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Foot (unit of length)

# Foot (unit of length)

1 foot =
International units
0.3048 m 304.8×10−6 km
304.8 mm 3.048×109 Å
2.0375×10−12 AU 32.2174×10−18 LY
US customary / Imperial units
12 in ft
0.3333 yd 189.3939×10−6 mi

A foot (plural: feet; symbol or abbreviation: ft or, sometimes, – a prime) is a 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 metre. The most commonly used foot today is the international foot. There are 3 feet in a yard and 12 inches in a foot.

## Definition

### International foot

In 1958 the United States and countries of the Commonwealth of Nations defined the length of the international yard to be 0.9144 metres. Consequently, the international foot is defined to be equal to 0.3048 metres (equivalent to 30.48 centimetres).

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, 6 feet 2 inches is denoted by 6′2″. This use can cause confusion, because the prime and double prime are also international standard symbols for arcminutes and arcseconds.

### United States survey foot

The United States survey foot is defined as exactly 12003937 metres, or 0.30480061 m. It is used only in connection with surveys by the U.S. Coast and Geodetic Survey. It is 610 nm greater than the international foot. [1]

## Historical origin

The foot as a measure was used in almost all cultures and was usually divided into 12, 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. This is most likely true, but when local authorities and national rulers began calibrating and defining measurements, the foot of no human being was probably used as the basis. 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 plowed 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 standardisation began in Scotland in 1150 and in England in 1303, but many different regional standards had existed in both these countries 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 standardise the unit of measurement in England. However this is unlikely, because there are records of the word being used approximately 70 years before his birth (Laws Æthelstan). This of course does not exclude the possibility that this old standard was redefined ("calibrated") according to the ruler's foot. In fact, there is evidence that this sort of process was common at least in earlier ages. In other words, a new important ruler could try to impose a new standard for an existent 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. This is consistent with the measure being convenient for practical purposes such as on building sites etc. People almost always pace out lengths whilst 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 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 12th 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 of course never used in surveying and in constructing more complicated buildings.

## Trivia

While the foot is an ancient measure, it coindidentally matches some common constants to a very high degree (under 2% error).

• There are 6080 feet in a nautical mile, which is approximately one minute of arc on the Earth's surface. This makes an arc second, which is 1/60 of an arc minute, about 101 feet.
• The speed of light is 983,571,056.16 feet per second, which makes a foot about 1.017 light nanoseconds.