Foot (unit)

1 foot =

SI units
0.3048 m	304.8 mm
US customary / Imperial units
0.333 yd	12 in

A foot (plural: feet; abbreviation or symbol: ft or ′ (the prime symbol) is a unit of length in a number of different systems including Ancient Greek, Ancient Roman, English units, Imperial units, United States customary units and the units of many Continental European countries. Its size varied from system to system, but in each is around a quarter to a third of a metre and most but not all were subdivided into 12 inches. The U.S. is the only industrialized nation that does not mainly use the metric system in its commercial and standards activities^[1], and uses the international foot (a customary unit of length) and the survey foot. The foot is still commonly used in the United Kingdom, which has partially metricated in some walks of life; it is still a legal unit, mandated for some purposes^{[citation needed]}.

Definition

International foot

On July 1, 1959, the length of the international yard in the United States and countries of the Commonwealth of Nations was defined as 0.9144 metres. Consequently, the international foot is defined to be equal to exactly 0.3048 metres (equivalent to 304.8 millimetres). This was 2 ppm shorter than the previous U.S definition and 1.7 ppm longer than the previous British definition.^[2]

The international standard symbol for a foot is ft (see ISO 31-1, Annex A). In some cases, the foot is denoted by a prime, which is often approximated by an apostrophe, and the inch by a double prime; for example, 2 feet 4 inches is sometimes denoted as 2′−4″, 2′ 4″ or 2′4″.

Survey foot

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 in India. The small difference between the survey and the international foot would not be detectable on a survey of a small parcel, but becomes significant for mapping, or when a state plane coordinate system is used, 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 in use for surveying in the US and India for many years, and are denoted survey feet to distinguish them from the international foot. The United Kingdom was unaffected by this problem, as the retriangulation of Great Britain (1936–62) had been done in metres.

The United States survey foot is defined as exactly ¹²⁰⁰⁄₃₉₃₇ metres, approximately 0.3048006096 m.^[3] In 1986 the National Geodetic Survey (NGS) released the North American Datum of 1983, which underlies the state plane coordinate systems and is entirely defined in meters. An NGS policy from 1991 has this to say about the units used with the new datum to define the SPCS 83:

In preparation for the adjustment of the North American Datum of 1983, 31 states enacted legislation for the State Plane Coordinate System of 1983 (SPCS 83). All states defined SPCS 83 with metric parameters. Within the legislation, the U.S. Survey Foot was specified in 11 states and the International Foot was specified in 6 states. In all other states the meter is the only referenced unit of measure in the SPCS 83 legislation. The remaining 19 states do not yet have any legislation concerning SPCS 83.^[4]

Since then, 42 states have abandoned the non-metric versions of SPCS 83: 7 states continue to keep location data in survey feet as well as in metres, while one state keeps data in international feet as well as in meters.^[5] State legislation is also important for determining the conversion factor to be used for everyday land surveying and real estate transactions, although the difference (2 ppm) is of no practical significance given the precision of normal surveying measurements over short distances (usually much less than a mile). 24 states have legislated that surveying measures should be based on the U.S. survey foot, 8 have legislated that they be made on the basis of the international foot, and 18 have not specified the conversion factor from metric units.^[5]

The Indian survey foot is defined as exactly 0.3047996 m,^[6] presumably derived from a measurement of the previous Indian standard of the yard. The current National Topographic Database of the Survey of India is based on the metric WGS-84 datum,^[7] which is also used by the Global Positioning System.

Pre-1959

In the United States, the foot was defined as 12 inches, with the inch being defined by the Mendenhall Order of 1893 by 39.37 inches = 1 m. In Imperial units, the foot was defined as ¹⁄₃ yard, with the yard being realized as a physical standard (separate from the standard metre). The yard standards of the different Commonwealth countries were periodically compared with one another.^[8] The value of the United Kingdom primary standard of the yard was determined in terms of the metre by the National Physical Laboratory in 1964 as 0.9143969 m,^[9] implying a pre-1959 foot in the UK of 0.3047990 m.

