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# Foot (length)

1 foot =
SI units
0.30480 m304.80 mm
US customary / Imperial units
0.3333 yd12 in

A foot (plural: feet or foot;[1] symbol or abbreviation: ft or, sometimes, – the prime symbol) is a non-SI unit of length, in a number of different systems, including English units, Imperial units, and United States customary units. Its size can vary from system to system, but in each is around a quarter to a third of a meter. The most commonly used foot today is the international foot. There are three feet in a yard and 12 inches in a foot.

## Definition

### International foot

Effective 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 meters. Consequently, the international foot is defined to be equal to 0.3048 meters (equivalent to 304.8 millimeters). 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″. This use can cause confusion, because the prime and double prime are also international standard symbols for arcminutes and arcseconds.

### Survey foot

By the time the international foot was defined in 1959, there was already a huge amount of survey data which had been collected based on the former definitions, especially in the United States and in India. The small difference between survey and international feet 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 miles from the point of interest. Hence the previous definitions continued in use for surveying in these two countries 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) was done in meters.

The United States survey foot is defined as exactly 12003937 meters, approximately 0.3048006 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 that time, several states have abandoned the non-metric versions of SPCS 83: seven states continue to keep location data in survey feet as well as in meters, while an eighth 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). Twenty-four states have legislated that surveying measures should be based on the U.S. survey foot, eight have legislated that they be made on the basis of the international foot, and eighteen 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 13 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.[8] 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 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 meter 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, 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.

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:[11]

• 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 there was little standardisation as is shown in the list of now-obsolete eigtheenth and nineteenth century feet. Many of the standards were perculiar to a particular city, especially in what is now Germany which, before German Unification in 1871 consisted of many kingdoms, principalities, free cities and so on. Most of the various feet in this list ceased to be used when the country concerned adopted the metric system - the Netherlands in 1812[12] (which included modern Belgium) and Germany in between 1869 and 1871[11]. See also metric feet (above).

It should be noted that many of the references in this table are to non-English language sites).

 Details Modern Country Value (mm) Reference and Comments Veurne Belgium 272.8 [12]voet Ieper/Ypres Belgium 272.9 [12]voet Brugge Belgium 274.28 [12]voet Brussels Belgium 275.75 [12] voet Nivelles Belgium 277.0 [12]pied Aals Belgium 277.0 [12] voet Mechelen Belgium 278.0 [12] voet Burgos and Castile Spain 278.635 [13]Pie (foot) de Burgos/Castellano (1752 to 1765) Aachen Germany 280.7 [12]fuß Weimar Germany 281.98 [11]fuß Amsterdam Netherlands 283.133 [14]voet - divided into 11 duimen (inches) Saxony Germany 283.19 [15]fuß Honsbossche en Rijpse Netherlands 285.0 [14]voet Leuven Belgium 285.5 [12] voet Württemberg Germany 286.49 [11] fuß ’s Hertogenbosch Netherlands 287.0 [14] voet Spain Spain 287.342 Spanish foot (till 1752) (Pie (foot) de Ribera/de Rey) = 12 Pulgadas Wroclaw Poland 288.0 [16]stopa wrocławska, till 1816 Darmstadt Germany 288.14 [11] fuß Bremen Germany 289.35 [11] fuß Aschaffenburg Germany 290.50 [11] fuß Liege Belgium 291.8 [12] pied Bavaria Germany 291.86 [17] fuß Hanover Germany 292.10 [18] fuß Hainaut Belgium 293.4 [12] pied Rotterdam Netherlands 296.0 [12]voet Augsburg Germany 296.17 [19] Römischer Fuß Oldenburg Germany 296.41 [19] Römischer Fuß Sweden Sweden 296.9 [20]fot = 12 tum (inches) Kortrijk Belgium 297.6 [12] voet Galicia / Lviv Poland 297.7 [16]stopa galicyjska / stopa lwowska, 1787-1856) Tournai Belgium 297.77 [12] pied Warsaw Poland 297.8 [16]stopa staropolska / stopa warszawska, till 1819 Kraków Poland 298.0 [16]stopa krakowska, 1836-1857 Bloois (Zeeland) Netherlands 301.0 [14]voet Nürnberg Germany 303.75 [11] Fuß Meiningen-Hildburghausen Germany 303.95 [11] Fuß Russia Russia 304.8 English foot (borrowed by Peter Ι) = 12 inches = 1/7 Russian sazhens Scotland United Kingdom 305.287 [21]Used until the Act of Union in 1707 Schouw Netherlands 311.0 [12]voet Norway Norway 313.75 [22]fot (after 1824) Prussia Germany 313.85 [23]Rheinfuß Denmark Denmark 313.85 [24]fod (after 1835) Rijnland/Cape Netherlands, South Africa 314.858 [14]voet Vienna Austria 316.08 [25] Gemeingriechischer Fuß Spain Spain 324.83 Pie de Rey = 12 Pulgadas (after 1765) France France 324.84 [26]pied du roi = 12 pouces (1688-1799) Portugal Portugal 328.5 Portuguese foot Venice Italy 347.73 [10]Venetian foot

