# Foot (unit)

Physical unit
Unit name foot
Unit symbol ${\ displaystyle \ mathrm {ft}}$, ′
Physical quantity (s) length
Formula symbol ${\ displaystyle l}$
dimension ${\ displaystyle {\ mathsf {L}}}$
system Anglo-American system of measurement
In SI units ${\ displaystyle \ mathrm {1 \, ft = 0 {,} 304 \, 8 \; m}}$
Named after foot

A foot ( listen ? / I ) ( English foot , plural feet ) or shoe is a measure of length used in many parts of the world , which, depending on the country, usually measured 28 to 32 cm, in extreme cases also 25 and 34 cm.

The foot is one of the oldest units of length next to the finger width , the hand width , the hand span , the cubit , the step and the fathom .

The only foot measurement still used today, the English foot, is 1 ft = 30.48 cm (12 inches ). Although it is not an SI unit , the foot unit is still widely used internationally, especially in the maritime and aviation sectors.

## Origins

Publicly accessible etalons of various lengths on the outer wall of the Royal Greenwich Observatory .

Since when the foot has been used as a unit of measurement is controversial. Sure conclusions can be drawn from the earliest finds of yardsticks. The oldest undamaged find of this type is the so-called nippur cubit from Mesopotamia. Notches reveal sub-units of 30 finger widths ( digiti à 1.73 cm), from which the units of measurement foot with 16 digiti (27.6 cm) and the hand width ( palmus = 4 digiti ) result. Attempts to check the length of the cubit on buildings resulted in a mean of 518.65 mm.

Whether a common standard can be derived from this - as in the case of the megalithic yard - is a matter of dispute among experts. Identical lengths or their sub-units in different cultures could also be a result of the uniformity of body measurements to which they are based.

## Antiquity

Even before the 4th pharaoh dynasty, Egyptian geometers divided the nippur cubit into only 28 parts. As a result, the foot grew as a measure to 51.8 cm ÷ 28 · 16 ≈ 29.6 cm. This is exactly the length of the Roman foot measurement. Accordingly, the megalithic or Nippur foot and the Roman foot maintain a ratio of exactly 28 to 30.

A foot (Latin pes ≈ 29.6 cm) is four hand widths (Latin palmus ≈ 7.4 cm) or sixteen finger widths (Latin digitus ≈ 1.85 cm). In addition to the official pes monetalis , the so-called pes drusianus (≈ 33.27 cm) was also used in some parts of the Roman north-west provinces, which was about 2 digiti longer than the official foot size . It was named after the general Nero Claudius Drusus . The "four-foot measure" was called ulna (ell) in Latin in late antiquity . The "measure of 1½ feet" is the natural cubit (Latin cubitus ). The "five-foot measure" is the double step (Latin passus ). The English yard is exactly three feet.

In ancient Greece, for example, in addition to the actual foot (Greek pous ) 16 finger widths that was mainly used, there was also a so-called pygme with 18 finger widths. This pygm (forearm to wrist) was often referred to in translations as “foot” for lack of a suitable word. Nevertheless, it can be said that throughout the history of civilization the foot has always been 16 finger widths, whereby the “finger” can be seen as the actual basic unit.

Among the diverse Greek systems, which are always derived from one another, the common Greek foot (scientifically also called pous metrios since Heron ), which later became the Austrian foot , as well as the Greek-Kyrenean foot of antiquity , which is particularly relevant for the geographic measurement of Eratosthenes, should be mentioned .

Greek foot measurements

• 1 foot (Aeginian) = 33.30 centimeters
• 1 foot (Old Attic) = 33.00 centimeters
• 1 foot (Attic) = 31.04 centimeters
• 1 foot (Doric) = 32.65 centimeters
• 1 foot (ionic) = 34.83 centimeters
• 1 foot (Macedonian) = 27.50 centimeters
• 1 foot (Olympic) = 32.05 centimeters
• 1 foot (solonic) = 29.60 centimeters

## Middle Ages and early modern times

Measurements of length at the old town hall in Regensburg: shoe (= foot), cubit and fathom
The Nieder-Erlenbacher shoe was 28.3 cm.

It was not until the Middle Ages, with his preference for the duodecimal system , that the foot was divided into twelve sub-units instead of sixteen. This resulted in the thumb width, the so-called inch (Latin uncia, English inch, French pouce ). Also in other cultures, e.g. B. in Japan or China , length measures in the size of the human foot are known.

A Carolingian foot measured 32.24 cm, the "Paris King's Foot" 32.48 cm (probably derived from pes drusianus ) and the widespread Rhine foot just under 31.4 cm.

