Foot (unit)

1 foot =

SI units
0.304800000 m	304.800000 mm
US customary / Imperial units
0.33333333 yd	12 in

A foot (plural: feet or foot;^[1] abbreviation or symbol: ft or ′ – 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.

Contents 1 Definition 1.1 International foot 1.2 Survey foot 1.3 Pre-1959 2 Obsolete use in different countries 2.1 Metric foot 2.2 Other Obsolete Feet 3 Historical origin 4 See also 5 Notes 6 External links

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″, 2′ 4″ or 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 1200⁄3937 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 ¹⁄₃ 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

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 eighteenth and nineteenth century feet. Many of the standards were peculiar 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).

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
Aalst	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
Wrocław	Poland	288.0	[11] fuß, 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	[16] fuß
Hanover	Germany	292.10	[17] fuß
Hainaut	Belgium	293.4	[12] pied
Rotterdam	Netherlands	296.0	[12] voet
Augsburg	Germany	296.17	[18] Römischer Fuß
Oldenburg	Germany	296.41	[18] Römischer Fuß
Sweden	Sweden	296.9	[19] fot = 12 tum (inches)
Kortrijk	Belgium	297.6	[12] voet
Galicia / Lviv	Poland	297.7	[20] stopa galicyjska / stopa lwowska, 1787–1856)
Tournai	Belgium	297.77	[12] pied
Warsaw	Poland	297.8	[20] stopa staropolska / stopa warszawska, till 1819
Kraków	Poland	298.0	[20] 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. Native names: Fuit, Fit; Troigh
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 adapted by the Greeks (the ποῦς or pous of between 296 mm and 330 mm)^[27] which subsequently became a more consistent measure (the pes of 296 mm) under the Romans.^[28]

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,^[29] 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 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.

See also

• anthropic units
• English unit
• History of measurement
• Imperial unit
• Inch
• International System of Units
• Systems of measurement
• United States customary units
• Units of measurement
• Weights and measures

Notes

External links

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