Obsolete use in different countries

Page from a German Language School Book - 1848^[10]

Metric foot

In 1799 the metre became the official unit of length in France. This was not fully enforced and in 1812 Napoleon introduced the system of mesures usuelles which restored the traditional French measurements in the retail trade, but redefined them in terms of metric units. The foot, or "pied metrique" was defined as one third of a metre. This unit of measure continued in use until 1837.^[11]

Other metric feet were introduced into what is now South Western Germany when, in 1806, the Confederation of the Rhine was founded. Three different reformed feet were defined, all of which were based on the metric system:^[12]

• In Hessen, the fuß (foot) was redefined as being 25 cm.
• In Baden, the fuß was redefined as being 30 cm.
• In the Pfalz, the fuß was redefined as being 33 1/3 cm.

Other obsolete feet

Prior to the introduction of the metric system, many European cities and countries used the foot, but it varied considerably: the voet in Ieper (Ypres), Belgium was 273.8 millimetres (10.78 in) while the piede in Venice was 347.73 millimetres (13.690 in). A list of conversions between the various units of measure were catalogued in many European reference works including:

• Traite, Paris - 1759^[13]
• Palaiseau - Bordeaux: 1816^[14]
• de Gelder, Amsterdam and s'Gravenhage - 1824^[15]
• Horace, Brussels - 1840^[16]
• Noback & Noback (2 volumes), Leipzig - 1851^[17][18]
• Bruhns, Leipzig - 1881^[19]

Many of these standards were peculiar to a particular city, especially in Germany (which, before German Unification in 1871, consisted of many kingdoms, principalities, free cities and so on). In many cases the conversion factors varied, depending on who took them - for example, the English foot was measured as 11 pouces 2.6 lignes (French inches and lines) by Picard, 11 pouces 3.11 lignes by Maskelyne and 11 pouces 3 lignes by D'Alembert.^[20]

Most of the various feet in this list ceased to be used as the countries concerned adopted the metric system: the Netherlands and modern Belgium adopted the metric system in 1817 having used the mesures usuelles under Napoleon^[21] and newly formed German Empire adopted the metric system in 1871 as its system of measure^[22]

The palm (typically 200 mm to 280 mm) was used in many Mediterranean cities instead of the foot - Horace, whose reference was published in Belgium which had the smallest foot measurements groups both units together while Palaiseau devoted three chapters to units of length - one for linear measures (palms and feet), one for cloth measures (ells) and one for distances travelled (miles and leagues). In the table below, arbitrary cut-off points of 270 mm and 350 mm have been chosen.

