Foot (unit)
Template:Short description Template:About Template:Use American English Template:Use mdy dates Template:CS1 config Template:Infobox unit The foot (standard symbol: ft)<ref name=IEEE /><ref>Template:Cite book</ref> is a unit of length in the British imperial and United States customary systems of measurement. The prime symbol, Template:Char, is commonly used to represent the foot.<ref>Template:Cite book</ref> In both customary and imperial units, one foot comprises 12 inches, and one yard comprises three feet. Since an international agreement in 1959, the foot is defined as equal to exactly 0.3048Template:Nbspmeters. The most common plural of foot is feet. However, the singular form may be used like a plural when it is preceded by a number, as in "that man is six foot tall".<ref>Template:Cite encyclopedia</ref>
Historically, the "foot" was a part of many local systems of units, including the Greek, Roman, Chinese, French, and English systems. It varied in length from country to country, from city to city, and sometimes from trade to trade. Its length was usually between Template:Cvt and Template:Cvt and was generally, but not always, subdivided into twelve inches or 16 digits.
The United States is the only industrialized country that uses the (international) foot in preference to the meter in its commercial, engineering, and standards activities.<ref name="World Factbook">Template:Cite book</ref> The foot is legally recognized in the United Kingdom; road distance signs must use imperial units (however, distances on road signs are 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.<ref>Template:Cite news</ref><ref>Alder, Ken (2002). The Measure of all Things—The Seven-Year-Odyssey that Transformed the World. London: Abacus.</ref> The foot is recognized as an alternative expression of length in Canada.<ref>Weights and Measures Act Template:Webarchive, 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).</ref> Both the UK and Canada have partially metricated their units of measurement. The measurement of altitude in international aviation (the flight level unit) is one of the few areas where the foot is used outside the English-speaking world.
Historical origin
Historically, the human body has been used to provide the basis for units of length.<ref name="Dilke1987-23">Template:Cite book</ref> The foot of an adult European-American male is typically about 15.3% of his height,<ref>Template:Cite journal</ref> giving a person of Template:Convert a foot-length of about Template:Convert, on average.
Archaeologists believe that in the past, the people of Egypt, India, and Mesopotamia preferred the cubit, while the people of Rome, Greece, and China preferred the footTemplate:Citation needed. Under the Harappan linear measures, Indus cities during the Bronze Age used a foot of Template:Convert and a cubit of Template:Convert.<ref>Kenoyer JM (2010) "Measuring the Harappan world," in Morley I & Renfrew C (edd) The Archaeology of Measurement, 117; Template:Cite web</ref> The Egyptian equivalent of the foot—a measure of four palms or 16 digits—was known as the Template:Lang and has been reconstructed as about Template:Convert.
The Greek foot (Template:Lang, Template:Lang) had a length of Template:Sfrac of a stadion,<ref>Template:Cite web</ref> one stadion being about Template:Convert;<ref>Template:Cite web</ref> therefore a foot was about Template:Convert. Its exact size varied from city to city and could range between Template:Convert and Template:Convert, but lengths used for temple construction appear to have been about Template:Convert to Template:Convert.
