Metre
The metre (symbol: m), also spelled meter in American English, is the base unit of length in the International System of Units (SI), used worldwide to measure distances and dimensions in science, engineering, and everyday applications. Defined since 1983 as the distance traveled by light in a vacuum during a time interval of exactly 1/299,792,458 of a second, this standard ensures the metre's precision and universality by linking it to the fixed speed of light, exactly 299,792,458 metres per second.[1][2][3] The metre's origins trace back to the French Revolution in the late 18th century, when scientists sought a rational, decimal-based system of measurement to replace disparate local standards. In 1791, the French Academy of Sciences proposed defining the metre as one ten-millionth of the distance from the Earth's equator to the North Pole along a meridian through Paris, a value determined through geodetic surveys led by Jean-Baptiste Delambre and Pierre Méchain between 1792 and 1798. Due to challenges in the surveys, this was realized by crafting a platinum prototype bar in 1799, which served as the physical artifact standard for the metre until later redefinitions.[1] Over time, the definition evolved to enhance accuracy and reproducibility amid advances in physics and metrology. In 1889, the 1st General Conference on Weights and Measures (CGPM) adopted an international prototype metre bar made of platinum-iridium alloy, preserved at the International Bureau of Weights and Measures (BIPM) in Sèvres, France, which served as the standard until 1960. That year, the 11th CGPM redefined the metre as 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between specific energy levels in krypton-86 atoms, shifting from a material artifact to an atomic reference for greater stability. The 1983 redefinition incorporated the speed of light, eliminating reliance on physical prototypes and aligning the metre with fundamental constants, a framework reaffirmed and clarified in 2019 to emphasize its exact dependence on the defined value of c (the speed of light). These changes reflect ongoing international collaboration under the Metre Convention of 1875, which established the BIPM to maintain SI coherence.[1][4][2] Today, the metre underpins derived SI units like area (square metre) and volume (cubic metre), as well as prefixes such as kilometre (1,000 metres) and nanometre (10⁻⁹ metres), facilitating precise measurements from cosmic scales to atomic structures. Its adoption by virtually all countries worldwide promotes global standardization in fields ranging from construction and navigation to particle physics and telecommunications.[5][6]Fundamentals
Definition and Symbol
The metre is the base unit of length in the International System of Units (SI), defined as the length of the path travelled by light in vacuum during a time interval of \frac{1}{299\,792\,458} of a second, with the speed of light in vacuum fixed at exactly 299 792 458 m/s.[7] This precise formulation establishes the metre as a fundamental measure of distance, directly linking it to a universal physical constant.[8] The symbol for the metre is m, a lowercase letter printed in roman (upright) type regardless of the surrounding text style, distinguishing it from italicized symbols used for physical quantities. In scientific writing, this upright typography ensures clarity, as unit symbols are treated as mathematical entities rather than abbreviations.[9] In dimensional analysis within the SI, the metre corresponds to the base dimension [L] for length, providing the foundation for derived units such as area in square metres (m², dimension [L²]) and volume in cubic metres (m³, dimension [L³]).[10] This dimensional role underscores the metre's centrality in expressing spatial quantities across physics and engineering.[11] The choice of this definition guarantees the metre's invariance and universality, as the speed of light in vacuum is a fundamental constant in special relativity, remaining the same for all inertial observers irrespective of their relative motion. It thereby anchors the unit to principles of relativistic physics, ensuring reproducibility independent of local conditions.[12] This reliance on the second as the SI base unit for time further integrates the metre into the coherent framework of the system.[7]Role in the SI System
