Meter

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

**1 metre** =
SI units
100 cm	1000 mm
US customary / Imperial units
3.2808 ft	39.370 in

The metre or meter^[1] is a measure of length. It is the basic unit of length in the metric system and in the International System of Units (SI), used around the world for general and scientific purposes. Historically, the metre was defined by the French Academy of Sciences as the length between two marks on a platinum-iridium bar, which was designed to represent ¹⁄_10,000,000 of the distance from the equator to the north pole through Paris. Today, it is defined by the International Bureau of Weights and Measures as the distance travelled by light in absolute vacuum in ¹⁄_299,792,458 of a second.

The symbol for metre is m (never capital M). Decimal multiples and submultiples of the metre, such as kilometre (1000 metres) and centimetre (¹⁄₁₀₀ metre), are indicated by adding SI prefixes to metre (see table below).

1 History
2 SI prefixed forms of metre
3 Equivalents in other units
4 See also
5 References
6 Notes
7 External links

History

The word metre is from the Greek metron (μέτρον), "a measure" via the French mètre. Its first recorded usage in English meaning this unit of length is from 1797.

Meridional definition

In the eighteenth century, there were two favoured approaches to the definition of the standard unit of length. One approach suggested defining the metre as the length of a pendulum with a half-period of one second. The other approach suggested defining the metre as one ten-millionth of the length of the Earth's meridian along a quadrant, that is the distance from the equator to the north pole. 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.

In order to establish a universally accepted foundation for the definition of the metre, measurements of this meridian more accurate than those available at that time were imperative. The Bureau des Longitudes commissioned an expedition led by Delambre and Pierre Méchain, lasting from 1792 to 1799, which measured the length of the meridian between Dunkerque and Barcelona. This portion of the meridian, which also passes through Paris, was to serve as the basis for the length of the half meridian, connecting the North Pole with the Equator.

However, in 1793, France adopted as its official unit of length a metre based on provisional results from the expedition as its official unit of length. Although it was later determined that the first prototype metre bar was short by a fifth of a millimetre due to miscalculation of the flattening of the Earth, this length became the standard. The circumference of the Earth through the poles is therefore slightly more than forty million metres.

Prototype metre bar

Historical International Prototype Meter bar, made of an alloy of platinum and iridium, that was the standard from 1889 to 1960.

In the 1870s and in light of modern precision, a series of international conferences were 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 would preserve the new prototype metre and kilogram standards when constructed, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organization created a new prototype 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 ninety percent platinum and ten percent iridium, measured at the melting point of ice.

Standard wavelength of krypton-86 emission

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 distance. 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 SI system 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. The original international prototype of the metre is still kept at the BIPM under the conditions specified in 1889.

Standard wavelength of helium-neon laser light

To further reduce uncertainty, the seventeenth CGPM in 1983 replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of time and the speed of light:

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.^[2]

Note that this definition had the effect of fixing the speed of light in a vacuum at precisely 299,792,458 metres per second. Although the metre is now defined in terms of time-of-flight, actual laboratory realisations of the metre are still delineated by counting the required number of wavelengths of light along the distance. An intended byproduct of the 17^th CGPM’s definition was that it enabled scientists to measure the wavelength of their lasers with one-fifth the uncertainty. To further facilitate reproducibility from lab to lab, the 17^th CGPM also made the iodine-stabilised helium-neon laser “a recommended radiation” for realising the metre. For purposes of delineating the metre, the BIPM currently considers the HeNe laser wavelength to be as follows: λ_HeNe = 632.99139822 nm with an estimated relative standard uncertainty (U) of 2.5 × 10^–11.^[3] This uncertainty is currently the limiting factor in laboratory realisations of the metre as it is several orders of magnitude poorer than that of the second (U = 5 × 10^–16).^[4] Consequently, a practical realisation of the metre is usually delineated (not defined) today in labs as 1,579,800.298728(39) wavelengths of helium-neon laser light in a vacuum.

Timeline of definition

1790 May 8 — 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.

1791 March 30 — 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 the Earth's meridian along a quadrant through Paris, that is the distance from the equator to the north pole.

1795 — Provisional metre bar constructed of brass.

