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Foot (unit)

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This article is about the unit of measure. For sizing of the human foot, seeShoe size.For other uses, seeFoot (disambiguation).

foot
A foot-long ruler
General information
Unit systemImperial/USunits
Unit ofLength
Symbolft, ′
Conversions
1 ftin...... is equal to...
Imperial/US units
  • ⁠1/3⁠yd
  • 12in
Metric(SI) units

Thefoot(standard symbol:ft)[1][2]is aunitoflengthin theBritish imperialandUnited States customarysystems ofmeasurement.Theprime symbol,′,is commonly used to represent the foot.[3]In both customary and imperial units, one foot comprises 12inches,and oneyardcomprises three feet. Sincean international agreement in 1959,the foot is defined as equal to exactly 0.3048 meters.

Historically, the "foot" was a part of many local systems of units, including theGreek,Roman,Chinese,French,andEnglishsystems. It varied in length from country to country, from city to city, and sometimes from trade to trade. Its length was usually between 250 mm and 335 mm and was generally, but not always, subdivided into 12 inches or 16digits.

The United States is the onlyindustrializedcountry that uses the (international) foot in preference to the meter in its commercial, engineering, and standards activities.[4]The foot is legally recognized in the United Kingdom; road distance signsmustuse imperial units (however, distances on road signs are always marked in miles or yards, not feet; bridge clearances are given in meters as well as feet and inches), while its usage is widespread among the British public as a measurement of height.[5][6]The foot is recognized as an alternative expression of length in Canada.[7]Both the UK and Canada have partiallymetricatedtheir units of measurement. The measurement ofaltitudein internationalaviation(theflight levelunit) is one of the few areas where the foot is used outside the English-speaking world.

The most common plural of foot isfeet.However, the singular form may be used like a plural when it is preceded by a number, as in "he is six foot tall."[8]

Historical origin

[edit]
See also:pous
Determination of the rod, using the length of the left foot of 16 randomly chosen people coming from church service. Woodcut published in the bookGeometreybyJakob Köbel(Frankfurt,c. 1535).

Historically, the human body has been used to provide the basis for units of length.[9]The foot of an adult European-American male is typically about 15.3% of his height,[10]giving a person of 175 cm (5 ft 9 in) a foot-length of about 268 mm (10.6 in), on average.

Archaeologists believe that, in the past, the people ofEgypt,India,andMesopotamiapreferred thecubit,while the people ofRome,Greece,andChinapreferred the foot. Under the Harappan linear measures, Indus cities during the Bronze Age used a foot of 13.2 inches (335 mm) and a cubit of 20.8 inches (528 mm).[11]TheEgyptianequivalent of the foot—a measure of four palms or 16 digits—was known as thedjeserand has been reconstructed as about 30 cm (11.8 in).

The Greek foot (πούς,pous) had a length of⁠1/600⁠of astadion,[12]one stadion being about 181.2 m (594 ft);[13]therefore a foot was, at the time, about 302 mm (11.9 in). Its exact size varied from city to city and could range between 270 mm (10.6 in) and 350 mm (13.8 in), but lengths used for temple construction appear to have been about 295 mm (11.6 in) to 325 mm (12.8 in); the former was close to the size of the Roman foot.

The standardRoman foot(pes) was normally about 295.7 mm (11.6 in) (97% of today's measurement),[14]but in some provinces, particularlyGermania Inferior,the so-calledpes Drusianus(foot ofNero Claudius Drusus) was sometimes used, with a length of about 334 mm (13.1 in). (In reality, this foot predated Drusus.)[15][16]

Originally both the Greeks and the Romans subdivided the foot into 16digits,but in later years, the Romans also subdivided the foot into 12unciae(from which both the English words "inch" and "ounce"are derived).

After the fall of the Roman Empire, some Roman traditions were continued but others fell into disuse. In AD 790Charlemagneattempted to reform the units of measure in his domains. His units of length were based on thetoiseand in particular thetoise de l'Écritoire,the distance between the fingertips of the outstretched arms of a man.[17]Thetoisehas 6pieds(feet) each of 326.6 mm (12.9 in).