The metre (symbol: m) is one of the seven base units of the International System of Units (SI), which also include the second (s) for time, kilogram (kg) for mass, ampere (A) for electric current, kelvin (K) for thermodynamic temperature, mole (mol) for amount of substance, and candela (cd) for luminous intensity.[7] These base units are dimensionally independent and serve as the foundation for deriving all other SI units, ensuring a coherent framework for measurements in physics, chemistry, and engineering.[10] The metre specifically defines length, providing the primary dimension for spatial quantities.[7] The metre's definition depends on the second, as it is realized through the fixed speed of light in vacuum, c = 299\,792\,458 m/s exactly, making the metre the distance light travels in vacuum in $1/299\,792\,458 of a second.[7] This dependency enables the formation of coherent derived units, such as velocity (m/s), force via the newton (N = kg·m/s²), and energy via the joule (J = kg·m²/s²), which combine the metre with other base units without additional scaling factors.[7] These derived units underpin fundamental physical laws and practical applications, from calculating motion in mechanics to quantifying work in thermodynamics.[10] The SI's coherence, with the metre as a core element, guarantees that equations from science and engineering hold numerically without conversion factors between units.[7] For instance, Ohm's law, V = I R, uses the coherent units volt (V), ampere (A), and ohm (Ω = kg·m²/s³·A²), where the metre contributes to the ohm's expression, allowing direct substitution in electrical engineering calculations.[7] As a universal standard, the metre facilitates global standardization across disciplines, enabling precise interoperability in engineering designs, scientific research, international trade, and technologies like GPS, where distances are computed in metres for navigation and positioning.[7][13] This consistency supports economic efficiency by ensuring SI-traceable measurements in manufacturing and commerce, reducing barriers in global supply chains.[13]Etymology and Nomenclature
Origins of the Term
The word "metre," denoting the unit of length in the metric system, derives from the ancient Greek noun métron (μέτρον), which signifies "measure," "limit," or "proportion," and also refers to poetic rhythm or meter. This root entered Latin as metrum, retaining meanings related to measurement and poetic structure, before passing into Old French as metre, where it similarly encompassed ideas of quantity and verse form.[14][15] In the late 18th century, during the development of the metric system in France, the term mètre was formally coined by a commission of the French Academy of Sciences to name the new unit of length, deliberately evoking the classical notion of rational measurement to align with scientific precision. This choice reflected the desire to create a universal standard rooted in ancient linguistic heritage while distinguishing the scientific unit from existing terms for poetic rhythm, particularly as the metric system gained international traction in English-speaking contexts. The name was proposed in reports dating to 1791, emphasizing a decimal-based measure independent of arbitrary local standards.[16][17] The semantic evolution of "metre" shifted from its broad connotation of any "measure" in antiquity—encompassing physical extents, proportions, and even moral limits—to a precise designation for a specific length unit, one ten-millionth of the Earth's meridian quadrant. This transformation was profoundly influenced by Enlightenment principles of rationality, universality, and standardization, which sought to replace fragmented traditional measures with a cohesive, scientifically grounded system accessible to all nations.[16][18] Early scientific applications of the term appeared in the works of key figures like Jean-Charles de Borda, who in 1791 advocated for the mètre as the foundational unit in academy commission reports, and Pierre Méchain, who employed it during meridian arc measurements from 1792 to 1798 to calibrate the standard against Earth's dimensions. These usages marked the term's transition into technical lexicon, underpinning the metric system's adoption amid the French Revolution's reforms.[17][19]Spelling Variations
In British and Commonwealth English, the unit of length is spelled "metre", while "meter" is reserved for measuring instruments, such as a parking meter or gas meter.[20] In contrast, American English uses "meter" for both the unit of length and measuring devices, reflecting a simplified orthography without the distinction.[21] The International Bureau of Weights and Measures (BIPM) SI Brochure recommends "metre" as the standard spelling for the unit in English, while acknowledging regional variations like "meter" in the United States.[7] Similarly, the ISO 80000 series of standards employs "metre" consistently, aligning with international conventions for scientific and technical documentation.[22] In other languages, the spelling varies: French uses "mètre" with a circumflex accent, Italian and Spanish use "metro" without accents, and German uses "Meter" capitalized as a noun.[23] English spellings omit accents, preserving the original French form without diacritics.[24] Historically, the spelling "metre" became standardized in the United Kingdom during the 19th century to distinguish the metric unit from "meter", which denoted poetic rhythm or measuring devices and could cause ambiguity.[20] Modern style guides reinforce these preferences: the Oxford University Press recommends "metre" for the unit in British English contexts, while the Associated Press (AP) Stylebook specifies "meter" for American English publications.[15][21]Historical Development
