metric system

metric system

metric system, system of weights and measures planned in France and adopted there in 1799; it has since been adopted by most of the technologically developed countries of the world. It is based on a unit of length, called the meter (m), and a unit of mass, called the kilogram (kg).

The system has changed somewhat since it was first developed; e.g., the definition of the meter has changed, and the unit for mass is different. The meter was originally intended to be 1/10,000,000 of the distance on the earth's surface between the equator and either pole; however, because of errors in the original survey for determining the meter and because of the impracticality of referring to such a standard, the meter was later redefined in terms of the standard prepared and kept at Sèvres, France, near Paris. Long defined as the distance between two scratches on a bar of platinum-iridium alloy, the meter in 1960 was first redefined in terms of an atomic standard. In 1983 the meter was officially redefined as the distance traveled by light in vacuum during 1/299,792,458 of a second.

The original unit of mass, the gram, was first defined as the mass of pure water at maximum density that would fill a cube whose edges are each 0.01 m. The unit of mass is now the kilogram, defined as the mass of a platinum-iridium cylinder kept at Sèvres. (A gram is now defined as a mass 1/1,000 kg.) Other metric units can be defined in terms of the meter and the kilogram. For example the are, the unit of area, is equal to the area of a square whose edges are each 10 m long. The liter, the metric unit of volume, is equal to the volume of a cube whose edges are each 1/10 m long.

Fractions and multiples of the metric units are related to each other by powers of 10, allowing conversion from one unit to a multiple of it simply by shifting a decimal point, and avoiding the lengthy arithmetical operations required by the English units of measurement. Standard prefixes (found in the table entitled Prefixes for Basic Metric Units) have been accepted for designating multiples and fractions of the meter, gram, are, and other units. Thus, 1,000 grams are a kilogram, 100 ares are a hectare, and 1/100 of a meter is a centimeter.

Several other systems of units based on the metric system have been in wide use. The cgs system is based on the centimeter of length, the gram of mass, and the second of time. The mks system is based on the meter of length, the kilogram of mass, and the second of time. Units in the mks system are larger than the corresponding cgs units. Electric and magnetic units have been defined for both of these systems; in fact, two different sets of electric units are defined in the cgs system. The mks system serves as the basis for the International System of Units, a comprehensive system of units for all physical quantities adopted in 1960 by the 11th General Conference on Weights and Measures.

See also decimal system.

See L. V. Judson, Weights and Measures Standards of the United States: A Brief History (1976; U.S. National Bureau of Standards Special Publication 447); K. Alder, The Measure of All Things (2002).

The metric system is a decimalised system of measurement. It exists in several variations, with different choices of base 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. However, the prefixes for multiples of one thousand are the most commonly used.


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 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-decimalconversion 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 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 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 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 1967-1968).

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 scientific uses other than astronomy) or angular mils.


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 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 and was in a position 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 so instead of simply standardising size of the existing units, the leaders of the French revolutionary governments decided that a completely new system should be adopted.

The first official adoption of such a system occurred in France in 1791 after the French Revolution of 1789. The creators of this metric system tried to choose units that were logical and practical. The revolution gave an opportunity for drastic change with an official ideology of "pure reason". It was proposed as a considerable improvement over the inconsistent collection of customary units that existed before, and that it be based on units of ten, because scientists, engineers, and bureaucrats at the time found this more convenient for the complex unit conversion they often must do.

The adoption of the metric system in France was slow, but its desirability as an international system was advocated by geodesists and others. Since then a number of variations on the system evolved. Their use spread throughout the world, first to the non-English-speaking countries, and more recently to the English-speaking countries.

The whole system was derived from the properties of natural objects, namely the size of the Earth and the density of water, and simple relations in between one unit and the other. In order to determine as precisely as possible the size of the Earth, several teams were sent over several years to measure the length of as long a segment of a meridian as feasible. It was decided to measure the meridian spanning Barcelona and Dunkirk which was the longest segment almost fully over land within French territory. It should be noted that even though, during the many years of the measurement, hostilities broke out between France and Spain, the development of such a standard was considered of such value that Spanish troops escorted the French team while in Spanish territory to ensure their safety.

The whole process ended in the proclamation on June 22, 1799 of the metric system with the storage in the Archives of the Republic of the physical embodiments of the standard, the prototype metre and the prototype kilogram, both made in a platinum alloy, witnessed by representatives of the French and several foreign governments and most important natural philosophers of the time. The motto adopted for the metric system was: "for all men, for all time".

In revolutionary France the system was not particularly well accepted, and the old units, now illegal, remained in widespread use. On February 12, 1812, Napoleon, who had other concerns than enforcement of the system, authorised the usage of Mesures usuelles, traditional French measures redefined on the base of Metric System (toise as 2 metres, livre as 500 grams, etc.), and finally in 1816 a law made these Mesures usuelles standards. This law was cancelled in 1825 and the metric system reinstated fully in 1837. It had already been reinstated in 1820 by a somewhat unlikely person, King William I of the neighbouring (United) Netherlands. Although he was generally considered more conservative, he was desperate to bring at least some form of unity to his rather disunited kingdom and stimulate the industrial development of the South. Although the imposed system was metric, a number of old local names like 'pond' (pound) and 'ons' (ounce) were substituted for 500 g and 100 g respectively, and although they were officially abolished in the 1870s, they survive to the present day. The king's attempts were in vain in that Belgium claimed its independence from the Netherlands, but the metric system survived and began a slow but steady conquest of the world. In 1866 the U.S. passed a law making the metric system legal.

