# Metric system explained

The metric system is an international decimalised system of measurement that was originally based on the mètre des archives and the kilogramme des archives introduced by France in 1799. Over the years the definitions of the metre and kilogram have been refined and the metric system extended to incorporate many more units. Although a number of variants of the metric system emerged in the late nineteenth and early twentieth centuries the term is now often used as a synonym for the "International System of Units" - the official system of measurement in almost every country in the world.

The United States is the only industrialized country that does not use the metric system as its official system of measurement, although the metric system has been officially sanctioned for use there since 1866.[1] Although the United Kingdom committed to officially adopting the metric system for many measurement applications, it is still not in universal use there and the customary imperial system is still in common and widespread use. Although the originators intended to devise a system that was equally accessible to all, it proved necessary to use prototype units under the custody of government or other approved authorities as standards. Until 1875, control of the prototype units of measure was maintained by the French Government when it passed to an inter-governmental organisation – the Conférence générale des poids et mesures (CGPM). It is now hoped that the last of these prototypes can be retired by 2014.

From its beginning, the main feature of the metric system was the standard set of inter-related base units and a standard set of prefixes in powers of ten. These base units are used to derive larger and smaller units and replaced a huge number of unstandardised units of measure that existed previously. While the system was first developed for commercial use, its coherent set of units made it particularly suitable for scientific and engineering purposes.

The uncoordinated use of the metric system by different scientific and engineering disciplines, particularly in the late 19th century, resulted in different choices of fundamental units, even though all were based on the same definitions of the metre and the kilogram. During the 20th century, efforts were made to rationalise these units and in 1960 the CGPM published the International System of Units ("Système international d'unités" in French, hence "SI") which, since then, has been the internationally recognised standard metric system.

## Features

Although the metric system has changed and developed since its inception, its basic features have remained constant.

### Universality

The metric system was, in the words of the French philosopher Condorcet to be "for all people for all time".[2] It was designed for ordinary people, for engineers who worked in human-related measurements and for astronomers and physicists who worked with numbers both small and large, hence the huge range of prefixes that have now been defined in SI.[3]

The metric system was designed to be universal, that is, available to all. When the French Government first investigated the idea of overhauling their system of measurement, Talleyrand, in the late 1780s, acting on Concordet's advice, invited Riggs, a British Parliamentarian and Jefferson, the American Secretary of State to George Washington, to work with the French in producing an international standard by promoting legislation in their respective legislative bodies. However, these overtures failed and the custody of the metric system remained in the hands of the French Government until 1875.[4]

To help make it universal, common unit symbols that are independent of language were developed. Thus the length unit symbol "km" is used in French and in British English for "kilometre", in German, Danish and in American English for "kilometer", in Spanish for "kilómetro", in Portuguese for "quilómetro", in Italian for "chilometro", in Greek for "χιλιόμετρα", in Russian for "Километр", in Urdu for "کلومیٹر" and so on.[5] [6]

### Decimal multiples

The metric system is decimal, except where the non-SI units for time and plane angle measurement are concerned. All multiples and divisions of the decimal units are factors of the power of ten, an idea first proposed by the Flemish mathematician Simon Stevin in 1586.

Decimal prefixes are a characteristic of the metric system; the use of base 10 arithmetic aids in unit conversion. Differences in expressing units are simply a matter of shifting the decimal point or changing an exponent; for example, the speed of light may be expressed as  km/s or .

The use of decimal multiples results in less convenient non-integer quantities for divisions commonly used prior to the introduction of the metric system, such as by 3, 6 and 12.

### Non-SI units

See main article: Non-SI units mentioned in the SI. The tonne ( kg), the litre (now defined as exactly 0.001 m3), and the hectare ( such units are widely used in science, military, and partially in industry, but customary units predominate in household use.[7] [8] At retail stores, the litre 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 standardised measuring systems other than metric are still in universal international use, such as nautical miles and knots in international aviation.