Pre-Metric Length Standards
Before the adoption of the metric system in the late 18th century, length measurements relied on a diverse array of units derived from human anatomy, natural objects, or local customs, resulting in significant regional variations that complicated trade, construction, and scientific endeavors. In ancient Egypt, the royal cubit served as a primary standard, defined as the length of the pharaoh's forearm from elbow to middle fingertip, measuring approximately 0.524 meters; this unit was inscribed on artifacts like the cubit rods found in tombs dating to around 2700 BCE, allowing for some reproducibility in monumental architecture but varying slightly by dynasty due to differences in physical proportions or wear on reference rods.[25] Similarly, the ancient Greek pous, or foot, averaged about 0.308 meters, based on the average adult foot length, though it fluctuated between 0.270 and 0.350 meters across city-states like Athens and Sparta, reflecting local adaptations for athletics, architecture, and land surveying.[26] The Roman pes, equivalent to roughly 0.296 meters, was standardized as the length of an average foot and subdivided into 12 unciae (inches), enabling consistent application in engineering feats like aqueducts, yet inconsistencies arose in provincial adaptations where local customs altered the base length by up to 5 percent.[27] During the medieval and Renaissance periods, these ancient influences persisted amid further fragmentation, as feudal and mercantile economies demanded practical units for cloth, land, and tools, often leading to royal interventions that proved ineffective. In England, the yard emerged around the 10th century as a cloth measure spanning three feet or the distance from a person's nose to outstretched thumb—decreed by King Henry I in the early 12th century—standardized at about 0.914 meters by the 14th century through statutes like the Assize of Measures, though local markets tolerated variations of 2-3 percent, fostering disputes in wool trade across counties.[28] France's pied du roi, or king's foot, measured approximately 0.325 meters and was tied to the toise (fathom) for surveying, with Charlemagne's 8th-century edicts and later Louis XIV's 1668 ordinance attempting nationwide uniformity, yet regional differences—such as the shorter pied in Provence—persisted due to entrenched guild practices and rural isolation, complicating cross-provincial commerce in textiles and wine.[29] These efforts at centralization, while progressive, failed to eliminate discrepancies, as enforcement relied on itinerant verifiers whose own tools varied, perpetuating a patchwork of standards that hindered economic integration in Europe. By the 17th and 18th centuries, scientific advancements during the Scientific Revolution and Enlightenment highlighted the flaws of anthropomorphic units, prompting proposals for universal, Earth-derived standards to enhance precision in astronomy, geodesy, and international exchange. French astronomer Jean Picard, in the 1670s, conducted the first accurate arc measurement along the Paris meridian using triangulation with a portable quadrant, determining one degree of latitude as about 110.46 kilometers and proposing a "universal foot" as one-third the length of a seconds pendulum at Paris—approximately 0.331 meters—to provide a reproducible basis independent of human variability.[30] Building on this, Jacques Cassini extended meridian surveys in the early 18th century, mapping a larger arc and advocating in 1720 for a geodetic unit derived from the Earth's quadrant, emphasizing decimal subdivisions for navigational and cartographic reliability, though adoption stalled amid national rivalries.[31] Enlightenment thinkers amplified these calls, critiquing arbitrary measures as relics of superstition that impeded rational progress, with figures like Gabriel Mouton independently proposing in 1670 a decimal system based on a minute of longitude arc, underscoring the intellectual shift toward invariant, nature-based units. The core challenge of pre-metric standards was their inherent lack of reproducibility, as units tied to bodies or objects changed with time, location, or user, fueling economic and intellectual friction. Trade disputes proliferated in marketplaces like medieval fairs, where a yard of cloth might differ by inches between English and Flemish merchants, leading to fraud accusations and legal battles documented in Hanseatic League records from the 15th century; similarly, inconsistent feet in shipbuilding caused mismatches in international ports, inflating costs by up to 10 percent in bulk goods like timber.[32] In navigation, varying inches—such as the English versus Dutch foot—introduced errors in dead reckoning and chart scaling during the Age of Sail, contributing to wrecks like those off the Scilly Isles in 1707, where miscalculated distances compounded longitude uncertainties and claimed over 2,000 lives.[33] These issues underscored the urgent need for a global, invariant standard, paving the way for metric reforms without resolving the era's chaotic diversity.Establishment of the Metric System