Location	Modern Country	Local name	Metric equivalent (mm)	Comments
Ieper/Ypres	Belgium	voet	273.8[23]
Brugge	Belgium	voet	274.3[23]
Brussels	Belgium	voet	275.75[23]
Aalst	Belgium	voet	277.2[23]
Mechelen	Belgium	voet	278.0[23]
Burgos and Castile	Spain	Pie de Burgos/ Castellano	278.6[13]	(1759) Quoted as "122.43 lignes"[Notes 1]
Toledo	Spain	Pie	279.0[13]	(1759) Quoted as "10 pouces 3.7 lignes"[Notes 1]
Weimar	Germany	fuß	281.98[12]
Aachen	Germany	fuß	282.1[17]
Leipzig	Germany	fuß	282.67[12]
Dresden	Germany	fuß	283.11[12]
Amsterdam	Netherlands	voet	283.133 [15]	Divided into 11 duimen (inches)
Saxony	Germany	fuß	283.19[19]
Frankfurt-am-Main	Germany	fuß	284.61[12]
Honsbossche en Rijpse	Netherlands	voet	285.0[15]
Leuven	Belgium	voet	285.5[23]
Württemberg	Germany	fuß	286.49[12]
Antwerp	Belgium	voet	286.8[23]
’s Hertogenbosch	Netherlands	voet	287.0[15]
Lübeck	Germany	fuß	287.62[19]
Aschaffenburg	Germany	fuß	287.5[16]
Darmstadt	Germany	fuß	287.6[16]	Unitl 1818, thereafter the Hessen "metric foot"
Bremen	Germany	fuß	289.35[19]
Bavaria	Germany	fuß	291.86[12]
Gelderland	Netherlands	voet	292.0[15]
Hanover	Germany	fuß	292.10[12]
Hainaut	Belgium	pied	293.39[16]
Liege	Belgium	pied	294.70[16]
Moravia	Czech Republic	stopa	295.95[12]
Augsburg	Germany	Römischer Fuß	296.17[17]
Prague	Czech Republic	stopa	296.4[18]	(1851) Bohemian foot or shoe
			301.7[13]	(1759) Quoted as "11 pouces 1¾ lignes"[Notes 1]
Oldenburg	Germany	Römischer Fuß	296.41[12]
Sweden	Sweden	fot	296.9[19]	= 12 tum (inches)
Kortrijk	Belgium	voet	297.6[23]
Galicia	Ukraine	stopa galicyjska	296.96[16]	Part of Austria before World War I
Tournai	Belgium	pied	297.77[16]
Warsaw	Poland	stopa	297.8[24]	until 1819
			288.0[16]	(From 1819) Polish stopa
Bloois (Zeeland)	Netherlands	voet	301.0[15]
Nürnberg	Germany	Fuß	303.75[17]
Meiningen-Hildburghausen	Germany	Fuß	303.95[12]
Scotland	United Kingdom	Fuit, Fit, Troigh	305.287[25]	[Notes 2]
Schouw	Netherlands	voet	311.0[15]
Rotterdam	Netherlands	voet	312.43[16]
Norway	Norway	fot	313.75[26]	(1824 - 1835)[Notes 3] Thereafter as for Sweden
Prussia	Germany	Rheinfuß	313.85[19]
Denmark	Denmark	fod	313.85[19]	Until 1835, thereafter the Prussian foot
			330.5[13]	(1759) Quoted as "2½ lines larger than the pied [de Paris]"[Notes 1]
Lisbon	Portugal	Pé	330.0[17]	(From 1835) [Notes 4]
Rijnland/Cape	Netherlands, South Africa	voet	314.858[15]
Vienna	Austria	Fuß	316.11[19]
France	France	pied du roi	324.84[27]	[Notes 5]
Tyrol	Austria	fuß	334.12[12]
Venice & Lombardy	Italy		347.73[12]

Notes

1. ^ ^{a b c d} The source document used pre-metric French units (pied, pouce and lignes)
2. ^ The Scots foot ceased to be legal after the Act of Union in 1707
3. ^ The Norweigian fot was defined in 1824 as the length of a (theoretical) pendulum that would have a period ¹²⁄₃₈ s at 45° from the equator
4. ^ Prior to 1835,the pé or 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 original metre was computed using pre-metric French Units

Historical origin

Determination of the mean length of a foot in a German town during the XVth or XVIth century, after a woodcut published in the book Geometrei by Jakob Koelbel (Frankfurt, ca. 1575).

Historically the human body has been used to provide the basis for units of length.^[28] The foot of a Caucasian male is about 15.3% of their height,^[29] giving a person of 160 cm (5 ft 3 in a foot of 245 mm and one of 180 cm (5 ft 10 in a foot of 275 mm. These figures are less than the foot used in most cities over time, suggesting that the "foot" was actually a synonym for a "shoe".

Archeologists believe that the Egyptians, Mesopotamians favoured the cubit while the Romans and the Greeks favoured the foot. Originally both the Greeks and the Romans subdivided the foot into 16 digits, but in later years, the Romans also subdivided the foot into 12 unica (from which both the English words "inch" and "ounce" are derived). The Greek foot (pous)varied from city to city and ranged between 270 mm and 350 mm, but lengths used for temple construction appear to be about 295 mm and 325 mm, the former being close to the size of the Roman foot. The standard Roman foot (pes) was normally about 295.7 mm, but in the provinces, the pes Drusianus (foot of Nero Claudius Drusus) having a length of about 334 mm was used. (In reality, this foot predated Drusus).^[28]

After the fall of the Roman Empire, some Roman traditions were continued but others fell into disuse. In 790 AD Charlemagne, who was to be crowned Holy Roman Emperor in 800 AD, attempted to reform the units of measure in his domains by placing them on a sound footing. His units of length were based on the toise and in particular the toise de l'Écritoire, the distance between the fingertips of the outstretched arms of a man.^[30] The toise has 6 pied (feet) each of 326.6 mm (12.86 in).

