Metric system

Countries which have officially adopted the metric system. Only three nations have not officially adopted the International System of Units as their primary or sole system of measurement: Burma, Liberia, and the United States.

File:Standard kilogram.jpg

One of two standard kilogram masses kept by the National Institute of Standards and Technology of the US government, that serves as the primary standard for all units of mass in the United States. It is an exact copy, made in 1884, of the international prototype kilogram kept at the Bureau International des Poids et Mesures in Sevres, France, that defines the unit of mass in the SI, the modern metric system. Forty such secondary kilograms were made in 1884, and distributed to nations to serve as national standards.

The metric system is an international decimalised system of measurement, first adopted by France in 1791, that is the common system of measuring units used by most of the world. It exists in several variations, with different choices of fundamental units, though the choice of base units does not affect its day-to-day use. Over the last two centuries, different variants have been considered the metric system. Since the 1960s the International System of Units ("Système International d'Unités" in French, hence "SI") has been the internationally recognised standard metric system. Metric units are widely used around the world for personal, commercial and scientific purposes. A standard set of prefixes in powers of ten may be used to derive larger and smaller units from the base units.

According to the US CIA World Factbook in 2006, the International System of Units is the official system of measurement for all nations except for Burma, Liberia, and the United States. (Some sources identify Burma and/or Liberia as metric, however.) However, a number of other jurisdictions have laws mandating or permitting other systems of measurement in some or all contexts, such as the United Kingdom — where for example the Traffic Sign Regulations only allow distance signs displaying imperial units (miles or yards) — or Hong Kong. In the United States, metric units are widely used in science and industry, but customary units predominate in household use. At retail stores, the liter is a commonly used unit for volume, especially on bottles of beverages, and milligrams are used to denominate the amounts of medications, rather than grains. Also, other standardized measuring systems other than metric are still in universal international use, such as nautical miles and knots in international aviation.

Overview

One goal of the metric system is to have a single unit for any physical quantity; another important one is not needing conversion factors when making calculations with physical quantities. All lengths and distances, for example, are measured in metres, or thousandths of a metre (millimetres), or thousands of metres (kilometre), and so on. There is no profusion of different units with different conversion factors, such as inches, feet, yards, fathoms, rods, chains, furlongs, miles, nautical miles, leagues, etc. Multiples and submultiples are related to the fundamental unit by factors of powers of ten, so that one can convert by simply moving the decimal place: 1.234 metres is 1234 millimetres, 0.001234 kilometres, etc. The use of fractions, such as 2⁄7 of a metre, is not prohibited, but uncommon, as it is generally not necessary.

The original metric system was intended to be used with the time units of the French Republican Calendar, but these fell into disuse. Today decimal time is not in everyday use. Submultiples of the second (the microsecond for example) are used in scientific work but for lengths of time greater than a second traditional units, with their non-decimal conversion factors, are more often used than decimal multiples of the second. In the late 18th century, Louis XVI of France charged a group of experts to develop a unified, natural and universal system of measurement to replace the disparate systems then in use. This group, which included such notables as Lavoisier, produced the metric system, which was then adopted by the revolutionary government of France.

In the early metric system, there were several fundamental or base units, the grad or grade for angles, the metre for length, the gram for mass and the litre for capacity. These were derived from each other via the properties of natural objects, mainly the Earth and water: 1 metre was originally defined as 1⁄10,000,000 of the distance between the North Pole and Earth's equator as measured along the meridian passing through Paris, the kilogram was originally defined as the mass of one litre (or, equivalently, 1 dm³) of water at its melting point (this definition was later revised to specify a temperature of 4 °C). The Celsius temperature scale was derived from the properties of water, with 0 °C being defined as its freezing point and 100 °C being defined as its boiling point under a pressure of one standard atmosphere. The metre was later redefined as the length of a particular bar of platinum-iridium alloy; then in terms of the wavelength of light emitted by a specified atomic transition; and now is defined as the distance travelled by light in an absolute vacuum during 1⁄299,792,458 of a second. The gram, originally one millionth of the mass of a cubic metre of water, is currently defined by one thousandth of the mass of a specific object that is kept in a vault in France; however there are efforts underway to redefine it in terms of physical quantities that could be reproduced in any laboratory with suitable equipment. The second, originally 1⁄86,400 of the mean solar day was redefined in 1967 to be 9,192,631,770 periods of vibration of the radiation emitted at a specific wavelength by an atom of caesium-133. Varying choices have been made for the fourth base unit, that which is needed to incorporate the field of electromagnetism; As of 2006, this is the ampere, being the base unit of electrical current.