During the French Revolution, efforts to standardize measurements culminated in the proposal for a universal decimal system by the French Academy of Sciences in 1790. Responding to a request from the National Assembly, the Academy recommended defining the base unit of length, the metre, as one ten-millionth (1/10,000,000) of the distance from the North Pole to the Equator along a meridian quadrant, aiming for an invariable, natural standard derived from the Earth itself. This approach sought to replace the inconsistent regional units prevalent in France and promote international uniformity, with the term "metre" derived from the Greek word for measure.[34] To realize this definition, astronomers Jean-Baptiste Joseph Delambre and Pierre François-André Méchain led a geodetic survey from 1792 to 1798, measuring a meridian arc spanning approximately 9 degrees of latitude from Dunkirk in the north to Barcelona in the south, passing through Paris. Delambre handled the northern section from Dunkirk to Rodez, while Méchain surveyed the southern portion from Rodez to Barcelona, employing triangulation techniques with baselines measured using platinum rods and accounting for the Earth's ellipsoidal shape through astronomical observations. The expedition faced significant challenges, including political instability, imprisonment of team members, and methodological adjustments for refraction and terrain, ultimately providing the data needed to compute the meridian's length.[35][36] In 1793, a provisional metre was defined as one ten-millionth of the meridian half-quadrant (from pole to equator), based on preliminary survey results and earlier geodetic data from Abbé de Lacaille's measurements. This provisional standard allowed for the crafting of the first prototype metre bar, a brass instrument constructed that same year to represent the unit physically. The metric system, including the metre and its decimal multiples such as the decametre (10 metres), was formally legalized on April 7, 1795, through a decree by the French National Convention, establishing it as the official system of weights and measures in the Republic.[34][36] Despite its revolutionary intent, adoption met resistance from artisans and merchants accustomed to traditional units like the pied and toise, who viewed the decimal system as disruptive to daily trade and craftsmanship. This led to the persistence of dual systems in France, with provisional "mesures usuelles" blending metric and customary units until the mid-19th century, when full enforcement occurred in 1840. The system's spread beyond France was facilitated by Napoleonic conquests, influencing adoption in regions like the Netherlands by 1820 and parts of Italy and Germany, though Napoleon temporarily suspended its mandatory use in 1812 to appease local preferences.[19][34]Artifact-Based Definitions (1799–1960)
The initial artifact-based definition of the metre emerged in 1799 with the creation of the mètre des Archives, a platinum bar constructed to represent one ten-millionth of the Earth's meridian quadrant from pole to equator, as determined by geodetic surveys conducted in the 1790s.[37] This bar, featuring a rectangular cross-section and measuring the defined length between its polished end faces at 0 °C, was forged by Étienne Lenoir and deposited in the Archives de la République in Paris on June 22, 1799, following ratification by French legislative decree as the official standard of length.[36] It served as France's legal metre until 1889, providing a tangible reference for metrication efforts despite the prototype's actual length being approximately 0.2 mm shorter than the theoretical quadrant-based value due to survey inaccuracies.[37] In 1889, the 1st General Conference on Weights and Measures (CGPM) established the International Prototype Metre to standardize the unit globally, replacing the mètre des Archives with a more durable artifact.[38] This prototype, an X-shaped bar made of a 90% platinum–10% iridium alloy for enhanced hardness and stability, was defined as the distance between two engraved lines on its neutral surface at 0 °C, calibrated to align closely with the original French standard while aiming to embody one millionth of the Earth's meridian quadrant.[37] Number 6 among 30 such bars produced, it has been stored since September 28, 1889, in a secure lower vault at the Pavillon de Breteuil in Sèvres, France, under controlled conditions including three protective glass domes to minimize environmental exposure.[1] The remaining 29 bars were distributed as national prototypes to signatory nations of the 1875 Metre Convention, enabling consistent international realizations of the metre.[37] Oversight of the International Prototype Metre fell to the International Bureau of Weights and Measures (BIPM), established in 1875 under the Metre Convention, which conducted periodic verifications starting in the early 20th century to monitor stability.