He was unsuccessful in introducing a standard unit of length throughout his realm: an analysis of the measurements of Charlieu Abbey shows that during the ninth century, the Roman foot 296.1 mm was used, during its rebuilding in the tenth century a foot of 320 mm^{[Note 1]} was used. At the same time, monastic buildings used the Carolignian foot of 340 mm.^{[Note 1][31]}

The verification of the foot as described in the 16th century by Jacob Koebel in his book Geometrei. Von künstlichem Feldmessen und absehen is:^[32]

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 lawful rood to measure and survey the land with, and the 16th part of it shall be the right and lawful foot.

See also

• Anthropic units
• English units
• History of measurement
• Imperial units
• Inch
• International System of Units
• Systems of measurement
• United States customary units
• Units of measurement

Notes

1. ^ ^{a b} The original reference was given in a round number of centimetres

References

1. ^ "Appendix G - Weights and Measures". The World Factbook. Washington: Central Intelligence Agency. January 17, 2007. https://www.cia.gov/library/publications/the-world-factbook/appendix/appendix-g.html. Retrieved February 4, 2007. 
2. ^ "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. http://www.npl.co.uk/reference/faqs/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-(faq-length). Retrieved 2010-07-13. 
3. ^ A. V. Astin & H. Arnold Karo, (1959), Refinement of values for the yard and the pound, Washington DC: National Bureau of Standards, republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, Filed, June 30, 1959, 8:45 a.m.)
4. ^ National Geodetic Survey, (January 1991), "Policy of the National Geodetic Survey Concerning Units of Measure for the State Plane Coordinate System of 1983.
5. ^ ^{a b} National Geodetic Survey (undated), "What are the 'official' conversions that are used by NGS to convert 1) metres to inches, and 2) metres to feet?", Frequently Asked Questions about the National Geodetic Survey, http://www.ngs.noaa.gov/faq.shtml#Feet, retrieved May 16, 2009 .
6. ^ Schedule to the Standards of Weights and Measures Act, 1976.
7. ^ Survey of India, "National Map Policy – 2005".
8. ^ 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).
9. ^ Bigg, P. H.; Anderton, Pamela (1964), "The United Kingdom standards of the yard in terms of the metre", Br. J. Appl. Phys. 15: 291–300, doi:10.1088/0508-3443/15/3/308, http://www.iop.org/EJ/abstract/0508-3443/15/3/308/ .
10. ^ 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
11. ^ Denis Février. "Un historique du mètre" (in French). Ministère de l'Economie, des Finances et de l'Industrie. http://www.industrie.gouv.fr/metro/aquoisert/metre.htm. Retrieved 2011-03-10. 
12. ^ ^{a b c d e f g h i j k l m} "Amtliche Maßeinheiten in Europa 1842 [Official measures in Europe 1842]" (in German). http://home.fonline.de/fo0126//geschichte/groessen/mas1.htm. Retrieved 22 October 2011. "(Precis) - Sources are listed" 
13. ^ ^{a b c d e} d' Anville, Jean Baptiste Bourguignon (1769) (in French). Traité des mesures itinéraires anciennes et modernes [Treatise of ancient and modern measures of distance]. Paris: de l'Imprimerie Royale. http://books.google.be/books?id=eAkOAAAAQAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false. Retrieved 24 October 2011. 
14. ^ 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. http://books.google.co.uk/books?id=ahjPAAAAMAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false. Retrieved 30 October 2011. 
15. ^ ^{a b c d e f g h} Jacob de Gelder (1824) (in Dutch). Allereerste Gronden der Cijferkunst [Introduction to Numeracy]. 's Gravenhage and Amsterdam: de Gebroeders van Cleef. pp. 163–176. http://books.google.co.uk/books?id=XYVbAAAAQAAJ&printsec=frontcover#v=onepage&q&f=false. Retrieved 2011-03-02. 
