Metre

The metre (American English: meter), symbol m, is the base unit of length in the International System of Units (SI). Its definition fixes the numerical value of the speed of light in vacuum at exactly 299,792,458 when expressed in metres per second. Equivalently, one metre is the distance light travels in vacuum in 1/299,792,458 of a second. The unit originated in late eighteenth-century France and has successively been represented by an Earth-based measurement, metal standards, an atomic wavelength, and a definition based on a fundamental constant. (nist.gov)

Definition and physical basis

The defining relation is

where $c$ is the speed of light in vacuum. It therefore follows that

The second is defined through the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, whose numerical value is fixed at 9,192,631,770 hertz. Together, these two fixed constants establish the SI scales of time and length. The metre remains a base unit of length even though its realization depends on the second. (nist.gov)

The reference to vacuum is essential: light propagating through air or another material does not generally have the same speed as light in vacuum. The definition specifies an invariant reference rather than the behaviour of light in an arbitrary measurement environment. The number 299,792,458 was adopted to preserve continuity with the preceding metre definition, within the uncertainty of its experimental realization. (bipm.org)

Historical development

Earth-based origin and the first standard

In 1791, the proposed metre was one ten-millionth of the distance from the equator to the North Pole along the meridian through Paris. This made its intended basis a dimension of the Earth, rather than a local customary measure. Beginning in 1792, astronomers Jean-Baptiste Delambre and Pierre Méchain surveyed the meridian arc between Dunkirk and Barcelona to support the determination of this length. (nist.gov)

In 1799, a platinum bar known as the Mètre des Archives embodied the resulting standard. Its metre was the distance between its polished ends. The Earth-based origin explains the intended scale of the unit, but the modern metre is not defined by a new measurement of the Earth's meridian. (nist.gov)

International prototype

The Metre Convention of 1875 established the institutional framework for international measurement standards, including the International Bureau of Weights and Measures (BIPM). In 1889, the first General Conference on Weights and Measures (CGPM) sanctioned an international prototype metre made from platinum–iridium. The unit was represented by the separation of two engraved lines on the bar at 0 °C. (nist.gov)

An artefact standard required carefully specified conditions and comparisons with national copies. It also tied the ultimate reference to one physical object. The prototype was superseded as the defining standard in 1960, although it remains preserved at the BIPM. (bipm.org)

Atomic wavelength and the speed of light

In 1960, the CGPM defined the metre as 1,650,763.73 vacuum wavelengths of radiation associated with a specified transition in krypton-86. This replaced the metal prototype with an atomic reference that could be reproduced through optical measurements. (bipm.org)

In 1983, the CGPM adopted the definition based on the distance light travels in vacuum during 1/299,792,458 of a second. This fixed the numerical value of $c$, rather than continuing to determine that value experimentally in independently defined metres and seconds. (bipm.org)

The SI revision adopted in 2018 and effective from 20 May 2019 expressed the definition explicitly in terms of the fixed numerical value of $c$. This changed the wording and its place in the constant-based SI framework, not the intended size of the metre. (bipm.org)

Practical realization and measurement

In metrology, a unit's definition is distinguished from its realization: an experiment or procedure that establishes a physical reference consistent with that definition. The metre need not be realized by directly timing a light pulse over a one-metre path. An alternative is to determine the vacuum wavelength $\lambda$ of light with frequency $f$:

A frequency-referenced laser can consequently provide a wavelength standard. Interferometry uses the resulting optical interference pattern to determine lengths or displacements. Time-of-flight methods instead infer distance from light's travel time; for a reflected signal, the measured time includes the outward and return paths. (bipm.org)

Practical measurements remain subject to measurement uncertainty. Optical measurements in air require attention to the refractive index, which depends on environmental conditions. Measurements of physical objects also depend on factors such as temperature, alignment, and the measurement instrument. An exact definition does not make every measured length exact. (bipm.org)

Through calibration and metrological traceability, laboratory realizations support working standards and measuring instruments. Thus an industrial or everyday length measurement can be related to the SI without each instrument independently reproducing the defining experiment. (nist.gov)

Multiples, submultiples, and notation

SI prefixes express decimal multiples and submultiples of the metre. Common examples are:

These relationships are exact. Prefixes attach directly to the unit symbol, while a space separates the numerical value from the symbol: 5 mm, not 5mm. Unit symbols are upright, do not take a plural ending, and are not followed by a full stop except at the end of a sentence. (bipm.org)

Powers apply to the entire prefixed unit. For example, $1\ \mathrm{cm^2}=10^{-4}\ \mathrm{m^2}$, not $10^{-2}\ \mathrm{m^2}$. This distinction matters when converting areas and volumes. (nist.gov)

Derived units and other length systems

The metre enters many SI derived units. Area and volume are expressed in square metres and cubic metres; speed and acceleration in metres per second and metres per second squared. The newton is $\mathrm{kg\,m\,s^{-2}}$, and the joule is $\mathrm{kg\,m^2\,s^{-2}}$. Length therefore participates in the measurement of mechanical quantities as well as distances. (nist.gov)

Several customary length units have exact definitions in terms of the metre:

• One inch equals 0.0254 m.
• One international foot equals 0.3048 m.
• One international yard equals 0.9144 m.
• One international mile equals 1,609.344 m. (nist.gov)

Exact conversion factors do not remove uncertainty from a measured quantity; they only convert its expression between units. Historical surveying records may also use a different foot. The former U.S. survey foot equals exactly $1200/3937$ m, slightly longer than the international foot. It was superseded for new U.S. applications from 1 January 2023, while remaining relevant to historical and legacy data. (nist.gov)

References

1. Definitions of SI Base Unitsnist.gov
2. metrebipm.org
3. SI Brochure - 9th ed./version 4.01bipm.org
4. Time Line for the Definition of the International System of Unitsnist.gov
5. Meternist.gov
6. Defining the International System of Units (SI)nist.gov
7. The Gage Block Handbookemtoolbox.nist.gov
8. Resolution 6 of the 11th CGPM (1960)bipm.org
9. Resolution 1 of the 17th CGPM (1983)bipm.org
10. Mise en pratique for the definition of the metre in the SIbipm.org
11. Recommendation 1 (2002)bipm.org
12. Engineering Metrology Toolboxemtoolbox.nist.gov