[37] Comparisons using optical interferometers and line standards revealed gradual drifts, such as a shortening of about 0.2 μm over several decades attributed to surface wear from handling and atmospheric exposure, prompting refinements in measurement protocols.[37] From 1921 to 1960, stability efforts intensified, including biennial and later triennial calibrations against national copies, improvements to the prototype's engraved lines via repolishing, and detailed studies of thermal effects to ensure reproducibility.[37] Temperature corrections were essential for accurate use, as the platinum-iridium alloy exhibits linear expansion; measurements were standardized at 0 °C, with adjustments applied using the material's coefficient of approximately $9 \times 10^{-6} /^\circ \text{C}, determined through comparator and Fizeau dilatometer methods with uncertainties around $10^{-7} /^\circ \text{C}.[37] Mercury-in-glass thermometers, calibrated against hydrogen gas standards, accompanied each national prototype, along with correction tables accounting for the bar's expansion.[37] In most countries, the legal metre remained tied to these national copies until the 1960 redefinition, which shifted to a wavelength-based standard to eliminate artifact-related instabilities.[39]Wavelength and Speed of Light Redefinitions (1960–1983)
In 1960, the 11th General Conference on Weights and Measures (CGPM) redefined the metre to overcome the instabilities of artifact-based standards, such as wear and thermal expansion in platinum-iridium bars. The new definition set the metre as the length equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the energy levels $2p_{10} and $5d_5 of the krypton-86 atom, an orange-red emission line at 605.78 nm.[39][1] This spectral standard markedly enhanced reproducibility and precision, lowering the relative uncertainty from approximately 0.2 ppm associated with the international prototype metre to better than 0.01 ppm.[40][41] It also enabled the widespread adoption of laser interferometry, allowing direct wavelength comparisons for high-accuracy length realizations without physical artifacts.[1] However, the krypton-86 definition was still anchored to a particular atomic property, limiting its universality compared to invariant constants of nature. During the 1970s, metrologists debated shifting to the speed of light in vacuum (c) as a more fundamental basis, citing its stability and independence from specific materials or isotopes. The 17th CGPM in 1983 implemented this change, abrogating the krypton standard and redefining the metre as the distance light travels in vacuum during 1/299,792,458 of a second, thereby establishing c = 299,792,458 m/s exactly and deriving length from the more precise second.[42] This transition retired the 1960 definition, promoting a metre invariant across space and time.[1]Modern Standards and Realization
1983 Definition and the Speed of Light
The 1983 redefinition of the metre emerged from a series of proposals developed between 1972 and 1983 by the Consultative Committee for the Definition of the Metre (CCDM) and related bodies, which sought to transition from wavelength-based standards to a more fundamental physical constant. These efforts built on the 1975 recommendation by the 15th CGPM to adopt a conventional value for the speed of light in vacuum, c = 299792458 m/s, to enhance measurement consistency across laboratories. The culmination was Resolution 1 of the 17th Conférence Générale des Poids et Mesures (CGPM), adopted on 21 October 1983 and effective immediately for new measurements, which abrogated the 1960 krypton-86 wavelength definition and established a new standard grounded in the invariance of light's propagation speed.[42][1] The primary rationale for this redefinition was to anchor the metre to the universal speed of light c, an invariant quantity from special relativity that is independent of location, medium, or reference frame, thereby eliminating reliance on physical artifacts prone to material degradation or environmental effects. This approach aligned the metre with the second, already defined since 1967 in terms of cesium-133 hyperfine transitions, creating a cohesive SI system where base units derive from reproducible natural phenomena rather than artifacts. By fixing c exactly, the definition addressed limitations in the prior standard's reproducibility, which suffered from uncertainties in atomic radiation frequencies and laser stabilization, achieving a relative uncertainty of \pm 4 \times 10^{-9} (three standard deviations).[42][1] Under the 1983 definition, the metre is the length of the path travelled by light in vacuum during a time interval of $1/299792458 of a second, equivalently stating that light travels exactly 1 metre in $1/299792458 s. This relation formally sets c = 299792458 m/s exactly, transforming the metre into a unit conceptually derived from the second and the fixed constant c, though it remained a base unit for practical metrology purposes. The shift enabled realizations via interferometry and time-of-flight methods with dramatically improved precision, reducing relative uncertainty in practical measurements to approximately $10^{-12}, limited primarily by laser frequency stability rather than definitional ambiguities.[42][1]2019 SI Revision and Implications