The standard Roman foot (Template:Lang) was normally about Template:Convert,<ref name=brit>Hosch, William L. (ed.) (2010) The Britannica Guide to Numbers and Measurement New York, NY: Britannica Educational Publications, 1st edition. Template:ISBN, p.206</ref> but in some provinces, particularly Germania Inferior, the so-called Template:Lang (foot of Nero Claudius Drusus) was sometimes used, with a length of about Template:Convert. (In reality, this foot predated Drusus.)<ref name="Dilke1987-26">Template:Cite book</ref><ref>Template:Cite journal</ref> 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 Template:Lang (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 790 Charlemagne attempted to reform the units of measure in his domains. His units of length were based on the Template:Lang and in particular the Template:Lang, the distance between the fingertips of the outstretched arms of a man.<ref>Template:Cite web</ref> The Template:Lang has 6 Template:Lang (feet) each of Template:Convert. 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 9th century the Roman foot of Template:Convert was used; when it was rebuilt in the 10th century, a foot of about Template:ConvertTemplate:Efn was used. At the same time, monastic buildings used the Carolingian foot of Template:Convert.Template:Efn<ref>Template:Cite journal</ref>
The procedure for verification of the foot as described in the 16th century posthumously published work by Jacob Köbel in his book Template:Lang is:<ref>Template:Cite book</ref><ref>Template:Cite web</ref> Template:Blockquote
England and Wales
The Neolithic long foot, first proposed by archeologists Mike Parker Pearson and Andrew Chamberlain, is based upon calculations from surveys of Phase 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 30 long feet, which they calculated to be 1.056 of a modern international foot (thus 12.672 inches or 0.3219 m). Furthermore, this unit is identifiable in the dimensions of some stone lintels at the site, and in the diameter of the "southern circle" at nearby Durrington Walls. Evidence that this unit was in widespread use across southern Britain is available from the Folkton Drums from Yorkshire (Neolithic artifacts made from chalk with circumferences that exactly divide as integers into ten long feet) and a similar object, the Lavant drum, excavated at Lavant, Sussex, again with a circumference divisible as a whole number into ten long feet.<ref>Template:Cite journal</ref>
The measures of Iron Age Britain are uncertain, and proposed reconstructions such as the megalithic yard are controversial. Later Welsh legend credited Dyfnwal Moelmud with the establishment of their units, including a foot of 9 inches. The Belgic or North German foot of Template:Convert was introduced to England either by the Belgic Celts during their invasions prior to the Roman conquest of Britain (AD 43) or by the Anglo-Saxons in the 5th and 6th centuries.
Roman units were introduced following their conquest. After the Roman withdrawal and the Saxon 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 the barleycorn, but by as early as 950 the English kings seem to have (ineffectually) ordered measures to be based upon an iron yardstick at Winchester and then London. Henry I was said to have ordered a new standard to be based upon the length of his own arm and, by the Template:Circa act concerning the Composition of Yards and Perches<ref name="Britain1762">Template:Cite book</ref> traditionally credited to Edward I or Edward II, the statute foot was a different measure, exactly Template:Sfrac of the old (Belgic) foot. The barleycorn, inch, ell, and yard were likewise shrunk, while rods and furlongs remained the same.<ref name="1977zupko">Template:Cite book</ref> The ambiguity over the length of the mile was resolved by the 1593 Act 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 the statute mile as comprising 5,280 feet. The 1959 adoption of the international foot completed a redefinition of the foot in terms of the meter.
Definition
International foot
The international yard and pound agreement of July 1959 defined the length of the international yard in the United States and countries of the Commonwealth of Nations as exactly 0.9144 meters. Consequently, since a foot is one third of a yard, the international foot is defined as exactly 0.3048 meters. This was 2 ppm shorter than the previous US definition and 1.7 ppm longer than the previous British definition.<ref>Template:Cite web</ref> The 1959 agreement concluded a series of step-by-step events, set off in particular by the British Standards Institution's adoption of a scientific standard inch of 25.4 millimeters in 1930.
The Institute of Electrical and Electronics Engineers standard symbol for a foot is "ft".<ref name="IEEE">Template:Cite web</ref> In some cases, the foot is denoted by a prime, often approximated by an apostrophe, and the inch by a double prime; for example, 2Template:Nbspfeet 4 inches is sometimes denoted 2′Template:Nbsp4″.<ref name="CMOS">Template:Cite book</ref>
Imperial units
In Imperial units, the foot was defined as Template:Sfrac yard, with the yard being realized as a physical standard (separate from the standard meter). The yard standards of the different Commonwealth countries were periodically compared with one another.<ref>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).</ref> The value of the United Kingdom primary standard of the yard was determined in terms of the meter by the National Physical Laboratory in 1964 to be Template:Val,<ref>Template:Cite journal</ref> implying a pre-1959 UK foot of Template:Val. The UK adopted the international yard for all purposes through the Weights and Measures Act 1963, effective January 1, 1964.<ref>Thoburn v Sunderland City Council [2002] EWHC 195 (Admin) (18 February 2002)</ref>
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 foot and the international foot would not be detectable on a survey of a small parcel but becomes significant for mapping or when the state 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 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 meters.