In almost all buildings throughout the Middle Ages, the foot was used as the basic dimension. It can be determined from the width dimensions of the respective structures by division. The various cathedral huts each used their own foot, which was either ancient foot measurements or their derivatives.

An instruction for the border measurement between the County of Nassau and the Landgraviate of Hessen-Darmstadt from the year 1719 stipulates under point 5 that "a rod of 18 shoes, the shoe of 12 inches" should be used for the measurement.

The following text by the arithmetic master , surveyor and town clerk Jakob Köbel from Oppenheim from 1535 shows how attempts were made in the early modern period to create "a just measuring rod" as averaging :

"A measuring rod of the right kind and artificial common use should therefore be made. There should be six toes man / small and large / like the one after the other outside the church / each put a shoe in front of the other / and with it a length / which understands / measure just six toes of the same shoe / the same length is / and should be / a fair / common measuring rod / so that one should measure the field / ... "

With the introduction of the decimal meter in France in 1793, a break was made for the first time in human history with the use of all basic dimensions specifically related to humans as well as with the traditional reference to other, already existing dimensions. The new reference should now be the circumference of the earth . In certain areas, such as land surveying and shipping, however, various "geographical miles " (e.g. in Germany 115  equatorial degrees long) and quantities derived from them were used before. The meter was defined purely abstractly as the ten millionth part of the distance from the pole to the equator . As a result, the classic human foot measurement disappeared within the scope of the meter.

To simplify and improve acceptance of the conversion to the meter, in the 19th century the old foot measurement was brought to round values ​​in the new system here and there. This renewed foot was exactly 25 cm in the Grand Duchy of Hesse , exactly 30 cm in the Grand Duchy of Baden and Switzerland (see also: Swiss foot ) and exactly 50 cm in the Duchy of Nassau . These units were then mostly divided into ten instead of the previous twelve inches. Other states limited themselves to defining their feet and other units of measurement in relation to the metric system.

## German-speaking area

From the textbook of complete arithmetic for the fourth grade of the secondary schools in the kk states

The various old German foot measurements were completely abandoned by the North German Confederation and the adoption of its laws when the German Empire was founded (1871) and the subsequent German accession to the International Meter Convention (1875).
In Austria , the pous metrios was predominantly 31.61 cm.

Terminologically, the foot corresponded regionally to the shoe.

Examples of foot measurements in some German cities and countries (rounded):

Reformed foot measurements in the Confederation of the Rhine (from 1806) or after the Congress of Vienna (1814/15) and in Switzerland (according to the Concordat of 1835 ):

Special foot dimensions:

## European foot measurements

Rhenish cubit and Rhenish foot, public measure at the old town hall Mannheim (1711)
Prussian yardstick and Prussian foot at the town hall of Bad Langensalza, Thuringia
Kulmbacher foot, 29 cm
Prussian foot at the town hall of Mühlhausen / Thuringia, 37.6 cm (1825)
Surname Paris lines millimeter
1 Amsterdam foot 125.48 283.0615
1 Ansbacher city foot 132.92 299.8447
1 Antwerp foot 126.6 285,588
1 Augsburg foot 131.29 296.1678
1 Aschaffenburg foot 127.45 287.5
1 Bamberg foot 124.296 280.3905
1 Berlin foot 139.13 313.8536
1 Braunschweig foot 126.5 285.3625
1 Breslau foot 127.65 287.9567
1 Brussels foot 122.2 275.6624
1 Danish foot 139.13 313.8536
1 Danzig foot 127.15 286.8287
1 Dresden foot 123.3 283.1066
1 Eichstädter foot 134.784 304.0498
1 Frankfurt foot 126.162 284.6
1 Fulda foot 125.4 282.881
1 old foot, Greece 135.8 306.3417
1 middle foot, Greece 138,6072 310.6473
1 hamburger foot 127.0 286.4903
1 Karlsruhe Feldfuß 123.336 278.2250
1 Karlsruhe plant base 129.0528 291.1212
1 Königsberg foot 136.4 307.6952
1 Krakow foot 158.0 356.4211
1 Leipzig foot 125.3 282.6555
1 London foot 135.1154 304.7974
1 Munich foot 129.38 291.8593
1 Nassauer Feldfuß 221.648 500.00
1 Nassau market foot 132.99 300.00
1 Nuremberg artillery foot 129.83 292.8703
1 Parisian foot 144.00 324.8394
1 Prague foot (Bohemia) 131.4 296,416
1 Regensburg foot 139.0 313.5603
1 Rhinelander foot 139.13 313.8536
1 roman old foot 130.68 294.7918
1 roman new foot (palmo) 099.03 223.3948
1 Russian foot 238.6 538.10
1 Salzburg foot 131.6 296.8672
1 Swedish foot 131.6 296.8672
1 spanish foot 125.8 282.6555
1 Tyrolean foot 148.11 334.111
1 venetian foot 154.0 347.3978
1 Viennese foot 140.127 316.1023
1 Württemberger foot 127.00 286.4904
1 Würzburg foot 129.3661 291.8279
1 Zurich foot 133.6005 301.38