In November 2018, the 26th General Conference on Weights and Measures (CGPM) adopted a comprehensive revision of the International System of Units (SI), redefining all seven base units in terms of fixed numerical values of fundamental physical constants. This included the Planck constant h, the Avogadro constant N_A, the Boltzmann constant k, and the elementary charge e, among others, marking a shift from artifact-based or partially empirical definitions to a fully invariant system grounded in nature's constants.[7] The metre's definition remained unchanged from its 1983 formulation, continuing to be realized by fixing the speed of light in vacuum at exactly c = 299\,792\,458 m/s, with the second defined via the caesium hyperfine transition frequency \Delta \nu_{\text{Cs}} = 9\,192\,631\,770 Hz.[43] For the metre specifically, the revision had no direct alteration but reinforced its stability within a more coherent SI framework. By linking the kilogram to the Planck constant—now fixed at h = 6.626\,070\,15 \times 10^{-34} J s—this change strengthened interconnections between length, mass, and energy scales, as the joule relates to metre through force and work.[44] The exact value of c carries zero uncertainty by definition, ensuring the metre's realization remains precise and reproducible without reliance on physical prototypes, while the system's overall invariance reduces propagation of measurement uncertainties across units.[7] Broader implications of the revision extend to future-proofing the SI, as explicit numerical values for constants like e = 1.602\,176\,634 \times 10^{-19} C and h enable advancements in quantum metrology without redefining units. The metre's foundational role, tied to the universal constant c, is thus solidified, supporting applications in fields such as interferometry and laser-based standards that bridge classical and quantum realms.[43] This coherence enhances the SI's applicability in high-precision science and technology, where length measurements often interface with redefined units like the ampere and kelvin. The revised SI entered into force on 20 May 2019, coinciding with World Metrology Day. The ninth edition of the SI Brochure, published by the International Bureau of Weights and Measures (BIPM), incorporates these changes, emphasizing explicit-formula representations for all base units to guide practical realizations and educational use.[44]Practical Measurement Techniques
The practical realization of the metre in laboratories relies primarily on optical interferometry using frequency-stabilized lasers, which leverages the fixed speed of light c and precise frequency measurements to determine length via the wavelength \lambda = c / f.[45] Helium-neon (He-Ne) lasers operating at 633 nm, stabilized to hyperfine transitions in iodine-127 molecules, serve as a widely adopted secondary standard for this purpose, achieving relative standard uncertainties on the order of $10^{-11}.[46] In this method, the interference pattern produced by the laser beam over a known path yields the length as l = m \lambda / 2, where m is the fringe order counted with a phase-measuring interferometer; corrections for environmental factors such as air refractive index (typically 0.00027 at standard conditions for 633 nm light) and thermal expansion ensure traceability to the SI definition.[47] These systems are portable and suitable for calibrating gauge blocks or machine tools, with the iodine stabilization providing long-term frequency stability better than 1 part in $10^{10}.[48] For longer distances, time-of-flight (ToF) methods measure the propagation time t of light pulses over a path, realizing length as l = c \cdot t / 2 in vacuum or adjusted for the medium.[45] This approach employs femtosecond lasers or modulated continuous-wave sources synchronized to atomic clocks, enabling precise timing with picosecond resolution; for instance, in the Global Positioning System (GPS), satellite signals use caesium atomic clocks to compute pseudoranges via ToF, where light travels approximately 300 m per microsecond, supporting metre-level positioning accuracy after relativistic and atmospheric corrections.[47] ToF is particularly effective for geodetic applications like lunar laser ranging, where relative uncertainties below $10^{-8} are achieved over interplanetary distances.[45] In everyday applications, length measurements with tools such as rulers and digital calipers maintain traceability to the SI metre through hierarchical calibration chains coordinated by national metrology institutes (NMIs).