United StatesTemplate:Anchor
In the United States, the foot was defined as 12 inches, with the inch being defined by the Mendenhall Order of 1893 via 39.37 inches = 1 m (making a US foot exactly Template:SfracTemplate:Nbspmeters, approximately Template:Val).Template:R<ref>A. V. Astin & H. Arnold Karo (1959). "Refinement of values for the yard and the pound". Template:Webarchive. Washington DC: National Bureau of Standards. Republished on National Geodetic Survey web site and the Federal Register (Doc. 59-5442, filed June 30, 1959)</ref>
On December 31, 2022, the National Institute of Standards and Technology, the National Geodetic Survey, and the United States Department of Commerce deprecated use of the US survey foot and recommended conversion to either the meter or the international foot (0.3048 m).<ref>Template:Cite web</ref><ref>"Measuring Unit Change Coming in 2022", National Geodetic Survey, June 14, 2019.</ref><ref name="NYT 2020-08-18">Template:Cite news</ref> However, the historic relevance of the US survey foot persists, as the Federal Register notes:<ref>Template:Cite web</ref>
State legislation is also important for determining the conversion factor to be used for everyday land surveying and real estate transactions, although the difference (two ppm) 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.<ref>"State Plane Coordinate System", National Geodetic Survey, May 4, 2019.</ref>
India
The Indian survey foot is defined as exactly Template:Val,<ref>Schedule to the Standards of Weights and Measures Act, 1976.</ref> 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,<ref>Survey of India, "National Map Policy – 2005" Template:Webarchive.</ref> which is also used by the Global Positioning System.
Historical use
Metric foot
An ISO 2848 measure of 3 basic modules (30 cm) is called a "metric foot",Template:Cn but there were earlier distinct definitions of a metric foot during metrication in France and Germany.
In 1799 the meter became the official unit of length in France. This was not fully enforced, and in 1812 Napoleon introduced the system of Template:Lang which restored the traditional French measurements in the retail trade, but redefined them in terms of metric units. The foot, or Template:Lang, was defined as one third of a meter. This unit continued in use until 1837.<ref name="historique">Template:Cite web</ref>
In southwestern Germany in 1806, the Confederation of the Rhine was founded and three different reformed feet were defined, all of which were based on the metric system:<ref name="DE1842">Template:Cite web</ref>
- In Hesse, the Template:Lang (Template:Lit) was redefined as Template:Cvt.
- In Baden, the Template:Lang was redefined as Template:Cvt.
- In the Palatinate, the Template:Lang was redefined as being Template:Cvt (as in France).
Other obsolete feet
Prior to the introduction of the metric system, many European cities and countries used the foot, but it varied considerably in length: the Template:Lang in Ypres, Belgium, was Template:Cvt while the Template:Lang in Venice was Template:Cvt. Lists of conversion factors between the various units of measure were given in many European reference works including:
- Traité, Paris – 1769<ref name="Traite">Template:Cite book</ref>
- Palaiseau – Bordeaux: 1816 <ref name="Palaiseau">Template:Cite book</ref>
- de Gelder, Amsterdam and The Hague – 1824<ref name="NL2">Template:Cite book</ref>
- Horace, Brussels – 1840<ref name="Horace">Template:Cite book</ref>
- Noback & Noback (2 volumes), Leipzig – 1851<ref name="DE1851">Template:Cite book</ref><ref name="DE1851V2">Template:Cite book</ref>
- Bruhns, Leipzig – 1881<ref name="Bruhns">Template:Cite book</ref>
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 length of the unit was not uniquely fixed: for example, the English foot was stated 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.<ref>Template:Cite web</ref>
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 the Template:Lang under Napoleon<ref>Template:Cite book</ref> and the German Empire adopted the metric system in 1871.<ref>Template:Cite webTemplate:Dead linkTemplate:Cbignore</ref>