## Historical origin

The foot as a unit of measure was used in most Western cultures and was usually divided into 12 or sometimes 10 inches/thumbs, or into 16 fingers/digits. The first known standard foot measure was from Sumer, where a definition is given in a statue of Gudea of Lagash from around 2575 BC. Some metrologists speculate that the imperial foot was adapted from an Egyptian measure by the Greeks, with a subsequent larger foot being adopted by the Romans.

The popular belief is that the original standard was the length of a man's foot. In rural regions and without calibrated rulers, many units of measurement were in fact based on the length of some part of body of the person measuring (or for example the area that could be ploughed in a day). In that sense, the human foot was no doubt the origin of the measuring unit called a "foot" and was also for a long time the definition of its length. To prevent discord and enable trade, many towns decided on a standard length and displayed this publicly. In order to enable simultaneous use of the different units of length based on different parts of the human body and other "natural" units of length, the different units were redefined as multiples of each other, whereby their lengths no longer corresponded to the original "natural" standards. This process of national standardization began in Scotland in 1150 and in England in 1303, where many different regional standards had existed long before.

Some believe that the original measurement of the English foot was from King Henry I, who had a foot 12 inches long; he wished to standardize the unit of measurement in England. Though there are records of the word "foot" being used approximately 70 years before his birth,[27] it is supposed that this old standard was redefined ("calibrated") according to Henry's foot. In fact, there is evidence that this sort of process was common before standardization. A new, important ruler could try to impose a new standard for an existing unit, but it is unlikely that any king's foot was ever as long as the modern unit of measurement.

The average foot length is about 9.4 inches (240 mm) for current Europeans. Approximately 99.6% of British men have a foot that is less than 12 inches long. One attempt to "explain" the "missing" inches is that the measure did not refer to a naked foot, but to the length of footwear, which could theoretically add an inch or two to the naked foot's length. This is consistent with the measure being convenient for practical uses such as building sites. People almost always pace out lengths while wearing shoes or boots, rather than removing them and pacing barefoot.

There are however historical records of definitions of the inch based on the width (not length) of a man's thumb that are very precise for the standards of the time. One of these was based on an average calculated using three men of different size, thereby enabling surprising accuracy and uniformity throughout a country even without calibrated rulers. It therefore seems likely that at least since about the Twelfth century, the precise length of a foot was in fact based on the inch, not the other way around. Since this length was fairly close to the size of most feet, at least in shoes, this enabled the above-mentioned use of one's shoes in approximating lengths without measuring devices. This sort of imprecise measuring that in addition excessively multiplied the measuring error due to repeated use of a short "ruler" (the foot) was never used in surveying and in constructing more complicated buildings.

## Notes

1. ^ BBC World Service
2. ^ National Physical Laboratory, 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?.
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) meters to inches, and 2) meters to feet?", Frequently Asked Questions about the National Geodetic Survey, 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 .
10. ^ a b 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. ^ a b c d e f g h i de:Fuß (Einheit) Foot (Unit of Measure) (in German)
12. ^ a b c d e f g h i j k l m n o p nl: Voet (lengtemaat) Foot (Unit of Measure) (In Dutch)
13. ^ es:Pie castellano Castillian foot (in Spanish)
14. ^ a b c d e Dutch units of measurement
15. ^ de:Alte Maße und Gewichte (Sachsen) Old weights and measures (Saxony) (in Geman)
16. ^ a b c d pl:Stopa polska Polish foot (in Polish)
17. ^ de:Alte Maße und Gewichte (Bayern) Old weights and measures (Bavaria) (in Geman)
18. ^ de:Alte Maße und Gewichte (Hannover) Old weights and measures (Hanover) (in Geman)
19. ^ a b de:Alte Maße und Gewichte (Römische Antike)
20. ^ se:Fot (enhet) Foot (Unit of measure) (in Swedish)
21. ^ "Scottish Weights and Measures: Distance and Area". Scottish Archive Network. Retrieved January 28, 2010.
22. ^ no:Fot (mål) Foot (Unit of measure) (in Norwegian)
23. ^ de:Alte Maße und Gewichte (Preußen) Old weights and measures (Prussia) (in Geman)
24. ^ dk:Fod (længdeenhed) Foot (Unit of measure) (in Danish)
25. ^ de:Alte Maße und Gewichte (Österreich) Old weights and measures (Austrai) (in Geman)
26. ^ fr:Pied (unité) Foot (Unit of measure) (in French)
27. ^ Laws Æthelstan

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