Other quantities are derived from the base units; for example, the basic unit of speed is metres per second. As each new definition is introduced, it is designed to match the previous definition as precisely as possible, so these changes of definition have not affected most practical applications. (See SI and individual unit articles for full definitions.)

The names of multiples and submultiples are formed with prefixes. They include deca- (ten), hecto- (hundred), kilo- (thousand), mega- (million), and giga- (billion); deci- (tenth), centi- (hundredth), milli- (thousandth), micro- (millionth), and nano- (billionth). The most commonly used prefixes for multiples depend on the application and sometimes tradition. For example, long distances are stated in thousands of kilometres, not megametres.

Most everyday users of the metric system measure temperature in degrees Celsius, though the SI unit is the kelvin, a scale whose units have the same "size", but which starts at absolute zero. Zero degrees Celsius equals 273.15 kelvins (the word "degree" is no longer to be used with kelvins since 1967-68).

Angular measurements have been decimalised, but the older non-decimal units of angle are far more widely used. The decimal unit, which is not part of SI, is the gon or grad, equal to one hundredth of a right angle. Subunits are named, rather than prefixed: the gon is divided into 100 decimal minutes, each of 100 decimal seconds. The traditional system, originally Babylonian, has 360 degrees in a circle, 60 minutes of arc (also called arcminutes) in a degree, and 60 seconds of arc (also called arcseconds) in a minute. The clarifier "of arc" is dropped if it is clear from the context that we are not speaking of minutes and seconds of time. Sometimes angles are given as decimal degrees, e.g., 26.4586 degrees, or in other units such as radians (especially in mathematical and scientific uses other than astronomy) or angular mils.

History

Countries by date of metrication. Green represents 1800, yellow 1900, red 1980, and black identifies countries that have not adopted the metric system as the primary measurement system.

See also: Metrication

Adoption of the metric system by the various countries, or metrication, is shown by year on the attached map.

In 1586, the Flemish mathematician Simon Stevin published a small pamphlet called De Thiende ("the tenth"). Decimal fractions had been employed for the extraction of square roots some five centuries before his time, but nobody established their daily use before Stevin. He felt that this innovation was so significant that he declared the universal introduction of decimal coinage, measures, and weights to be merely a question of time.

The idea of a metric system has been attributed to John Wilkins, first secretary of the Royal Society of London in 1668. The idea did not catch on, and England continued with its existing system of various weights and measures.

In 1670, Gabriel Mouton, a French abbot and scientist, proposed a decimal system of measurement based on the circumference of the Earth. His suggestion was a unit, milliare, that was defined as a minute of arc along a meridian. He then suggested a system of sub-units, dividing successively by factors of ten into the centuria, decuria, virga, virgula, decima, centesima, and millesima.

His ideas attracted interest at the time, and were supported by Jean Picard as well as Huygens in 1673, and also studied at the Royal Society in London. In 1673, Gottfried Leibniz independently made proposals similar to those of Mouton.

The proliferation of disparate measurement systems was one of the most frequent causes of disputes amongst merchants and between citizens and tax collectors. A unified country with a single currency and a countrywide market, as most European countries were becoming by the end of the 18th century, had a very strong economic incentive to break with this situation and standardise on a measuring system. The inconsistency problem was not one of different units but one of differing sized units. Instead of simply standardising the size of the existing units, the leaders of the French revolutionary Assemblée Constituante decided that a completely new system should be adopted. It was felt that no country would accept standardizing on the units of another country, but that there would be less resistance if a completely new system made change compulsory for all countries.

Metric seal

On 20 May 1875, an international treaty known as the Convention du Mètre (Metre Convention) was signed by 17 states. This treaty established the following organisations to conduct international activities relating to a uniform system for measurements:

• Conférence générale des poids et mesures (CGPM), an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;
• Comité international des poids et mesures (CIPM), consisting of selected scientists and metrologists, which prepares and executes the decisions of the CGPM and is responsible for the supervision of the International Bureau of Weights and Measures;
• Bureau international des poids et mesures (BIPM), a permanent laboratory and world centre of scientific metrology, the activities of which include the establishment of the basic standards and scales of the principal physical quantities and maintenance of the international prototype standards.

Replicable Prototypes

The usual way to establish a standard was to make prototypes of the base units and distribute copies. This would make the new standard reliant on the original prototypes, which would be in conflict with the previous goal, since all countries would have to refer to the one holding the prototypes.