In the countries of the Commonwealth of Nations the metric system has replaced the imperial system by varing degrees: Australia, New Zealand and Commonwealth countries in Africa are almost totally metric, India is mostly metric, Canada is partly metric while in the United Kingdom the metric system, the use of which was first permitted for trade in 1864,[9] is used in much government business, in most industries including building, health and engineering and for pricing by measure or weight in most trading situations, both wholesale and retail. However the imperial system continues to be used in many unregulated applications and is in widespread daily use.[7]

A number of other jurisdictions, such as Hong Kong,[10] have laws mandating or permitting other systems of measurement in parallel with the metric system in some or all contexts.

### Variations in spelling

The SI symbols for the metric units are intended to be identical, regardless of the language used. For example, the SI unit symbol for kilometre is "km" everywhere in the world, even though the local language word for the unit name may vary. Language variants for the kilometre unit name include: chilometro (Italian), Kilometer (German), kilometer (Dutch, Malay), kilomètre (French), χιλιόμετρο (Greek), quilómetro (Portuguese) and Километър (Bulgarian).[11] Variations are also found with the spelling of unit names in countries using the same language, including differences in American English and British spelling. For example meter and liter are used in the United States whereas metre and litre are used in other English-speaking countries. 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. Gram is also sometimes spelled gramme in English-speaking countries other than the United States, though this older usage is declining.[12]

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.

## Conversion and calculation errors

The dual usage of metric and non metric units has resulted in serious errors. These include:

• The degree of overloading of an American International Airways aircraft flying from Miami to Maiquetia, Venezuela on 26 May 1994 was consistent with a cargo weighed in kilograms, not pounds.[13]
• The Institute for Safe Medication Practices has reported that confusion between grains and grams led to a patient receiving phenobarbital 0.5 grams instead of 0.5 grains (0.03 grams) after the practitioner misread the prescription.[14]
• The Canadian "Gimli Glider" accident in 1983, when a Boeing 767 jet ran out of fuel in mid-flight because of two mistakes in calculating the fuel supply of Air Canada's first aircraft to use metric measurements.[15]
• The root cause of NASA's 1999 loss of the \$125 million Mars Climate Orbiter which crashed into Mars was a mismatch of units - the spacecraft engineers calculated the thrust forces required for velocity changes using US customary units (lbf·s) whereas the team who built the thrusters were expecting a value in metric units (N·s) as per the agreed specification.[16] [17]

## Conversion between SI and legacy units

See main article: Conversion of units. During its evolution, the metric system has adopted many units of measure. The introduction of SI rationalised both the way in which units of measure were defined and also the list of units in use. These are now catalogued in the official SI Brochure.[18] The table below lists the units of measure in this catalogue and shows the conversion factors connecting them with the equivalent units that were in use on the eve of the adoption of SI.

QuantityDimensionSI unit and symbolLegacy unit and symbolConversion
Time

T

second (s)second (s)1
Length

L

metre (m)centimetre (cm)
ångström (Å)
0.01
10−10
Mass

M

kilogram (kg)gram (g)0.001
Area

L2

square metre (m2)are (are)100
Acceleration

LT-2

(ms−2)gal (gal)10−2
Electric current

I

ampere (A)international ampere
abampere or biot
statampere
1.000022
10.0
3.335641×10−10
Temperature

\Theta

kelvin (K)
degrees Celsius (°C)
centigrade (°C)K = °C + 273.15
1
Luminous intensity

J

candela (cd)international candle0.982
Amount of substance

N

mole (mol)No legacy unitn/a
Frequency

T-1

hertz (Hz)cycles per second1
Energy

L2MT-2

joule (J)erg (erg)10−7
Power

L2MT-3

watt (W)(erg/s)
horsepower (HP)
Pferdestärke (PS)
10−7
745.7
735.5
Force

LMT-2

newton (N)dyne (dyn)
sthene (sn)
kilopond (kp)
10−5
103
9.80665
Pressure

L-1MT-2

pascal (Pa)barye (Ba)
pieze (pz)
atmosphere (at)
0.1
103
1.0197×10−5
Electric charge