(Source below)

Limprand foot

With limprandischer foot addition to the normal or ordinary walking the length dimension was walking in Alessandria referred. The difference was in length

• 1 Limprandic foot = 12 inches = 227.7 Paris lines = 0.51367 meters
• 1 ordinary foot = 8 inches = 151.8 Paris lines = 0.342435 meters

(Source below)

## present

The international unit symbol today is ft for engl. foot or feet, often also abbreviated with the minute sign ' (in Unicode the "PRIME" sign U + 2032), alternatively half the typographical quotation mark '. This always refers to the international foot ("Anglo-Saxon compromise foot ", 1959), which corresponds to a third of a yard or twelve international inches per 2.54 cm, i.e. measures exactly 30.48 cm:

• 1 ft = 1 ′ = 12 in. = ⅓ yd. = 30.48 cm = 0.3048 m = about 1/6000 nautical mile
• 1 m = about 3.2808 ft

### US land survey

In the US national survey , the previous definition also applies , with which exactly 39.37 inches fit into one meter (instead of 39  47127 = about 39.370 078 740). This means that the international foot is exactly 0.999 998 times as large as the US survey foot, i.e. H. 0.0002% or one five hundred thousandth smaller. The US survey foot should no longer be used after 2022.

US survey foot
exactly 12003937 m = 12 survey inch = about 0.304 800 609 m

### science

In science, the decimal metric system of measurement applies internationally , and even in the USA the foot is no longer used in this area .

However, the old units still lead to conversion errors today. During the construction of the Hubble space telescope , for example, the air density in the laboratory was incorrectly reduced to the vacuum and later repaired by astronauts was required.

### technology

In many technical areas there are still feet and especially inches in order to be compatible with the important North American market . Since the use of the metric system is required by law in most countries, these units only appear in generic terms (e.g. 17 ″ monitor), or the actual feet or inches are converted metrically and then often rounded.

ANSI and the standard-setting professional association of mechanical engineers in the USA, ASME , currently state the nominal diameter for pipe dimensions according to series C, ASME-BPE 1997 in inches (¼ ", ⅜", ½ ", ¾", 1 ", 1½", ... ). In Germany, on the other hand, metric information should be given in accordance with DIN EN ISO 228-1. Nevertheless, in the context of heating and sanitary technology in trade and craft, only inch dimensions are used. In the case of threads or screws , unnoticed small differences in particular lead to major problems.

### logistics

Much of the information is given in feet and inches; B. the dimensions of the ISO containers used around the world . The length dimensions are particularly important here, as they represent the basis of the classifications from which all other dimensions are essentially derived. The standard are 20 ', 40' and 45 'containers.

### aviation

Direct values ​​in feet are most common in aviation , where they represent the most common unit of measurement for flight altitude as feet . In geographical Elevation in aeronautical charts (especially for airports and mountains), the term "is related to the indication in feet elevation " (ELEV) is used. In the air space above the transition altitude are flight levels (ger .: flight level , FL) named after its height in multiples of 100 feet. Example: The height specification "FL120" means: "12000 ft above the standard reference surface ".

### shipping

Many measurements are based on or are still given directly in feet and inches . Dimensions for building regulations for z. B. Entrances, room heights or the guard rail were defined in feet or inches and are now given as millimeter values ​​(height of the railing 2 feet corresponds to 610 mm, the distance between the supports at most 7 feet corresponds to 2134 mm). Limit values ​​for ship classes are often whole feet. A register ton is 100  cubic feet . Draft marks, the so-called Ahmings , which are attached to the bow and stern of a seagoing ship and sometimes also amidships, are often scaled in feet. In the manufacture of chain links, the inch is mostly used, while the products are marked in millimeters (the links of a ¼ inch chain are 6.35 mm thick, but are referred to as a 6-millimeter chain; ⅜ inches is 9.53 mm, but are sold as 10 mm; and ½ inch is 12.7 mm, but means 13 mm). On all official American charts and nautical publications, water depths are given in feet. In contrast, the nautical charts of the British Admiralty are now almost all metric.