Instead, the designers developed definitions of the base units such that any laboratory equipped with proper instruments should be able to make their own models of them. The original base units of the metric system could be derived from the length of a meridian of the Earth and the weight of a certain volume of pure water. For a time, the Assemblée Constituante considered using the length of a pendulum beating the second in Paris as the base of the metre; when they heard that the British Parliament was discussing a similar proposal, based on the length of the pendulum beating the second in London, the Assemblée contacted their counterparts in London and offered to standardise on the London pendulum. Instead, the UK abandoned the idea of metrication for another two centuries, and the meridian definition of the metre was adopted. The pendulum was not a likely choice for a prototype in any case, since its period (or, inversely, the length of the string holding the bob for the same period) changes around the Earth. Likewise, they discarded using the circumference of the Earth over the Equator since not all countries have access to the Equator while all countries have access to a section of a meridian.

Decimal multiples

The metric system is decimal, in the sense that all multiples and submultiples of the base units are factors of powers of ten of the unit. Fractions of a unit are not used formally. The practical benefits of a decimal system are such that it has been used to replace other non-decimal systems outside the metric system of measurements; for example currencies.

The simplicity of decimal prefixes encouraged the adoption of the metric system. Clearly the advantages of decimal prefixes derive from our using base 10 arithmetic. At most, differences in expressing results are simply a matter of shifting the decimal point or changing an exponent; for example, the speed of light may be expressed as 299,792.458 km/s or 2.99792458×10⁸ m/s.

Prefixes

Main article: SI prefix

All derived units would use a common set of prefixes for each multiple. Thus the prefix kilo could be used for mass (kilogram) or length (kilometre) both indicating a thousand times the base unit. This did not prevent the popular use of names for some derived units such as the tonne which is a megagram; derived from old customary units and rounded to metric.

The function of the prefix is to multiply or divide the measure by a factor of ten, one hundred or a positive integer power of one thousand. If the prefix is Greek-derived, the measure is a positive power. If the prefix is Latin-derived, it is a negative power, except by 10⁻⁶ (micro~) which is also Greek-derived. The Greek prefix kilo~ and the Latin prefixes centi~ and milli~ are those most familiar from everyday use.

metre

Unit	Relation to base
megametre	106 metres
kilometre	103 metres
hectometre	102 metres
decametre	101 metres
decimetre	10−1 metres
centimetre	10−2 metres
millimetre	10−3 metres
micrometre	10−6 metres
nanometre	10−9 metres
picometre	10−12 metres
femtometre	10−15 metres

litre

Unit	Relation to base
megalitre	106 litres
kilolitre	103 litres
hectolitre	102 litres
decalitre	101 litres
decilitre	10−1 litres
centilitre	10−2 litres
millilitre	10−3 litres
microlitre	10−6 litres
nanolitre	10−9 litres
picolitre	10−12 litres
femtolitre	10−15 litres

A similar application of Greek and Latin prefixes can be made with other metric measurements.

Practicality

The base units were chosen to be of similar magnitude to customary units. The metre, being close to half a toise (French yard equivalent), became more popular than the failed decimal hour of the Republican Calendar which was 2.4 times the normal hour.

The kilometre was originally defined as the length of an arc spanning a decimal minute of latitude, a similar definition to that of the nautical mile which was the length of an arc of one (non-decimal) minute of latitude.

Originally, units for volume and mass were directly related to each other, with mass defined in terms of a volume of water. Even though that definition is no longer used, the relation is quite close at room temperature and nearly exact at 4 °C. So as a practical matter, one can fill a container with water and weigh it to get the volume. For example,

• 1000 litres = 1 cubic metre ≈ 1 tonne of water
• 1 litre = 1 cubic decimetre ≈ 1 kilogramme of water
• 1 millilitre = 1 cubic centimetre ≈ 1 gramme of water
• 1 microlitre = 1 cubic millimetre ≈ 1 milligramme of water

Coincidental similarities

Two important values, when they were expressed in the metric system, turned out to be very close to a power of 10. The standard acceleration due to gravity on Earth, g_n, has been defined to be 9.80665 m/s² exactly. Accordingly the force exerted on a mass of one kilogram in Earth gravity (F = m·a) is about 10 newtons (kg·m/s²). This simplified the metrication of many machines such as locomotives, which were simply re-labelled from, e.g., 85 tonnes (i.e., tonne-force) to 850 kN. A closer approximation is π² (≈ 9.86960) m/s², which means a seconds pendulum is almost one metre long.

Also, the standard atmospheric pressure, previously expressed in atmospheres, when given in pascals, is 101.325 kPa. Since the difference between 10 atmospheres and 1 MPa is only 1.3%, many devices were simply re-labelled by dividing the scale by ten (e.g., 1 atm was changed to 0.1 MPa).

In addition, the speed of light in a vacuum turned out to be close (0.07% different) to 3×10⁸ m/s; the exact value, 299792458, has since become the definition.