He was unsuccessful in introducing a standard unit of length throughout his realm: an analysis of the measurements ofCharlieu Abbeyshows that during the 9th century the Roman foot of 296.1 mm (11.66 in) was used; when it was rebuilt in the 10th century, a foot of about 320 mm (12.6 in)[Note 1]was used. At the same time, monastic buildings used the Carolingian foot of 340 mm (13.4 in).[Note 1][18]

The procedure for verification of the foot as described in the 16th century posthumously published work byJacob Köbelin his bookGeometrei. Von künstlichem Feldmessen und absehenis:[19][20]

Stand at the door of a church on a Sunday and bid 16 men to stop, tall ones and small ones, as they happen to pass out when the service is finished; then make them put their left feet one behind the other, and the length thus obtained shall be a right and lawfulroodto measure and survey the land with, and the 16th part of it shall be the right and lawful foot.

England

[edit]
The unofficial publicimperial measurementstandardserected at theRoyal ObservatoryinGreenwichin the 19th century
See also:Yard

TheNeolithiclong foot,first proposed by archeologistsMike Parker Pearsonand Andrew Chamberlain, is based upon calculations from surveys ofPhase 1 elements at Stonehenge.They found that the underlying diameters of the stone circles had been consistently laid out using multiples of a base unit amounting to 30long feet,which they calculated to be 1.056 of a moderninternational foot(thus 12.672 inches or 0.3219 m). Furthermore, this unit is identifiable in the dimensions of some stonelintelsat the site and in the diameter of the "southern circle" at nearbyDurrington Walls.Evidence that this unit was in widespread use across southern Britain is available from theFolkton DrumsfromYorkshire(neolithicartifacts, made from chalk, with circumferences that exactly divide asintegersinto ten long feet) and a similar object, theLavant drum,excavated atLavant,Sussex, again with a circumference divisible as a whole number into ten long feet.[21]

The measures ofIron Age Britainare uncertain and proposed reconstructions such as theMegalithic Yardare controversial. LaterWelsh legendcreditedDyfnwal Moelmudwith the establishment oftheir units,including a foot of 9 inches. The Belgic or North German foot of 335 mm (13.2 in) was introduced to England either by theBelgic Celtsduring their invasions prior to the Romans or by theAnglo-Saxonsin the 5th and 6th century.

Roman unitswere introduced followingtheir invasionin AD 43. Following theRoman withdrawalandSaxon invasions,the Roman foot continued to be used in the construction crafts while the Belgic foot was used for land measurement. Both the Welsh and Belgic feet seem to have been based on multiples of thebarleycorn,but by as early as 950 the English kings seem to have (ineffectually) ordered measures to be based upon an iron yardstick atWinchesterand thenLondon.Henry Iwas said to have ordered a new standard to be based upon the length of his own arm and, by thec. 1300Act concerning theComposition of Yards and Perches[22]traditionally credited toEdward IorII,the statute foot was a different measure, exactly⁠10/11⁠of the old (Belgic) foot. Thebarleycorn,inch,ell,andyardwere likewise shrunk, whilerodsandfurlongsremained the same.[23]The ambiguity over the state of themilewas resolved by the 1593Act against Converting of Great Houses into Several Tenements and for Restraint of Inmates and Inclosures in and near about the City of London and Westminster,which codified thestatute mileas comprising 5,280 feet. The differences among the various physical standard yards around the world, revealed by increasingly powerfulmicroscopes,eventually led to the 1959 adoption of theinternational footdefined in terms of the meter.

Definition

[edit]

International foot

[edit]

Theinternational yard and poundagreement of July 1959 defined the length of the international yard in the United States and countries of theCommonwealth of Nationsas exactly 0.9144meters.Consequently, since a foot is one third of a yard, the international foot is defined to be equal to exactly 0.3048 meters. This was 2ppmshorter than the previous US definition and 1.7 ppm longer than the previous British definition.[24]

The 1959 agreement concluded a series of step-by-step events, set off in particular by theBritish Standards Institution's adoption of a scientific standard inch of 25.4millimetersin 1930.

Symbol

[edit]

The IEEE standard symbol for a foot is "ft".[1]In some cases, the foot is denoted by aprime,often approximated by anapostrophe,and the inch by a double prime; for example, 2feet 4 inches is sometimes denoted 2′4″.[25]

Imperial units

[edit]

InImperial units,the foot was defined as⁠1/3⁠yard, with the yard being realized as a physical standard (separate from the standard meter). The yard standards of the differentCommonwealthcountries were periodically compared with one another.[26]The value of the United Kingdom primary standard of the yard was determined in terms of the meter by theNational Physical Laboratoryin 1964 to be0.9143969m,[27]implying a pre-1959 UK foot of0.3047990m.

