86
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
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
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
"a recommended radiation" for realising the metre. For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, λHeNe, 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
(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 .
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
(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
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
for a length measurement:
Uncertainty in vacuum wavelength of the source
Uncertainty in the refractive index of the medium
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:
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
of the medium in which the 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.
Closeup of National Prototype Metre Bar No. 27, made in 1889 by the
(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
1790, May 8 – The
decides that the length of the new metre would be equal to the length of a
with a half- of one .
1791, March 30 – The French National Assembly accepts the proposal by the
that the new definition for the metre be equal to one ten-millionth of the length of the Earth's
along a quadrant through Paris, that is the distance from the equator to the north pole.
;– Provisional metre bar constructed of . Based on
ellipsoid and legally equal to 443.44
on the toise du Pérou (a standard
from 1747).
1799, December 10  – The French National Assembly specifies the platinum metre bar, constructed on 23 June 1799 and deposited in the , as the final standard. Legally equal to 443.296 lines on the toise du Pérou.
1889, September 28 – The 1st
(CGPM) defines the metre as the distance between two lines on a standard bar of an alloy of
with 10% , measured at the melting point of ice.
1927, October 6 – The 7th CGPM redefines the metre as the distance, at 0  (273 ), between the axes of the two central lines marked on the prototype bar of platinum-iridium, this bar being subject to one standard
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.
1960, October 14 – The 11th CGPM defines the metre as 1650763.73
corresponding to the transition between the 2p10 and 5d5 quantum levels of the -86 .
1983, October 21 – The 17th
defines the metre as the length of the path travelled by
during a time interval of 1/299 792 458 of a .
(CIPM) considers the metre to be a unit of
and thus recommends this definition be restricted to "lengths l which are sufficiently short for the effects predicted by
to be negligible with respect to the uncertainties of realisation".
Definitions of the metre since 1795
Basis of definition
uncertainty
uncertainty
1/10 000 000 part of the quarter of a meridian, astronomical measure by Bessel (443.44 lines)
500–100 μm (0.5–0.1 mm)
1/10 000 000 part of the quarter of a meridian, measurement by Delambre and Mechain (443.296 lines)
500–100 μm
First prototype Metre des Archives platinum bar standard
50–10 μm
Platinum-iridium bar at melting point of ice (1st )
0.2–0.1 um (200-100 nm)
Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM)
1650763.73 wavelengths of light from a specified transition in -86 (11th CGPM)
Length of the path travelled by light in a vacuum in 1/299 792 458 of a second (17th CGPM)
0.1 nm
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,
(149.6 Gm),
(10 Pm), or
(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
zeptometre
zettametre
yoctometre
yottametre
Common prefixed units are in bold face.
Metric unit
expressed in non-SI units
Non-SI unit
expressed in metric units
centimetres
millimetres
1 ?ngstr?m
1 ?ngstr?m
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.
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
was about 0.5 m (surviving rods are 523–529 mm.) Scottish and English definitions of the
(two cubits) were 941 mm (0.941m) and 1 143 mm (l.143 m), respectively. The ancient Parisian toise (fathom) was slightly shorter than 2 m, and was standardised at exactly 2 m in the
system, such that 1 m was exactly 1/2 toise. The Russian
was 1.0668 km. The
was 10.688 km, but was changed to 10 km when Sweden converted to metric units.
for comparisons with other units
 – standard reference temperature for length measurements
The most recent official brochure about the International System of Units (SI), written in French by the Bureau international des poids et mesures,
uses the spelling metre; an English translation, included to make the SI standard "more widely accessible" also uses the spelling metre.(, p. 130ff) However, in 2008 the U.S. English translation published by the U.S.
chose to use the spelling meter in accordance with the United States Government Printing Office Style Manual. The Metric Conversion Act of 1975 gives the Secretary of Commerce of the US the responsibility of interpreting or modifying the SI for use in the US. The Secretary of Commerce delegated this authority to the Director of the
(NIST) (). In 2008, NIST published the US version () of the English text of the eighth edition of the BIPM publication Le Système international d'unités (SI) (BIPM, 2006). In the NIST publication, the spellings "meter", "liter" and "deka" are used rather than "metre", "litre" and "deca" as in the original BIPM English text (). The Director of the NIST officially recognised this publication, together with , as the "legal interpretation" of the SI for the United States (). Thus, the spelling metre is referred to as the "international spelling"; the spelling meter, as the "American spelling".
. . 2008., s.v. ammeter, meter, parking meter, speedometer.
American Heritage Dictionary of the English Language (3rd ed.). Boston: . 1992., s.v. meter.