A useful conversion used in meteorology is 1 m/s ≈ 2 knots, or actually 1.94384 kn (3% error).

Metric systems

Original system

The metric system, including the metre, was first fully described by Englishman John Wilkins in 1668 in a treatise presented to the Royal Society, some 120 years before the French adopted the system.

It is believed that the system was transmitted to France from England via the likes of Benjamin Franklin (who spent a great deal of time in London), and produced the by-product of the decimalised paper currency system, before finding favor with American revolutionary ally Louis XVI.

The original French system continued the tradition of having separate base units for geometrically related dimensions, e.g., metre for lengths, are (100 m²) for areas, stère (1 m³) for dry capacities, and litre (1 dm³) for liquid capacities. The hectare, equal to a hundred ares, is the area of a square 100 metres on a side (about 2.47 acres), and is still in use.

The base unit of mass is the kilogram. This is the only base unit that has a prefix, for historical reasons. Originally the kilogram was called the "grave", and the "gram" was an alternative name for a thousandth of a grave. After the French Revolution, the word "grave" carried negative connotations, as a synonym for the title "count". The grave was renamed the kilogram. This also serves as the prototype in the SI. It included only few prefixes from milli (one thousandth) to myria (ten thousand).

Several national variants existed thereof with aliases for some common subdivisions. In general, this entailed a redefinition of other units in use (e.g., 500-gram pounds or 10-kilometre miles or leagues). An example of these is measures usuelles. However, it is debatable whether such systems are true metric systems.

Centimetre-gram-second systems

Early on in the history of the metric system, various versions of centimetre gram second system of units (CGS) had been in use. These units were particularly convenient in science and technology. For example, in CGS the density of water is approximately one gram per cubic centimetre.

Metre-kilogram-second systems

Later metric systems were based on the metre, kilogram and second (MKS) to improve the value of the units for practical applications. Metre-kilogram-second-coulomb (MKSC) and metre-kilogram-second-ampere (MKSA) systems are extensions of these.

The International System of Units (System international units or SI) is the current international standard metric system and the system most widely used around the world. It is based on the metre, kilogram, second, ampere, kelvin, candela and mole.

Metre-tonne-second systems

The metre-tonne-second system of units (MTS) was based on the metre, tonne and second. It was invented in France and mostly used in the Soviet Union from 1933 to 1955.

Millimetre-newton-second systems

This system is based on the millimetre, newton and second. It is used in simulation of mechanical systems using tools like finite_element solvers. The geometry, loading and time are all convenient, common and intuitive. A consequence of this is that the density term is in mega-grams per cubic millimetre. To convert from g/cm³, a common unit for density, requires multiplication by 10⁹.

Gravitational systems

Gravitational metric systems use the kilogram-force (kilopond) as a base unit of force, with mass measured in a unit known as the hyl, TME, mug or metric slug. Note these are not part of the International System of Units (SI).

Variations in terminology

In keeping with American English spelling, meter, liter, etc. are used in the United States. In addition, the official US spelling for the rarely used SI prefix for ten is deka. In American English the term metric ton is the normal usage whereas in other varieties of English tonne is common.

The US government has approved this terminology for official use. In scientific contexts only the symbols are used; since these are universally the same, the differences do not arise in practice in scientific use.

Gram is also sometimes spelled gramme in English-speaking countries other than the United States, though it is an older spelling and its usage is declining.

Conversion and calculation errors

• Cargo errors

The confusion between pounds (mass) and kilograms sometimes means that aircraft are overloaded. "the shipper's weights had been in kilograms, not pounds, and that, as a result, the aircraft was more than 30,000 pounds overweight".

• Gimli Glider

In 1983 a Boeing 767 jet ran out of fuel in mid-flight because of two mistakes in figuring the fuel supply of Air Canada's first aircraft to use metric measurements.

• Mars Climate Orbiter

In 1999 NASA lost a $125 million Mars orbiter because one engineering team used metric units while another used US customary units for a calculation.

• Medical errors

Medical errors in the US are sometimes attributed to the confusion between grains and grams. A patient received phenobarbital 0.5 grams instead of 0.5 grains (0.03 grams) after the prescriber misread the prescription.

See also

• Conversion of units
• History of measurement
• International system of units
• ISO 31, metric writing style
• Mesures usuelles (French: customary measurements), a compromise between metric and traditional units employed until 1839
• Metric time

• Metrication, the process of introducing the SI metric system as the worldwide standard for physical measurements
  (a long-term series of independent and systematic conversions from the various separate local systems of weights and measures)

• Antimetrication
• Metrication Board
• Metric Martyrs

• Metrology
• SI prefix
• Units of measurement

Multimedia

• CBC Radio Archives Talking about the history of Metric.