The UK adopted the international yard for all purposes through theWeights and Measures Act 1963,effective January 1, 1964.[28]

Survey foot

[edit]

When the international foot was defined in 1959, a great deal of survey data was already available based on the former definitions, especially in the United States and inIndia.The small difference between the survey foot and the international foot would not be detectable on a survey of a small parcel, but becomes significant for mapping, or when thestate plane coordinate system(SPCS) is used in the US, because the origin of the system may be hundreds of thousands of feet (hundreds of miles) from the point of interest. Hence the previous definitions continued to be used for surveying in the United States and India for many years, and are denotedsurvey feetto distinguish them from the international foot. The United Kingdom was unaffected by this problem, as theretriangulation of Great Britain(1936–62) had been done in meters.

US survey foot

[edit]

In the United States, the foot was defined as 12 inches, with the inch being defined by theMendenhall Orderof 1893 via 39.37 inches = 1 m (making a US foot exactly⁠1200/3937⁠meters, approximately0.30480061m).[29][30]

On December 31, 2022, theNational Institute of Standards and Technology,theNational Geodetic Survey,and theUnited States Department of Commercedeprecated use of the US survey foot and recommended conversion to either the meter or theinternational foot(0.3048 m).[31][32][29]However, the historic relevance of the US survey foot persists, as theFederal Registernotes:[33]

The date of December 31, 2022, was selected to accompany the modernization of the National Spatial Reference System (NSRS) byNOAA's National Geodetic Survey (NGS). The reason for associating the deprecation of the U.S. survey foot with the modernization of the NSRS is that the biggest impact of the uniform adoption of the international foot will be for users of the NSRS, due to very large coordinate values currently given in U.S. survey feet in many areas of the U.S. Impacts related to the change to international feet will be minimized if a transition occurs concurrently with others [sic] changes in the NSRS....

The difference in timelines will have no effect on users of the existing NSRS (National Spatial Reference System), because NGS (NOAA's National Geodetic Survey)will continue to support the U.S. survey foot for components of the NSRS where it is used now and in the past[emphasis added]. In other words, to minimize disruption in the use of U.S. survey foot for existing NSRS coordinate systems, the change will apply only to the modernized NSRS.

State legislation is also important for determining the conversion factor to be used for everyday land surveying and real estate transactions, although the difference (twoparts per million) is of no practical significance given the precision of normal surveying measurements over short distances (usually much less than a mile). Out of 50 states and six other jurisdictions, 40 have legislated that surveying measures should be based on the US survey foot, six have legislated that they be made on the basis of the international foot, and ten have not specified.[34]

Indian survey foot

[edit]

The Indian survey foot is defined as exactly0.3047996m,[35]presumably derived from a measurement of the previous Indian standard of the yard. However, it is now obsolete as the current National Topographic Database of theSurvey of Indiais based on the metricWGS-84datum,[36]which is also used by theGlobal Positioning System.

Historical use

[edit]
Page from AustrianLehrbuch des gesammten Rechnens für die vierte Classe der Hauptschulen in denk.k.Staaten– 1848[37](Combined mathematics textbook for the fourth form of senior schools in theImperial–royalstates.)

Metric foot

[edit]

AnISO 2848measure of 3 basic modules (30 cm) is called a "metric foot",[citation needed]but there were earlier distinct definitions of a metric foot duringmetricationin France and Germany.

France

[edit]

In 1799 the meter became the official unit of length inFrance.This was not fully enforced, and in 1812Napoleonintroduced the system ofmesures usuelleswhich restored the traditional French measurements in the retail trade, but redefined them in terms of metric units. The foot, orpied métrique,was defined as one third of a meter. This unit continued in use until 1837.[38]

Germany

[edit]

In southwestern Germany in 1806, theConfederation of the Rhinewas founded and three differentreformed feetwere defined, all of which were based on the metric system:[39]

  • InHesse,theFuß(foot) was redefined as 25 cm.
  • InBaden,theFußwas redefined as 30 cm.
  • In thePalatinate,theFußwas redefined as being⁠33+1/3⁠cm (as in France).