On May 20, 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:

  1. Conférence générale des poids et mesures (CGPM), an intergovernmental conference of official delegates of member nations and the supreme authority for all actions;
  2. 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;
  3. 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.

Later improvements in the measurement of both the size of the Earth and the properties of water revealed discrepancies between the metric standards and their originally intended values. The Industrial Revolution was well under way and the standardisation of mechanical parts, mainly bolts and nuts, was of great importance and they relied on precise measurements. Though these discrepancies would be mostly hidden in the manufacturing tolerances of those days, changing the prototypes to conform to the new and more precise measurements would have been impractical particularly since new and improved instruments would continually change them.

It was decided to break the linkage between the prototypes and the natural properties they were derived from. The prototypes then became the basis of the system. The use of prototypes, however, is problematic for a number of reasons. There is the potential for loss, damage or destruction. There is also the problem of variance of the standard with the changes that any artifact can be expected to go through, though they be slight. Also whilst there may be copies, there must be only one official prototype which cannot be universally accessible.

The metre had been defined in terms of such a prototype and remained so until 1960. At that time, the metre was defined as a certain number of wavelengths of a particular frequency of light emitted by krypton. Since 1983 the metre has been defined as the distance light travels in a given fraction of a second in a vacuum. Thus the definition of the metre ultimately regained a linkage with a natural property, this time a property thought immutable in our universe and truly universal. The kilogram is now the only base unit still defined in terms of a prototype. Since 1899, the kilogram has been formally anchored to a single platinum-iridium cylinder in Sèvres, France.

The metric system is used widely for scientific purposes but there are some exceptions, especially at large and small scales, such as the parsec. By the 1960s, the majority of nations were on the metric system and most that were not had started programmes to fully convert to the metric system (metrication). As of 2006, 95% of the world's population live in metricated countries, although non-metric units are still used for some purposes in some countries. Only three countries, Burma, Liberia, and the United States had not officially adopted the metric system.


The metric system was designed with several goals in mind.

Neutral and universal

The designers of the metric system meant to make it as neutral as possible so that it could be adopted universally.


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.

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. They discarded the use of a pendulum 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 m/s.


All derived units would use a common set of prefixes for each multiple. Thus the prefix kilo could be used both 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 while a quintal is accepted as 100 kilograms; both are derived from old customary units and were 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 multiplied by this factor. If the prefix is Latin-derived, it is divided. The Greek prefix kilo~ and the Latin prefixes centi~ and milli~ are those most familiar from everyday use.

metre (common base unit)
kilometre = 1000 metres
hectometre = 100 metres (not commonly used)
decametre = 10 metres (a measure used in naval artillery)
decimetre = of a metre
centimetre = of a metre
millimetre = of a metre
nanometre = of a metre (a measure used in nanotechnology)
litre (common base unit)
kilolitre = 1000 litres (not commonly used)
hectolitre = 100 litres (used for beer kegs, 1 keg is approx. of a hectolitre)
decalitre = 10 litres (not a commonly used measure)
decilitre = of a litre
centilitre = of a litre
millilitre = of a litre

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


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 ("cubic metre" is commonly used instead of "kilolitre")
1 litre = 1 cubic decimetre ≈ 1 kilogram of water
1 millilitre = 1 cubic centimetre ≈ 1 gram of water
1 microlitre = 1 cubic millimetre ≈ 1 milligram of water

Coincidental similarities

Two important values, when they were expressed in the metric system, turned out to be very close to a multiple of 10. The standard acceleration due to gravity on Earth gn has been defined to be 9.80665 m/s² exactly, which is the value at about 45° north or south of the equator. Accordingly the force exerted on a mass of one kilogram in Earth gravity (F = m·a) is about ten newtons (kg-m/s²). This simplified the metrication of many machines such as locomotives, which were simply re-labelled from e.g. "85 tonnes" to "850 kN". A closer approximation is π² m/s², which means a one-metre pendulum has a period of almost exactly two seconds.

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 turns out to be astonishingly close (0.07% error) to 3×108 m/s.

A useful conversion used in meteorology is 1 m/s ≈ 2 knots with less than a 3% error, actually 1.94384 knots (to 5 decimal places). The equivalent conversion for distance is not so "rounded", 1 nautical mile = 1.852 km (exactly) = 1 minute of arc Latitude (approximately).

Metric systems

Original system

The metric system, and 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 favour with American revolutionary ally Louis XV.

The original French system continued the tradition of having separate base units for geometrically related dimensions, i.e. metre for lengths, are (100 m²) for areas, stere (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 2.5 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 "gramme" 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 mesures 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 centimetre gram second systems 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 1 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 (Système international d'unités 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.

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 practise 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.

Notes and references

See also

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