Even if it is not exactly correct, non-English people also use foot values ​​in the name of a boat type or a brand to specify the boat more precisely (boats of the Melges 24 class are 750 cm long, the Swan 48 is 1483 cm and incorrect 1463.04 cm = 48 ft).

### Sports

In some sports, measurements were originally round feet, but are now often specified in meters and only sometimes rounded to smooth values. The basketball hoop, for example, hangs 10 feet high (equivalent to 3.048 m). The dimensions of a football goal date from the time when the first rules such as the eight-eight rule were established in England. 8 ft (2.44 m) high and 8 yd (24 ft = 7.32 m) wide. The British dimensions are still given today in the FIFA regulations parallel to the metric dimensions. All given dimensions of a baseball field are basically feet.

### Organ building

In organ building today, the foot is used to indicate the pitch of organ pipes . The so-called footnote number indicates the sounding pitch of an organ register . With an 8′-register, the C key also sounds the note C, with a 4′-register the tone c 0 , etc. A theoretical standard whistle for the C key is assumed. For today's mood, a foot in organ building is about 32 cm. Depending on the design, the actual length of a pipe differs from the length given in feet at the same pitch.

The differences in the usual regional foot dimensions in historical organ building also played no role in the naming of the footnote number, as it was only given roughly. For example, the measure 2⅔ 'was regularly written as 3'.

## Individual evidence

1. ^ Rolf CA Rottländer: Ancient measures of length. Investigations into their connections. Vieweg, Braunschweig 1979, ISBN 3-528-06851-5 , p. 7 f.
2. See e.g. BOAW Dilke: Mathematics, measures and weights in antiquity (translated by R. Ottway), Reclam, Stuttgart 1991, ISBN 3-15-008687-6 , p. 15. R. Rottländer argues for a uniform standard .
3. ^ Clive J. Bridger: The Pes Monetalis and the Pes Drusianus in Xanten. In: Britannia 15, 1984, p. 85 ff.
4. Wolfgang Trapp : Small manual of the dimensions, numbers, weights and the time calculation. Bechtermünz Verlag im Weltbildverlag GmbH, Augsburg 1996, p. 206, ISBN 3-86047-249-6 .
5. ^ Rolf CA Rottländer on the distribution of pre-metric units of length
6. Jakob Köbel: Geometrey. First edition: Frankfurt a. M. 1535 (posthumously). Online version: Saxon State Library - Dresden State and University Library, reprint 1598.
7. Jürgen W. Koch: The Hamburg syringe master and mechanic Johann Georg Repsold (1770-1830). Diss. Hamburg 2001, p. 179 (Google Books).
8. ↑ The locations of the towers and the observatory in Hamburg against the tower of the great Michaeliskirche, along with their height differences and tables, in order to transform the Hamburg foot measure into Danish, Prussian, French and English measure, and the foreign measure into Hamburg foot measure . S. 8. Perthes-Besser & Mauke, Hamburg 1843. Digitized
9. Dr. Franz Mozhnik: Textbook of the entire arithmetic for the fourth class of the secondary schools in the kk states. Published by the kk school books wear administration at St. Anna in Johannisgasse, Vienna 1848. P. 131 as a jpg file .
10. ^ A b c Johann Christian Nelkenbrecher: General pocket book of measurement, weight and coinage, exchange, money and fund courses, etc. for bankers and merchants. Sandersche Buchhandlung, Berlin 842, p. 444.
11. Johann Schön: The numerical calculation . 2nd, revised edition. Goebhardt'sche Buchhandlung, Bamberg / Würzburg 1815, p. 318–320 ( full text in Google Book Search). ; for Zurich Hans Kläui, Otto Sigg: History of the municipality of Zell. Zurich 1983 (exemplary for a number of local chronicles).
12. ^ Gotthard Oswald Marbach: Popular physical lexicon. Volume 2, Otto Wigand, Leipzig 1835, p. 470.
13. Johann Friedrich Krüger : Complete manual of the coins, measurements and weights of all countries in the world. Gottfried Basse, Quedlinburg / Leipzig 1830, p. 100.
14. en: Foot (length)
15. Measuring Unit Change Coming in 2022 , National Geodetic Survey, 2019-06-14.
16. The Customs and the Pipe , gewinde-normen.de, accessed May 28, 2016.
17. FIFA - Laws of the Game 2015/2016 , PDF 2.41 MB; P. 9, accessed July 6, 2017.