Other obsolete feet

[edit]

Prior to the introduction of the metric system, many European cities and countries used the foot, but it varied considerably in length: thevoetinYpres,Belgium, was 273.8 millimeters (10.78in) while thepiedein Venice was 347.73 millimeters (13.690in). Lists of conversion factors between the various units of measure were given in many European reference works including:

Many of these standards were peculiar to a particular city, especially in Germany (which, beforeGerman unificationin 1871, consisted of many kingdoms, principalities, free cities and so on). In many cases the length of the unit was not uniquely fixed: for example, the English foot was stated as 11pouces2.6lignes(French inches and lines) byPicard,11pouces3.11lignesbyMaskelyne,and 11pouces3lignesbyD'Alembert.[47]

Most of the various feet in this list ceased to be used when the countries adopted the metric system. The Netherlands and modern Belgium adopted the metric system in 1817, having used themesures usuellesunder Napoleon[48]and the newly formedGerman Empireadopted the metric system in 1871.[49]

Thepalm(typically 200–280 mm, ie. 7⁠7/8⁠to 11⁠1/32⁠inches) was used in many Mediterranean cities instead of the foot. Horace Doursther, whose reference was published[clarification needed]in Belgium which had the smallest foot measurements, grouped both units together, while J. F. G. Palaiseau devoted three chapters to units of length: one for linear measures (palms and feet); one for cloth measures (ells); and one for distances traveled (miles and leagues).[citation needed]

Obsolete feet details

[edit]
Location Modern country Local name Metric
equivalent
(mm) 		Comments
Vienna Austria Wiener Fuß 316.102[46][50][circular reference]
Tyrol Austria Fuß 334.12[39]
Ypres (Ieper) Belgium voet 273.8[51]
Bruges/Brugge Belgium voet 274.3[51]
Brussels Belgium voet 275.75[51]
Hainaut Belgium pied 293.39[43]
Liège Belgium pied 294.70[43]
Kortrijk Belgium voet 297.6[51]
Aalst Belgium voet 277.2[51]
Mechelen Belgium voet 278.0[51]
Leuven Belgium voet 285.5[51]
Tournai Belgium pied 297.77[43]
Antwerp Belgium voet 286.8[51]
China China tradesman's foot 338.3[52]
China China mathematician's foot 333.2[52]
China China builder's foot 322.8[52]
China China surveyor's foot 319.5[52]
Moravia Czech Republic stopa 295.95[39]
Prague Czech Republic stopa 296.4[45] (1851) Bohemian foot or shoe
301.7[40] (1759) Quoted as "11pouces⁠1+3/4⁠lignes"[Notes 1]
Denmark Denmark fod 313.85[46] Until 1835, thereafter the Prussian foot
330.5[40] (1759) Quoted as "⁠2+1/2⁠ligneslarger than thepied[of Paris] "[Notes 1]
France France pied du roi 324.84[53] [Notes 2]
Angoulême France pied d'Angoulême 347.008[54]
Bordeaux(urban) France pied de ville de Bordeaux 343.606[54]
Bordeaux (rural) France pied de terre de Bordeaux 357.214[54]
Strasbourg France pied de Strasbourg 294.95[54]
Württemberg Germany Fuß 286.49[39]
Hanover Germany Fuß 292.10[39]
Augsburg Germany römischer Fuß 296.17[44]
Nuremberg Germany Fuß 303.75[44]
Meiningen-Hildburghausen Germany Fuß 303.95[39]
Oldenburg Germany römischer Fuß 296.41[39]
Weimar Germany Fuß 281.98[39]
Lübeck Germany Fuß 287.62[46]
Aschaffenburg Germany Fuß 287.5[43]
Darmstadt Germany Fuß 287.6[43] Until 1818, thereafter the Hessen "metric foot"
Bremen Germany Fuß 289.35[46]
Rhineland Germany Fuß 313.7[52]
Berlin Germany Fuß 309.6[52]
Hamburg Germany Fuß 286.8[52]
Bavaria Germany Fuß 291.86[39]
Aachen Germany Fuß 282.1[44]
Leipzig Germany Fuß 282.67[39]
Dresden Germany Fuß 283.11[39]
Saxony Germany Fuß 283.19[46]
Prussia Germany, Poland, Russia etc. Rheinfuß 313.85[46]
Frankfurt am Main Germany Fuß 284.61[39]
Venice&Lombardy Italy 347.73[39]
Turin Italy 323.1[52]
Rome Italy piede romano 297.896[54]
Riga Latvia pēda 274.1[52]
Malta Malta pied 283.7[52]
Utrecht Netherlands voet 272.8[52]
Amsterdam Netherlands voet 283.133[42] Divided into 11duimen(inches,lit. 'thumbs')
Hons Boss che en Rijpse[nl] Netherlands voet 285.0[42]
's-Hertogenbosch Netherlands voet 287.0[42]
Gelderland Netherlands voet 292.0[42]
Bloois (Zeeland) Netherlands voet 301.0[42]
Schouw Netherlands voet 311.0[42]
Rotterdam Netherlands voet 312.43[43]
Rijnland Netherlands voet 314.858[42]
Norway Norway fot 313.75[55] (1824–1835)[Notes 3]Thereafter as for Sweden.
Warsaw Poland stopa 297.8[56] Until 1819
288.0[43] (From 1819) Polishstopa
Lisbon Portugal pé 330.0[44] (From 1835)[Notes 4]
South Africa South Africa Cape foot 314.858[57] Originally equal to the Rijnland foot; redefined as 1.033 English feet in 1859.
BurgosandCastile Spain pie de Burgos/
Castellano 		278.6[40] (1759) Quoted as "122.43lignes"[Notes 1]
Toledo Spain pie 279.0[40] (1759) Quoted as "10pouces3.7lignes"[Notes 1]
Sweden Sweden fot 296.9[46] = 12tum(inches). The Swedishfotwas also used in Finland (jalka).
Zürich Switzerland 300.0[52]
Galicia Ukraine, Poland stopa galicyjska 296.96[43] Part of Austria–Hungary before World War I
Scotland United Kingdom 305.287[58] [Notes 5]