The palm (typically 200–280 mm, ie. 7Template:Sfrac to 11Template:Sfrac inches) was used in many Mediterranean cities instead of the foot. Horace Doursther, whose reference was publishedTemplate:Clarify 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).Template:Citation needed
| Location | Modern country | Local name | Metric equivalent (mm) |
Comments |
|---|---|---|---|---|
| Vienna | Austria | Template:Lang | 316.102<ref name=Bruhns/>Template:Sfnp | |
| Tyrol | Austria | Template:Lang | 334.12<ref name=DE1842/> | |
| Ypres (Ieper) | Belgium | Template:Lang | 273.8<ref name=Flanders/> | |
| Bruges/Brugge | Belgium | Template:Lang | 274.3<ref name=Flanders/> | |
| Brussels | Belgium | Template:Lang | 275.75<ref name=Flanders/> | |
| Hainaut | Belgium | Template:Lang | 293.39<ref name=Horace/> | |
| Liège | Belgium | Template:Lang | 294.70<ref name=Horace/> | |
| Kortrijk | Belgium | Template:Lang | 297.6<ref name=Flanders/> | |
| Aalst | Belgium | Template:Lang | 277.2<ref name="Flanders">Template:Cite web</ref> | |
| Mechelen | Belgium | Template:Lang | 278.0<ref name=Flanders/> | |
| Leuven | Belgium | Template:Lang | 285.5<ref name=Flanders/> | |
| Tournai | Belgium | Template:Lang | 297.77<ref name=Horace/> | |
| Antwerp | Belgium | Template:Lang | 286.8<ref name=Flanders/> | |
| China | China | tradesman's foot | 338.3<ref name=rose/> | |
| China | China | mathematician's foot | 333.2<ref name=rose/> | |
| China | China | builder's foot | 322.8<ref name=rose/> | |
| China | China | surveyor's foot | 319.5<ref name=rose/> | |
| Moravia | Czech Republic | Template:Lang | 295.95<ref name=DE1842/> | |
| Prague | Czech Republic | Template:Lang | 296.4<ref name=DE1851V2/> | (1851) Bohemian foot or shoe |
| 301.7<ref name=Traite/> | (1759) Quoted as "11 Template:Lang Template:Sfrac Template:Lang"<ref group=Notes name=lignes/> | |||
| Denmark | Denmark | Template:Lang | 313.85<ref name=Bruhns/> | Until 1835, thereafter the Prussian foot |
| 330.5<ref name=Traite/> | (1759) Quoted as "Template:Sfrac Template:Lang larger than the Template:Lang [of Paris]"<ref group=Notes name=lignes/> | |||
| France | France | Template:Lang | 324.84<ref name="CGCP">Template:Cite web</ref> | <ref group=Notes>The original meter was computed using pre-metric French units.</ref> |
| Angoulême | France | Template:Lang | 347.008<ref name="Guilhiermoz">Template:Cite journal</ref> | |
| Bordeaux (urban) | France | Template:Lang | 343.606<ref name=Guilhiermoz/> | |
| Bordeaux (rural) | France | Template:Lang | 357.214<ref name=Guilhiermoz/> | |
| Strasbourg | France | Template:Lang | 294.95<ref name=Guilhiermoz/> | |
| Württemberg | Germany | Template:Lang | 286.49<ref name=DE1842/> | |
| Hanover | Germany | Template:Lang | 292.10<ref name=DE1842/> | |
| Augsburg | Germany | Template:Lang | 296.17<ref name=DE1851/> | |
| Nuremberg | Germany | Template:Lang | 303.75<ref name=DE1851/> | |
| Meiningen-Hildburghausen | Germany | Template:Lang | 303.95<ref name=DE1842/> | |
| Oldenburg | Germany | Template:Lang | 296.41<ref name=DE1842/> | |
| Weimar | Germany | Template:Lang | 281.98<ref name=DE1842/> | |
| Lübeck | Germany | Template:Lang | 287.62<ref name=Bruhns/> | |
| Aschaffenburg | Germany | Template:Lang | 287.5<ref name=Horace/> | |
| Darmstadt | Germany | Template:Lang | 287.6<ref name=Horace/> | Until 1818, thereafter the Hessen "metric foot" |
| Bremen | Germany | Template:Lang | 289.35<ref name=Bruhns/> | |
| Rhineland | Germany | Template:Lang | 313.7<ref name=rose/> | |
| Berlin | Germany | Template:Lang | 309.6<ref name=rose/> | |
| Hamburg | Germany | Template:Lang | 286.8<ref name=rose/> | |
| Bavaria | Germany | Template:Lang | 291.86<ref name=DE1842/> | |
| Aachen | Germany | Template:Lang | 282.1<ref name=DE1851/> | |
| Leipzig | Germany | Template:Lang | 282.67<ref name=DE1842/> | |
| Dresden | Germany | Template:Lang | 283.11<ref name=DE1842/> | |
| Saxony | Germany | Template:Lang | 283.19<ref name=Bruhns/> | |
| Prussia | Germany, Poland, Russia etc. | Template:Lang | 313.85<ref name=Bruhns/> | |
| Frankfurt am Main | Germany | Template:Lang | 284.61<ref name=DE1842/> | |
| Venice & Lombardy | Italy | 347.73<ref name=DE1842/> | ||