IT

coulomb (C)abcoulomb
statcoulomb or franklin
10
3.335641×10−10
Potential difference

L2MT-3I-1

volt (V)international volt
abvolt
statvolt
1.00034
10−8
2.997925×102
Capacitance

L-2M-1T4I2

109
1.112650×10−12
Inductance

L2MT-2I-2

henry (H)abhenry
stathenry
10−9
8.987552×1011
Electric resistance

L2MT-3I-2

ohm (Ω)international ohm
abohm
statohm
1.00049
10−9
8.987552×1011
Electric conductance

L-2M-1T3I2

siemens (S)mho (℧)
abmho
statmho
0.99951
109
1.112650×10−12
Magnetic flux

L2MT-2I-1

weber (Wb)maxwell (Mx)10−8
Magnetic flux density

MT-2I-1

tesla (T)gauss (G)1×10−4
Magnetic field strength

IL-1

(A/m)oersted (Oe)103/4π = 79.57747
Dynamic viscosity

ML-1T-1

(Pa·s)poise (P)0.1
Kinematic viscosity

L2T-1

(m2s−1)stokes (St)10−4
Luminous flux

J

lumen (lm)stilb (sb)104
Illuminance

JL-2

lux (lx)phot (ph)104

T-1

becquerel (Bq)curie (Ci)3.70×1010

L2T-2

gray (Gy)roentgen (R)
2.58
0.01

L2T-2

sievertroentgen equivalent man (rem)0.01
Catalytic activity

NT-1

katal (kat)No legacy unitn/a

The SI brouchure also catalogues certain non-SI units that are widely used with the SI in matters of everyday life or units that are exactly defined values in terms of SI units and are used in particular circumstances to satisfy the needs of commercial, legal, or specialised scientific interests. These units include:

QuantityDimensionUnit and symbolEquivalence
Mass

M

tonne (t)1000 kg
Area

L2

hectare (ha)0.01 km2
104 m2
Volume

L3

litre (L or l)0.001 m3
Time

T

minute (min)
hour (h)
day (d)
60 s
3600 s
86400 s
Pressure

L-1MT-2

bar100 kPa
Plane angle

none

degree (°)
minute (ʹ)
second (″)

## References

• [Alder] Book: Alder, Ken. The Measure of all Things - The Seven-Year-Odyssey that Transformed the World. 2002. Abacus. London. 0 349 11507 9.
• [SI Brochure]

## Notes and References

1. Web site: The United States and the metric system. 2011-11-02. The United States is now the only industrialized country in the world that does not use the metric system as its predominant system of measurement.. NIST.
2. Alder - Prologue, p 1
3. SI Brochure - §3.1 SI prefixes - p 103
4. Alder; page 92
5. Web site: Online Translation- Offering hundreds of dictionaries and translation in more than 800 language pairs. Babylon. 2011-01-24.
6. Book: International vocabulary of metrology — Basic and general concepts and associated terms (VIM). Joint Committee for Guides in Metrology/International Bureau for Weights and Measures. 2008. 9. 2011-03-05.
7. Alder pg 361-366
8. Web site: Metric usage and metrication in other countries. U.S. Metric Association. 22 July 2009. 2011-09-09.
9. Book: Alder, Ken. The Measure of all Things - The Seven-Year Odyssey that Transformed the World. 2002. Abacus. London. 360. 0 349 11507 9.
10. Web site: HK Weights and Measures Ordinance. 2011-09-20.
11. Web site: Online Translation- Offering hundreds of dictionaries and translation in more than 800 language pairs. Babylon. 2011-02-05.
12. Web site: Weights and Measures Act 1985 (c. 72). The UK Statute Law Database. Office of Public Sector Information. §92.. 2011-01-26.
13. Web site: NTSB Order No. EA-4510. 1996. Washington, D.C.. National Transportation Safety Board. 3 August 2008.