In Belgium, the wordspied(French) andvoet(Dutch) would have been used interchangeably.[citation needed]

Notes

[edit]
  1. ^abcdThe source document used pre-metric French units (pied,pouceandligne).
  2. ^The original meter was computed using pre-metric French units.
  3. ^The Norwegianfotwas defined in 1824 as the length of a (theoretical) pendulum that would have a period of⁠12/38⁠seconds at 45° from the equator.
  4. ^Prior to 1835, thepéor foot was not used in Portugal; instead a palm was used. In 1835 the size of the palm was increased from 217.37 mm (according to Palaiseau) to 220 mm.
  5. ^The Scots foot ceased to be legal after theAct of Unionin 1707.

Present day uses

[edit]

International ISO-standard and other intermodal shipping containers

[edit]

International Standards Organisation(ISO)-definedintermodal containersfor efficient global freight/cargo shipping, were defined using feet rather than meters for their leading outside (corner) dimensions. All ISO-standard containers to this day are eight feet wide, and their outer heights and lengths are also primarily defined in, or derived from feet.
Quantities of global shipping containers are still primarily counted inTwenty-foot Equivalent Units,or TEUs.

Aviation

[edit]

Everyday global (civilian) air traffic / aviation continues to be controlled inflight levels(flying altitudes) separated by thousands of feet (although typically read out in hundreds – e.g. flight level 330 actually means 33,000 feet, or about 10 kilometres in altitude).

Relation to shoe size

[edit]

The length of the (international) foot corresponds to a human foot withshoe sizeof 13 (UK), 14 (US male), 15.5 (US female) or 48 (EU sizing).[59][better source needed]

Dimension

[edit]

In measurement, the term "linear foot" (sometimes incorrectly referred to as "lineal foot" ) refers to the number of feet in a length of material (such as lumber or fabric) without regard to the width; it is used to distinguish fromsurface areainsquare foot.[60]

See also

[edit]

Notes

[edit]
  1. ^abThe original reference was given in a round number of centimeters.