1799 December 10 — The French National Assembly specifies the platinum metre bar, constructed on 23 June 1799 and deposited in the National Archives, as the final standard.

1889 September 28 — The first General Conference on Weights and Measures (CGPM) defines the length as the distance between two lines on a standard bar of an alloy of platinum with ten percent iridium, measured at the melting point of ice.

1927 October 6 — The seventh CGPM adjusts the definition of the length to be the distance, at 0 °C, 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 one centimetre diameter, symmetrically placed in the same horizontal plane at a distance of 571 millimetres from each other.

1960 October 20 — The eleventh CGPM defines the length to be equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the 2p¹⁰ and 5d⁵ quantum levels of the krypton-86 atom.

1983 October 21 — The seventeenth CGPM defines the length as equal to the distance travelled by light in vacuum during a time interval of ¹⁄_299,792,458 of a second.

SI prefixed forms of metre

Orders of magnitude (length) in E notation
0 m 1 E-24 m 1 E-23 m 1 E-22 m 1 E-21 m 1 E-20 m 1 E-19 m 1 E-18 m 1 E-17 m 1 E-16 m 1 E-15 m 1 E-14 m 1 E-13 m 1 E-12 m 1 E-11 m 1 E-10 m 1 E-9 m 1 E-8 m 1 E-7 m 1 E-6 m 1 E-5 m 1 E-4 m 1 E-3 m 1 E-2 m 1 E-1 m 1 E0 m	1 E+1 m 1 E+2 m 1 E+3 m 1 E+4 m 1 E+5 m 1 E+6 m 1 E+7 m 1 E+8 m 1 E+9 m 1 E+10 m 1 E+11 m 1 E+12 m 1 E+13 m 1 E+14 m 1 E+15 m 1 E+16 m 1 E+17 m 1 E+18 m 1 E+19 m 1 E+20 m 1 E+21 m 1 E+22 m 1 E+23 m 1 E+24 m 1 E+25 m 1 E+26 m

SI prefixes are often employed to denote decimal multiples and submultiples of the metre, as shown in the table below.

SI multiples for metre (m)

Submultiples			Multiples
Value	Symbol	Name	Value	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.^[5]

Equivalents in other units

Metric unit expressed in non-SI unit				Non-SI unit expressed in metric unit
1 metre	≡	10⁻⁴	mil	1 Norwegian/Swedish mil	≡	10⁴	metres
1 metre	≈	39.37	inches	1 inch	≡	0.0254	metres
1 centimetre	≈	0.3937	inch	1 inch	≡	2.54	centimetres
1 millimetre	≈	0.03937	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" means "international inch".

References

Bureau International des Poids et Mesures. The BIPM and the evolution of the definition of the metre. Retrieved 2006 June 3.
———. Resolutions of the CGPM. Retrieved 2006 June 3.
Penzes, William B. at the U.S. National Institute of Standards and Technology Precision Engineering Division (2005 December 29). Time Line for the Definition of the Meter. Retrieved 2006 June 3.
U.S. National Institute of Standards and Technology (October 2000). The NIST Reference on Constants, Units, and Uncertainty: International System of Units (SI):
- SI base units. Retrieved 2006 June 3.
- Definitions of the SI base units. Retrieved 2006 June 3.
- Historical context of the SI: meter. Retrieved 2006 June 3.
- Peter Mohr CODATA presentation October 2006
- CODATA recommendations 2006

Notes

^ See American and British English spelling differences
^ Resolution 1 of the seventeenth CGPM (1983): Definition of the metre
^ Citations: Time Line for the Definition of the Meter by the NIST; and these papers from a search at the BIPM database; particularly Optical Frequency - Maintaining the SI Metre by the National Research Council Canada
^ NIST: NIST-F1 Cesium Fountain Atomic Clock.
^ Based upon cutoff point of one million combined Google hits on the plural form of both the international and U.S. spellings. The bolded values returned an aggregate of between 3.66 and 51.4 million hits. Whereas the micrometer is also a device for measuring small distances, a search in September 2007 yielded over four million hits on the two variations of the micrometre. In comparison, the most common prefixed form of the metre that didn’t reach the cutoff threshold—the decimetre—yielded a total of only 322,000 hits even though it is often employed to explain the volume of a litre.