16. ^ ^{a b c d e f g h i} Doursther, Horace (1840). Dictionnaire universel des poids et mesures anciens et modernes. Bruxelles: M. Hayez. pp. 402 - 418. http://books.google.co.uk/books?id=KAibOR651tkC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q=liege&f=false. Retrieved 25 October 2011. 
17. ^ ^{a b c d e} Noback, Christian; Noback, Friedrich Eduard (1851) (in German). Vollständiges tasehenbuch der Münz-, Maass- und Gewichts-Verhältnisse etc. aller Länder und Handelsplätze. I. Leipzig: F. А. Вrockhaus. http://books.google.fr/books?id=AkhTAAAAMAAJ&printsec=titlepage#v=onepage&q&f=false. Retrieved 24 October 2011. 
18. ^ ^{a b} Noback, Christian; Noback, Friedrich Eduard (1851) (in German). Vollständiges tasehenbuch der Münz-, Maass- und Gewichts-Verhältnisse etc. aller Länder und Handelsplätze. II. Leipzig: F. А. Вrockhaus. http://books.google.co.uk/books?id=KEpTAAAAMAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false. Retrieved 24 October 2011. 
19. ^ ^{a b c d e f g h} Bruhns, Carl (1881). new manual of logarithms to seven places of decimals. Leipzig: Bernhard Tauchnitz. p. 610. http://books.google.co.uk/books?id=GoMNAQAAIAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false. Retrieved 26 October 2011. 
20. ^ Thomas Jefferson (13 July 1790). "Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States". United States House of Representatives. http://avalon.law.yale.edu/18th_century/jeffplan.asp. Retrieved 8 November 2011. 
21. ^ Jacob de Gelder (1824) (in Dutch). Allereerste Gronden der Cijferkunst [Introduction to Numeracy]. 's Gravenhage and Amsterdam: de Gebroeders van Cleef. pp. 155–157. http://books.google.co.uk/books?id=XYVbAAAAQAAJ&printsec=frontcover#v=onepage&q&f=false. Retrieved 2011-03-02. 
22. ^ Andreas Dreizler et al (20 April 2009). "Metrologie" (in German). Technische Universität Darmstaft. http://www.csi.tu-darmstadt.de/media/csi/institutes/nearwallreactiveflows/bilderdateien_1/messtechnik/mtmnormen.pdf. Retrieved 2011-03-28. 
23. ^ ^{a b c d e f g h} "Maten en gewichten" (in Dutch). Vlaamse Vereniging voor Familiekunde (Flemmish Association for Family History). 2011. http://www.familiekunde-vlaanderen.be/maten-en-gewichten. Retrieved 24 October 2011. 
24. ^^{[citation needed]} - Information copied frompl:Stopa polska
25. ^ "Scottish Weights and Measures: Distance and Area". Scottish Archive Network. http://www.scan.org.uk/measures/distance.asp. Retrieved January 28, 2010. 
26. ^ halbo, leif (21 July 2005). "Mål, vekt og norsk selvstendighet [Dimensions, weight and Norwegian independence]". Aftenposten. 
27. ^ "Les anciennes unités et leurs équivalences [Old units and their equivalences]" (in French). Le Cybergroupe Généalogique de Charente Poitevine. 2011. http://www.cgcp.asso.fr/FAQ/divers/anciennes_unites.php. Retrieved 2011-02-25. 
28. ^ ^{a b} Dilke, OAW (1987). Mathematics and Measurement. Reading the past. British Museum Press. ISBN 0-7141-8067-X. 
29. ^ Fessler, Daniel M; Haley, Kevin J; Lal, Roshni D (January–February 2005). "Sexual dimorphism in foot length proportionate to stature". Annals of Human Biology, 32 (1): 44–59. http://www.sscnet.ucla.edu/anthro/faculty/fessler/pubs/AHBFootSizeDimorphism.pdf. 
30. ^ Russ Rowlett. "How Many? A Dictionary of Units of Measurement". Center for Mathematics and Science Education, University of North Carolina at Chapel Hill. http://www.unc.edu/~rowlett/units/dictT.html. Retrieved 2011-02-28. 
31. ^ Sutherland, Elizabeth R (May 1957). "Feet and dates at Charlieu". Journal of the Society of Architectural Historians 16 (2). http://www.jstor.org/pss/987740. Retrieved 17 November 2011. 
32. ^ Jacob Koebel (16th century). Geometrei. Von künstlichem Feldmessen und absehen. http://www.robweir.com/blog/2007/12/right-and-lawful-rood.html. 

External links

• Library of Units and Constants
• Measurements and Conversions
• Does the Foot Fit Britannia?