[49] Ruler graduations are verified against gauge blocks calibrated via interferometry at NMIs, while digital calipers trace their scales to these standards through intermediate artifacts like step gauges, ensuring an unbroken chain documented per ISO/IEC 17025 guidelines. This process typically involves annual recalibrations, with environmental controls limiting deviations to within 0.1 mm for metre-scale tools. Routine laboratory realizations of the metre achieve absolute uncertainties around $10^{-8} m, while primary standards using iodine-stabilized He-Ne lasers reach $10^{-11} relative precision; international consistency is verified through the BIPM's Consultative Committee for Length (CCL) key comparisons, such as CCL-K11, where participating NMIs compare optical frequency standards at 633 nm with degrees of equivalence typically within \pm 10 \times 10^{-12} (95% confidence).[45][50] These comparisons, conducted periodically, underpin global equivalence of length measurements by linking NMIs to the CIPM reference values.[51]Multiples, Submultiples, and Equivalents
SI Prefixes for the Metre
The SI prefixes provide a systematic way to denote decimal multiples and submultiples of the metre, enabling the expression of lengths from the subatomic scale to astronomical distances using powers of 10. These prefixes are standardized and applied directly to the base unit symbol 'm', resulting in derived units like km for kilometre (10³ m) or nm for nanometre (10⁻⁹ m). The full range spans from quecto- (q, 10⁻³⁰), added in 2022 for extreme subatomic scales, to quetta- (Q, 10³⁰) for immense cosmological distances, with practical applications for the metre typically falling within a narrower subset. Prefix rules, as outlined in international standards, require that only one prefix be used per unit, with the prefix symbol attached without spaces or hyphens to the unit symbol (e.g., μm for micrometre).[52][53] The following table summarizes the standard SI prefixes applicable to the metre:| Prefix | Symbol | Power of 10 | Metre unit example |
|---|---|---|---|
| quetta | Q | 10³⁰ | Qm |
| ronna | R | 10²⁷ | Rm |
| yotta | Y | 10²⁴ | Ym |
| zetta | Z | 10²¹ | Zm |
| exa | E | 10¹⁸ | Em |
| peta | P | 10¹⁵ | Pm |
| tera | T | 10¹² | Tm |
| giga | G | 10⁹ | Gm |
| mega | M | 10⁶ | Mm |
| kilo | k | 10³ | km |
| hecto | h | 10² | hm |
| deca | da | 10¹ | dam |
| (none) | - | 10⁰ | m |
| deci | d | 10⁻¹ | dm |
| centi | c | 10⁻² | cm |
| milli | m | 10⁻³ | mm |
| micro | µ | 10⁻⁶ | µm |
| nano | n | 10⁻⁹ | nm |
| pico | p | 10⁻¹² | pm |
| femto | f | 10⁻¹⁵ | fm |
| atto | a | 10⁻¹⁸ | am |
| zepto | z | 10⁻²¹ | zm |
| yocto | y | 10⁻²⁴ | ym |
| ronto | r | 10⁻²⁷ | rm |
| quecto | q | 10⁻³⁰ | qm |
Conversions to Other Units
The conversions between the metre and non-SI units from imperial, US customary, nautical, and other traditional systems are standardized through international agreements to ensure precision in engineering, navigation, and international trade. These factors derive primarily from the 1959 International Yard and Pound Agreement, which defined the yard as exactly 0.9144 metres to align US and British standards with the metric system.[57] In the imperial and US customary systems, the metre relates exactly to the inch via the definition of 1 inch = 0.0254 metres, yielding 1 metre = 39.37007874 inches.[57] Since 1 foot = 12 inches and 1 yard = 3 feet, this extends to 1 metre ≈ 3.280839895 feet and 1 metre ≈ 1.093613298 yards.[57] For longer distances, the statute mile (used in engineering and land measurement) is defined as 5280 feet, resulting in exactly 1609.344 metres per mile.[57] The international nautical mile, adopted for maritime and aviation navigation, is exactly 1852 metres, so 1 metre ≈ 0.539956803 nautical miles. In other traditional systems, conversions are approximate due to historical variations, but modern standardized equivalents exist. The Chinese chi (市尺), a common unit in contemporary usage, measures approximately 0.333 metres.[58] Similarly, the Japanese shaku (尺), part of the traditional shakkanhō system, is approximately 0.303 metres.[59] Historical cubits, used in ancient civilizations like Egypt and Mesopotamia, varied significantly; the short (anthropological) cubit was typically around 0.444 to 0.457 metres, while the long (architectural) cubit ranged from 0.518 to 0.529 metres, reflecting regional and temporal differences in standardization.[60]| Unit | Conversion to Metre | Notes |
|---|---|---|
| Inch (in) | 1 m = 39.37007874 in | Exact, from 1 in = 0.0254 m (1959 agreement)[57] |
| Foot (ft) | 1 m ≈ 3.280839895 ft | Derived from yard definition[57] |
| Yard (yd) | 1 m ≈ 1.093613298 yd | From 1 yd = 0.9144 m exactly (1959 agreement)[57] |
| Statute mile (mi) | 1 mi = 1609.344 m | Exact, 5280 ft per mile[57] |
| Nautical mile (nm) | 1 nm = 1852 m | Exact, international standard since 1929 |
| Chinese chi (市尺) | 1 chi ≈ 0.333 m | Modern usage, 1 m ≈ 3 chi[58] |
| Japanese shaku (尺) | 1 shaku ≈ 0.303 m | Traditional shakkanhō system[59] |
| Cubit (historical) | ≈ 0.444–0.529 m | Variations: short ~0.444–0.457 m; long ~0.518–0.529 m[60] |