# Length Conversions

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Meter - The metre or meter (from the Greek /'metron/) is a unit of proper length. It is the basic unit of length in the metric system and in the International System of Units (SI), used around the world for general and scientific purposes. Historically, the metre was defined by the French Academy of Sciences as the length between two marks on a platinum-iridium bar, which was designed to represent 1/10,000,000 of the distance from the equator to the north pole through Paris. In 1983, it was redefined by the International Bureau of Weights and Measures (BIPM) as the distance travelled by light in free space in 1/299,792,458 of a second. The symbol for metre is a lower case m. Decimal multiples and submultiples of the metre, such as kilometre (1000 metres) and centimetre (1/100 metre), are indicated by adding SI prefixes to metre.

Meridional definition - In the eighteenth century, there were two favoured approaches to the definition of the standard unit of length. One approach suggested defining the metre as the length of a pendulum with a half-period of one second, a 'seconds pendulum'. The other approach suggested defining the metre as one ten-millionth of the length of the Earth's meridian along a quadrant, that is the distance from the Equator to the North Pole. In 1791, the French Academy of Sciences selected the meridional definition over the pendular definition because the force of gravity varies slightly over the surface of the Earth, which affects the period of a pendulum.

In order to establish a universally accepted foundation for the definition of the metre, measurements of this meridian more accurate than those available at that time were imperative. The Bureau des Longitudes commissioned an expedition led by Delambre and Pierre Mechain, lasting from 1792 to 1799, which measured the length of the meridian between Dunkerque and Barcelona. This portion of the meridian, which also passes through Paris, was to serve as the basis for the length of the half meridian, connecting the North Pole with the Equator.

However, in 1793, France adopted as its official unit of length a metre based on provisional results from the expedition as its official unit of length. Although it was later determined that the first prototype metre bar was short by a fifth of a millimetre due to miscalculation of the flattening of the Earth, this length became the standard. The circumference of the Earth through the poles is therefore slightly more than forty million metres.

In the 1870s and in light of modern precision, a series of international conferences were held to devise new metric standards. The Metre Convention (Convention du Metre) of 1875 mandated the establishment of a permanent International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sevres, France. This new organisation would preserve the new prototype metre and kilogram standards when constructed, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation created a new prototype bar in 1889 at the first General Conference on Weights and Measures (CGPM: Conference Generale des Poids et Mesures), establishing the International Prototype Metre as the distance between two lines on a standard bar composed of an alloy of ninety percent platinum and ten percent iridium, measured at the melting point of ice.

In 1893, the standard metre was first measured with an interferometer by Albert A. Michelson, the inventor of the device and an advocate of using some particular wavelength of light as a standard of distance. By 1925, interferometry was in regular use at the BIPM. However, the International Prototype Metre remained the standard until 1960, when the eleventh CGPM defined the metre in the new SI system as equal to 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum. The original international prototype of the metre is still kept at the BIPM under the conditions specified in 1889.

Kilometer - The kilometre (American spelling: kilometer), symbol km is a unit of length in the metric system, equal to one thousand metres. It is the conventionally used measurement unit for expressing distances between geographical places in countries which use the metric system. While it is defined exactly as 1000 m, it equals roughly a ten minutes' walk. Slang terms for kilometre include click (sometimes spelled klick or klik) and kay (or k).

The United Kingdom and the United States are the only two developed countries which continue to use miles on road signs. Although the UK has officially adopted the metric system, there are currently no plans to replace the mile on road signs in the near future, owing to the British public's attachment to traditional imperial units of distance, i.e., miles, yards and inches, and the cost of changing speed signs (which could not be replaced during general maintenance, like distance signs, for safety reasons). As of 11 September 2007, the EU has not challenged Britain's use of the imperial systems. EU commissioner Gunter Verheugen said: "There is not now and never will be any requirement to drop imperial measurements."

In the US, the National Highway System Designation Act of 1995 prohibits the use of federal-aid highway funds to convert existing signs or purchase new signs with metric units. However, the Manual on Uniform Traffic Control Devices since 2000 is published in both metric and American Customary Units.

Mile - A mile is a unit of length, usually used to measure distance, in a number of different systems. In contemporary English contexts, mile most commonly refers to the statute mile of 5,280 feet (exactly 1,609.344 meters) or the nautical mile of 1,852 meters (about 6,076.1 ft). There are many other historical miles, and similar units in other systems translated as miles in English, varying between one and fifteen kilometers. It is about a third of the old measurement, a League.

The measurement is now used almost exclusively in the United States and the United Kingdom. It has been replaced by the kilometer as a measure of distance elsewhere. It is sometimes retained as a customary unit. There have been several abbreviations for mile (with and without trailing period): mi, ml, m, M. In the United States, the National Institute of Standards and Technology now uses and recommends mi but in everyday usage (at least in the United States and in the United Kingdom) usages such as miles per hour and miles per gallon are almost always abbreviated as mph or mpg (rather than mi/h or mi/gal).

The formula "multiply by 8 and divide by 5" to convert international miles to kilometers gives a conversion of 1.6, which, at less than 1 percent high, makes a useful approximation.

The statute mile was defined by English Act of Parliament (hence the name) in 1592, during the reign of Queen Elizabeth I; it is equal to 1760 yards (5280 feet). For surveying, the statute mile is divided into eight furlongs; each furlong is ten chains; each chain is four rods (also known as poles or perches); and each rod is 25 links. This makes the rod equal to 5.5 yards or 16.5 feet in both Imperial and U.S. usage.

The exact conversion of the mile to SI units depends on which definition of the yard is in use. The different English-speaking countries maintained independent physical standards for the yard that were found to differ by small but measurable amounts, and even to slowly shorten in length. The United States redefined the U.S. yard in 1893, but this meant that U.S. and Imperial units with the same names had very slightly different values. The confusion was resolved in 1959 with the definition of the international yard in terms of the metre by Australia, Canada, New Zealand, South Africa, the United Kingdom, and the United States. The "international mile" of 1760 international yards is exactly 1609.344 metres.

The difference from the previous standards was about 2 ppm, or about a tenth of an inch in each mile, the old U.S. standard being slightly longer and the old Imperial standards slightly shorter than the international mile. The older standards for the yard (and hence the foot and the mile) continue in use for some surveying purposes in the United States and in India.

For most applications, the difference between the two definitions is insignificant - one international foot is exactly 0.999998 of a U.S. survey foot, for a difference of about 3 millimeters per mile - but it affects the definition of the State Plane Coordinate Systems (SPCSs), which can stretch over hundreds of miles. When international measure was introduced in the English-speaking countries, the basic geodetic datum in North America was the North American Datum of 1927 (NAD27), which had been constructed by triangulation based on the definition of the foot in the Mendenhall Order of 1893, that is 1 foot = 1200/3937 meters: this definition was retained for data derived from NAD27, but renamed the U.S. survey foot to distinguish it from the international foot.

The NAD27 was replaced in the 1980s by the North American Datum of 1983 (NAD83), which is defined in meters. The SPCSs were also updated, but the National Geodetic Survey left the decision of which (if any) definition of the foot to use to the individual states. All SPCSs are defined in meters, but seven states also have SPCSs defined in U.S. survey feet and an eighth state in international feet: the other 42 states use only meter-based SPCSs. The current National Topographic Database of the Survey of India is based on the metric WGS-84 datum, which is also used by the Global Positioning System.

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). In the U.S., 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.