Foot (unit)

A foot (plural: feet; abbreviation or symbol: ft or ′ (the prime symbol) is a unit of length. Since 1960 the term has usually referred to the international foot, defined as being one third of a yard, making it 0.3048 meters exactly. It is an integral part of both the imperial and United States customary systems of units. It is subdivided into 12 inches.

Historically the foot, which was used in Ancient Greece, Ancient Rome, England, Scotland and many Continental European countries and which varied from country to country and in some cases from city to city, was part local systems of units. Its length was usually between 250 mm and 335 mm and was generally, but not always, subdivided into 12 inches or 16 digits.

The United States is the only industrialized nation that uses the international foot and the survey foot (a customary unit of length) in preference to the meter in its commercial, engineering and standards activities.^[2] The foot is still legally recognized as an alternative expression of length in Canada^[3] officially defined as a unit derived from the meter^[4] and still commonly used in the United Kingdom, although both have partially metricated their units of measurement. The measurement of altitude in the aviation industry is one of the few areas where the foot is widely used outside the English-speaking world.

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, the international foot is defined to be equal to exactly 0.3048 meters. This was 2 ppm shorter than the previous U.S definition and 1.7 ppm longer than the previous British definition.^[5]

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 marked 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 the state plane coordinate system 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.

The United States survey foot is defined as exactly ¹²⁰⁰⁄₃₉₃₇ meter, approximately 0.3048006096 m.^[6] 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.^[7]

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 meters, while one state keeps data in international feet as well as in meters.^[8] 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.^[8]

The Indian survey foot is defined as exactly 0.3047996 m,^[9] 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,^[10] 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.^[11] 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,^[12] implying a pre-1959 foot in the UK of 0.304799 m.

Historical units called the foot in different countries

Page from Austrian Lehrbuch des gesammten Rechnens für die vierte Classe der Hauptschulen in den k.k. Staaten – 1848^[1]

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 in the retail trade, but redefined them in terms of metric units. The foot, or pied metrique, was defined as one third of a meter. This unit continued in use until 1837.^[13]

Other "metric feet" were introduced into South Western Germany in 1806, when the Confederation of the Rhine was founded. Three different reformed feet were defined, all of which were based on the metric system:^[14]

• In Hesse, the Fuß (foot) was redefined as 25 cm.
• In Baden, the Fuß was redefined as 30 cm.
• In the Palatinate, the Fuß was redefined as being 33⅓ cm (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 voet in Ieper (Ypres), Belgium was 273.8 millimetres (10.78 in) while the piede in Venice was 347.73 millimetres (13.690 in). Lists of conversion factors between the various units of measure were given in many European reference works including:

• Traite, Paris – 1769^[15]
• Palaiseau – Bordeaux: 1816 ^[16]
• de Gelder, Amsterdam and 's-Gravenhage – 1824^[17]
• Horace, Brussels – 1840^[18]
• Noback & Noback (2 volumes), Leipzig – 1851^[19][20]
• Bruhns, Leipzig – 1881^[21]

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.^[22]

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 mesures usuelles under Napoleon^[23] and the newly formed German Empire adopted the metric system in 1871.^[24]

The palm (typically 200 mm to 280 mm) was used in many Mediterranean cities instead of the foot. Horace Doursther, whose reference was published 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). In the table below, arbitrary cut-off points of 270 mm and 350 mm have been chosen.

(In Belgium, the words pied (French) and voet (Dutch) would have been used interchangeably.)

Notes

1. ↑ 1.0 1.1 1.2 1.3 The source document used pre-metric French units (pied, pouce and lignes)
2. ↑ The original meter was computed using pre-metric French Units
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 Scots foot ceased to be legal after the Act of Union in 1707

Historical origin

Determination of the rod, using the length of the left foot of 16 randomly chosen people coming from church service. Woodcut published in the book Geometrei by Jakob Köbel (Frankfurt, c. 1536).

Historically the human body has been used to provide the basis for units of length.^[34] The foot of a Caucasian male is typically about 15.3% of his height,^[35] giving a person of 160 cm (5 ft 3 in) a foot of 245 mm and one of 180 cm (5 ft 11 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 and 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 unciae (from which both the English words "inch" and "ounce" are derived). The Greek foot (ποὐς,pous) varied from city to city and ranged between 270 mm and 350 mm, but lengths used for temple construction appear to have been about 295 mm or 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) with a length of about 334 mm was used. (In reality, this foot predated Drusus).^[36]

After the fall of the Roman Empire, some Roman traditions were continued but others fell into disuse. In AD 790 Charlemagne attempted to reform the units of measure in his domains. 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.^[37] 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 9th century the Roman foot of 296.1 mm was used; when it was rebuilt in the 10th century, a foot of about 320 mm^{[Note 1]} was used. At the same time, monastic buildings used the Carolignian foot of 340 mm.^{[Note 1][38]}

The procedure for verification of the foot as described in the 16th century by Jacob Koebel in his book Geometrei. Von künstlichem Feldmessen und absehen is:^[39]

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.

In England

Imperial measurement standards, Royal Observatory, Greenwich

The Roman foot was introduced to Britain in the 1st century AD. The length of the Roman foot has been estimated at 296 mm or 11.65 inches. In the 5th century, the Anglo-Saxons introduced the North German foot of 335 mm (13.2 inches). The new foot was used for land measurement, while the Roman foot continued to be used in the construction crafts. Some time between 1266 and 1303 the weights and measures of England were radically revised by a law known as the Composition of Yards and Perches (Compositio ulnarum et perticarum)^[40] often known as the Compositio for short. This law, attributed to either Henry III or his successor Edward I, instituted a new foot that was exactly 10/11 the length of the old foot, with corresponding reductions in the size of the yard, ell, inch, and barleycorn. Miles, furlongs and rods, however, remained the same. The furlong remained an eighth of a mile, but changed from 600 old feet to 660 new feet. The rod remained the same length, but changed from 15 old feet to 16½ new feet.^[41]

Ordinatum est, quod tria grana ordei sicca et rotunda faciunt pollicem, duodecim pollices faciunt pedem, tres pedes faciunt ulnam, quinque ulnae et dimidia faciunt perticam, et quadraginta perticae in longitudine et quatuor in latitudine faciunt unam acram. — Compositio ulnarum et perticarum

"It is ordained that three dry round grains of barley make an inch, 12 inches make a foot, three feet make a yard, five yards and a half make a perch, and 40 perches in length and four in breadth make one acre."

See also

• Anthropic units
• English units
• History of measurement
• Imperial units
• International System of Units
• Mermin's foot
• Systems of measurement
• United States customary units
• Units of measurement

Notes

1. ↑ 1.0 1.1 The original reference was given in a round number of centimeters

References