| Turin | Italy | 323.1<ref name=rose/> | ||
| Rome | Italy | Template:Lang | 297.896<ref name=Guilhiermoz/> | |
| Riga | Latvia | Template:Lang | 274.1<ref name=rose/> | |
| Malta | Malta | Template:Lang | 283.7<ref name=rose/> | |
| Utrecht | Netherlands | Template:Lang | 272.8<ref name="rose">Template:Cite book</ref> | |
| Amsterdam | Netherlands | Template:Lang | 283.133<ref name=NL2/> | Divided into 11 Template:Lang (inches, Template:Literally) |
| Template:Ill | Netherlands | Template:Lang | 285.0<ref name=NL2/> | |
| 's-Hertogenbosch | Netherlands | Template:Lang | 287.0<ref name=NL2/> | |
| Gelderland | Netherlands | Template:Lang | 292.0<ref name=NL2/> | |
| Bloois (Zeeland) | Netherlands | Template:Lang | 301.0<ref name=NL2/> | |
| Schouw | Netherlands | Template:Lang | 311.0<ref name=NL2/> | |
| Rotterdam | Netherlands | Template:Lang | 312.43<ref name=Horace/> | |
| Rijnland | Netherlands | Template:Lang | 314.858<ref name=NL2/> | |
| Norway | Norway | Template:Lang | 313.75<ref>Template:Cite news</ref> | (1824–1835)<ref group="Notes">The Norwegian Template:Lang was defined in 1824 as the length of a (theoretical) pendulum that would have a period of Template:Sfrac seconds at 45° from the equator.</ref> Thereafter as for Sweden. |
| Warsaw | Poland | Template:Lang | 297.8<ref name="PolishLocal">Template:Cn – Information copied from Template:Ill</ref> | Until 1819 |
| 288.0<ref name=Horace/> | (From 1819) Polish Template:Lang | |||
| Lisbon | Portugal | Template:Lang | 330.0<ref name=DE1851/> | (From 1835)<ref group=Notes>Prior to 1835, the Template:Lang 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.</ref> |
| South Africa | South Africa | Cape foot | 314.858<ref>Template:Cite web</ref> | Originally equal to the Rijnland foot; redefined as 1.033 English feet in 1859. |
| Burgos and Castile | Spain | Template:Lang | 278.6<ref name=Traite/> | (1759) Quoted as "122.43 Template:Lang"<ref group=Notes name=lignes/> |
| Toledo | Spain | Template:Lang | 279.0<ref name=Traite/> | (1759) Quoted as "10 Template:Lang 3.7 Template:Lang"<ref group=Notes name=lignes>The source document used pre-metric French units (Template:Lang, Template:Lang and Template:Lang).</ref> |
| Sweden | Sweden | Template:Lang | 296.9<ref name=Bruhns/> | = 12 Template:Lang (inches). The Swedish Template:Lang was also used in Finland (Template:Lang). |
| Zürich | Switzerland | 300.0<ref name=rose/> | ||
| Galicia | Ukraine, Poland | Template:Lang | 296.96<ref name=Horace/> | Part of Austria–Hungary before World War I |
| Scotland | United Kingdom | 305.287<ref>Template:Cite web</ref> | <ref group=Notes>The Scots foot ceased to be legal after the Act of Union in 1707.</ref> |
In Belgium, the words Template:Lang (French) and Template:Lang (Dutch) would have been used interchangeably.Template:Citation needed
Notes
<references group=Notes/>
Present day uses
International ISO-standard and other intermodal shipping containers
International Organization for Standardization (ISO)-defined intermodal containers for 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 Template:Convert 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 in twenty-foot equivalent units (TEUs).
Aviation
Everyday global (civilian) air traffic and aviation continues to be controlled in flight levels (flying altitudes) separated by thousands of feet (although typically read out in hundreds; for example, "flight level 330" means Template:Convert in altitude.
Relation to shoe size
The length of the (international) foot corresponds to a human foot with shoe size of 13 (UK), 14 (US male), 15.5 (US female) or 48 (EU sizing).<ref>Template:Cite web (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)</ref>Template:Better source
Dimension
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 from surface area in square foot.<ref>Template:Cite web</ref>
See also
- Anthropic units
- History of measurement
- International System of Units
- Korean units of measurement
- Mermin's foot
- Pous
- Systems of measurement
Notes
References
Sources
Template:Imperial units Template:United States Customary Units Template:Authority control