References

[edit]
  1. ^ab"Recommended Unit Symbols, SI Prefixes, and Abbreviations"(PDF).RetrievedApril 7,2021.
  2. ^BS350:Part 1:1974 Conversion factors and tables Part 1. Basis of tables. Conversion factors.British Standards Institution. 1974. pp. 5, 91.
  3. ^Chicago Manual of Style(17th ed.). University of Chicago Press. 2017. ¶ 10.66.
  4. ^"Appendix G – Weights and Measures".The World Factbook.Washington:Central Intelligence Agency.January 17, 2007.Archivedfrom the original on February 23, 2011.RetrievedFebruary 4,2007.
  5. ^Kelly, Jon (December 21, 2011)."Will British people ever think in metric?".BBC.Archivedfrom the original on April 24, 2012.
  6. ^Alder, Ken (2002). The Measure of all Things—The Seven-Year-Odyssey that Transformed the World. London: Abacus.
  7. ^Weights and Measures ActArchivedDecember 28, 2014, at theWayback Machine,accessed January 2012, Act current to January 18, 2012. Basis for units of measurement 4.(1) All units of measurement used in Canada shall be determined on the basis of the International System of Units established by the General Conference of Weights and Measures. (...) Canadian units (5) The Canadian units of measurement are as set out and defined in Schedule II, and the symbols and abbreviations therefore are as added pursuant to subparagraph 6(1)(b)(ii).
  8. ^"foot, noun".Oxford English Dictionary.Oxford University Press.RetrievedJune 13,2024.
  9. ^Oswald Ashton Wentworth Dilke(May 22, 1987).Mathematics and measurement.University of California Press. p.23.ISBN978-0-520-06072-2.RetrievedFebruary 2,2012.
  10. ^Fessler, Daniel M; Haley, Kevin J; Lal, Roshni D (January–February 2005)."Sexual dimorphism in foot length proportionate to stature"(PDF).Annals of Human Biology.32(1): 44–59.doi:10.1080/03014460400027581.PMID15788354.S2CID194735.Archived fromthe original(PDF)on June 8, 2011.
  11. ^Kenoyer JM (2010) "Measuring the Harappan world," in Morley I & Renfrew C (edd) The Archaeology of Measurement, 117;"Archived copy"(PDF).Archived fromthe original(PDF)on June 26, 2015.RetrievedJanuary 11,2015.{{cite web}}:CS1 maint: archived copy as title (link)
  12. ^Herodotus; Rawlinson, George (May 14, 1861)."History of Herodotus: a new English version".New York D. Appleton – via Internet Archive.
  13. ^"Epidauros, Stadium (Building)".perseus.tufts.edu.Archivedfrom the original on May 10, 2017.
  14. ^Hosch, William L. (ed.) (2010)The Britannica Guide to Numbers and MeasurementNew York, NY: Britannica Educational Publications, 1st edition.ISBN978-1-61530-108-9,p.206
  15. ^Oswald Ashton Wentworth Dilke(May 22, 1987).Mathematics and measurement.University of California Press. p.26.ISBN978-0-520-06072-2.RetrievedFebruary 2,2012.
  16. ^Duncan-Jones, R. P. (1980)."Length-Units in Roman Town Planning: The Pes Monetalis and the Pes Drusianus".Britannia.11:127–133.doi:10.2307/525675.JSTOR525675.S2CID164149478.
  17. ^Russ Rowlett."How Many? A Dictionary of Units of Measurement".Center for Mathematics and Science Education,University of North Carolina at Chapel Hill.Archivedfrom the original on December 24, 2012.RetrievedFebruary 28,2011.
  18. ^Sutherland, Elizabeth R (May 1957). "Feet and dates at Charlieu".Journal of the Society of Architectural Historians.16(2): 2–5.doi:10.2307/987740.JSTOR987740.
  19. ^Jacob Koebel(1535).Geometrei. Von künstlichem Feldmessen und absehen(in German).Archivedfrom the original on November 16, 2011.
  20. ^"Geometrey".digital.slub-dresden.de(in German). Saxon State Library.RetrievedFebruary 22,2019.
  21. ^Teather, Anne; et al. (February 8, 2019). "Getting the Measure of Stonehenge".British Archaeology(165): 48–51.
  22. ^Great Britain (1762).The statutes at large: from the Magna Charta, to the end of the eleventh Parliament of Great Britain, anno 1761 (continued to 1807).Vol. 1. Printed by J. Bentham. p. 400.RetrievedNovember 30,2011.
  23. ^Zupko, Ronald Edward(1977).British Weights and Measures: A History from Antiquity to the Seventeenth Century.University of Wisconsin Press. pp. 6, 10, 20.ISBN978-0-299-07340-4.
  24. ^"On what basis is one inch exactly equal to 25.4 mm? Has the imperial inch been adjusted to give this exact fit and if so when?".National Physical Laboratory.Archived fromthe originalon August 7, 2012.RetrievedJuly 24,2012.