George Sarton (1935). . Isis 23 (1): 153–244. :.
('decimalization is not of the essence
the real significance of this is that it was the first great attempt to define terrestrial units of measure in terms of an unvarying astronomical or geodetic constant.) The metre was in fact defined as one ten millionth of one quarter of the earth's circumference at sea-level.' , , Cambridge University Press, 1962 vol.4, pt.1, p.42.
Paolo Agnoli,Il senso della misura: la codifica della realtà tra filosofia, scienza ed esistenza umana, Armando Editore, 2004 pp.93-94,101.
(in French). Gallica.bnf.fr. .
Paolo Agnoli and Giulio D’Agostini, December, 2004 pp.1-29.
, Clarendon Press 2nd ed.1989, vol.IX p.697 col.3.
Marion, Jerry B. (1982). Physics For Science and Engineering. CBS College Publishing. p. 3.  .
(PDF). MEP (Mise en Pratique). BIPM. .
The term "relative standard uncertainty" is explained by NIST on their web site: . The NIST Reference on constants, units, and uncertainties: Fundamental physical constants. NIST 2011.
A more detailed listing of errors can be found in Beers, John S; Penzes, William B (December 1992).
(PDF). NIST length scale interferometer m NIST document NISTIR 4998. pp. 9 ff 2011.
The formulas used in the calculator and the documentation behind them are found at . NIST. September 23, . The choice is offered to use either the
or the . The documentation provides
between the two possibilities.
. Engineering metrology toolbox: Refractive index of air calculator. NIST. September 23, .
Dunning, F. B.; Hulet, Randall G. (1997). "Physical limits on accuracy and resolution: setting the scale". . Academic Press. p. 316.  . The error [introduced by using air] can be reduced tenfold if the chamber is filled with an atmosphere of helium rather than air.
The BIPM maintains a list of recommended radiations on their web site.
Resolution 1 of the 17th meeting of the CGPM (1983)
Well-known conversion, publicised at time of metrication.[]
17th . (1983).
Astin, A. V. & Karo, H. Arnold, (1959), , Washington DC: National Bureau of Standards, republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, Filed, 30 June  a.m.)
Barbrow, Louis E. & Judson, Lewis V. (1976).
(Special Publication 447).. National Institute of Standards and Technology.
Beers, J.S. & Penzes, W. B. (1992).
(NISTIR 4998). .
(PDF) (in French). Bureau International des Poids et Mesures. .
. Retrieved 24 August 2008.
Bureau International des Poids et Mesures. (n.d.).
(search facility). Retrieved 3 June 2006.
Bureau International des Poids et Mesures. (n.d.). . Retrieved 3 June 2006.
Cardarelli, Francois (2003). Encydopaedia of scientific units, weights, and measures: their SI equivalences and origins, Springer-Verlag London Limited, , page 5, table 2.1, data from Giacomo, P., Du platine a la lumiere, Bull. Bur. Nat. Metrologie, 102 (.
Humerfelt, Sigurd. (26 October 2010). . Retrieved 29 April 2011.
Layer, H.P. (2008). . 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). . Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 18 August 2008.
National Institute of Standards and Technology. (December 2003).
(web site):
. Retrieved 18 August 2008.
. Retrieved 18 August 2008.
. Retrieved 26 May 2010.
National Institute of Standards and Technology. (27 June 2011). . Author.
National Physical Laboratory. (25 March 2010). . Author.
National Research Council Canada. (5 February 2010). . Retrieved 4 December 2010.
Penzes, W. (29 December 2005). . Gaithersburg, MD: National Institute of Standards and Technology – Precision Engineering Division. Retrieved 4 December 2010.
Taylor, B.N. and Thompson, A. (Eds.). (2008a). . 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).
(Special Publication 811). Gaithersburg, MD: National Institute of Standards and Technology. Retrieved 23 August 2008.
Tibo Qorl. (2005)
(Translated by Sibille Rouzaud). Retrieved 18 August 2008.
Turner, J. (Deputy Director of the National Institute of Standards and Technology). (16 May 2008).. Federal Register Vol. 73, No. 96, p. 28432-3.
Wilkins, J. (c. 2007). .[Also available .] Metrication Matters. (Reprinted from title page and pp. 190–194 of original, 1668, London: Royal Society)
Zagar, B.G. (1999).
in J.G. Webster (ed.). The Measurement, Instrumentation, and Sensors Handbook. CRC Press. isbn=0-.
Wikimedia Commons has media related to .
Alder, Ken. (2002). The Measure of All Things : The Seven-Year Odyssey and Hidden Error That Transformed the World. Free Press, New York
: Hidden categories:}