  25. ^Chicago Manual of Style(17th ed.). University of Chicago Press. 2017. ¶ 10.66.
  26. ^See, for example,Report on the Comparisons of the Parliamentary Copies of the Imperial Standards with the Imperial Standard Yard and the Imperial Standard Pound and with each other during the Years 1947 to 1948(H.M.S.O., London, 1950).Report on the Comparisons of the Parliamentary Copies of the Imperial Standards with each other during the Year 1957(H.M.S.O., London, 1958).
  27. ^Bigg, P. H.; Anderton, Pamela (March 1964)."The United Kingdom standards of the yard in terms of the meter".British Journal of Applied Physics.15(3): 291–300.Bibcode:1964BJAP...15..291B.doi:10.1088/0508-3443/15/3/308.Archived fromthe originalon August 3, 2012.RetrievedMay 16,2009.
  28. ^Thoburn v Sunderland City Council [2002] EWHC 195 (Admin) (18 February 2002)
  29. ^abMitchell, Alanna (August 18, 2020)."America Has Two Feet. It's About to Lose One of Them".The New York Times.ISSN0362-4331.RetrievedAugust 19,2020.
  30. ^A. V. Astin & H. Arnold Karo (1959)."Refinement of values for the yard and the pound".ArchivedAugust 21, 2006, at theWayback Machine.Washington DC: National Bureau of Standards. Republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, filed June 30, 1959)
  31. ^"U.S. Survey Foot".National Institute of Standards and Technology.January 4, 2023.RetrievedApril 4,2024.
  32. ^"Measuring Unit Change Coming in 2022",National Geodetic Survey, June 14, 2019.
  33. ^"Deprecation of the United States (U.S.) Survey Foot".Federal Register.October 5, 2020.
  34. ^"State Plane Coordinate System",National Geodetic Survey, May 4, 2019.
  35. ^Schedule to theStandards of Weights and Measures Act, 1976.
  36. ^Survey of India,"National Map Policy – 2005"ArchivedMarch 31, 2010, at theWayback Machine.
  37. ^Dr. Franz Mozhnik:Lehrbuch des gesammten Rechnens für die vierte Classe der Hauptschulen in den k.k. Staaten.Im Verlage der k.k. Schulbücher Verschleiß-Administration bey St. Anna in der Johannisgasse – Wien 1848
  38. ^Denis Février."Un historique du mètre"(in French). Ministère de l'Économie, des Finances et de l'Industrie.Archivedfrom the original on February 28, 2011.RetrievedMarch 10,2011.
  39. ^abcdefghijklm"Amtliche Maßeinheiten in Europa 1842"[Official measures in Europe 1842] (in German).Archivedfrom the original on July 23, 2013.RetrievedSeptember 22,2012.
  40. ^abcded'Anville, Jean Baptiste Bourguignon (1769).Traité des mesures itinéraires anciennes et modernes[Treatise of ancient and modern measures of distance] (in French). Paris: de l'Imprimerie Royale.RetrievedOctober 24,2011.
  41. ^Palaiseau, JFG (October 1816).Métrologie universelle, ancienne et moderne: ou rapport des poids et mesures des empires, royaumes, duchés et principautés des quatre parties du monde.Bordeaux.RetrievedOctober 30,2011.
  42. ^abcdefghJacob de Gelder (1824).Allereerste Gronden der Cijferkunst[Introduction to Numeracy] (in Dutch). 's-Gravenhage (The Hague) and Amsterdam: de Gebroeders van Cleef. pp.163–176.RetrievedMarch 2,2011.
  43. ^abcdefghiDoursther, Horace (1840).Dictionnaire universel des poids et mesures anciens et modernes.Brussels: M. Hayez. pp.402–418.RetrievedOctober 25,2011.liege.
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  45. ^abNoback, Christian; Noback, Friedrich Eduard (1851).Vollständiges tasehenbuch der Münz-, Maass- und Gewichts-Verhältnisse etc. aller Länder und Handelsplätze[Comprehensive pocketbook of money, weights and measures for all counties and trading centres] (in German). Vol. II. Leipzig: F. А. Brockhaus.RetrievedOctober 24,2011.
  46. ^abcdefghBruhns, Carl (1881).new manual of logarithms to seven places of decimals.Leipzig: Bernhard Tauchnitz. p. 610.RetrievedOctober 26,2011.
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  50. ^File
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  59. ^Melissa (March 30, 2016)."Why are shoe sizes as they are?".Today I found out.(12×3=36. US(m): 36−22=14, UK: 36−23=13, EU:30.5×1.5=45.75 then +2 "for comfort" plus rounding = 48)
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