International System of Units

The International System of Units is the standard modern form of the metric system. The name of this system can be shortened or abbreviated to SI, from the French name Système International d'unités.

The International System of Units is a system of measurement based on 7 base units: the metre (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (quantity), and candela (brightness). These base units can be used in combination with each other. This creates SI derived units, which can be used to describe other quantities, such as volume, energy, pressure, and velocity.

The system is used almost globally. Only Myanmar, Liberia, and the United States do not use SI as their official system of measurement.^[1] In these countries, though, SI is commonly used in science and medicine.

History and use

The metric system was created in France after the French Revolution in 1789. The original system only had two standard units, the kilogram and the metre. The metric system became popular amongst scientists.

In the 1860s, James Clerk Maxwell and William Thomson (later known as Lord Kelvin) suggested a system with three base units – length, mass, and time. Other units would be derived from those three base units. Later, this suggestion would be used to create the centimetre-gram-second system of units (CGS), which used the centimetre as the base unit for length, the gram as the base unit for mass, and the second as the base unit for time. It also added the dyne as the base unit for force and the erg as the base unit for energy.

As scientists studied electricity and magnetism, they realized other base units were needed to describe these subjects. By the middle of the 20th century, many different versions of the metric system were being used. This was very confusing.

In 1954, the 9th General Conference on Weights and Measures (CGPM) created the first version of the International System of Units. The six base units that they used were the metre, kilogram, second, ampere, Kelvin, and candela.^[2] The seventh base unit, the mole, was added in 1971.^[3]

SI is now used almost everywhere in the world, except in the United States, Liberia and Myanmar, where the older imperial units are still widely used. Other countries, most of them historically related to the British Empire, are slowly replacing the old imperial system with the metric system or using both systems at the same time.

Units of measurement

Base units

The SI base units are measurements used by scientists and other people around the world. All the other units can be written by combining these seven base units in different ways. These other units are called "derived units".

SI base units^[4]^: 23^[5]^[6]
Unit name	Unit symbol	Dimension symbol	Quantity name	Definition^{[n 1]}
second	s	T	time	Prior: ${\frac {1}{86400}}$ of a day of 24 hours of 60 minutes of 60 seconds Interim (1956): ${\frac {1}{31556925.9747}}$ of the tropical year for 1900 January 0 at 12 hours ephemeris time. Current (1967): The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
metre	m	L	length	Prior (1793): ${\frac {1}{10000000}}$ of the meridian through Paris between the North Pole and the Equator.^FG Interim (1960): 1650763.73 wavelengths in a vacuum of the radiation corresponding to the transition between the 2p¹⁰ and 5d⁵ quantum levels of the krypton-86 atom. Current (1983): The distance travelled by light in vacuum in ${\frac {1}{299792458}}$ second.
kilogram ^{[n 2]}	kg	M	mass	Prior (1793): The grave was defined as being the mass (then called weight) of one litre of pure water at its freezing point.^FG Interim (1889): The mass of a small squat cylinder of ~47 cubic centimetres of platinum-iridium alloy kept in the International Bureau of Weights and Measures, Paris, France.^[7] Current (2019): The kilogram is defined by setting the Planck constant h exactly to 6.62607015×10⁻³⁴ J⋅s (J = kg⋅m²⋅s⁻²), given the definitions of the metre and the second.^[8] Then the formula would be 1 kg = ^h⁄_{6.62607015 × 10^-34⋅m²⋅s⁻¹}
ampere	A	I	electric current	Prior (1881): A tenth of the electromagnetic CGS unit of current. The [CGS] electromagnetic unit of current is that current, flowing in an arc 1 cm long of a circle 1 cm in radius, that creates a field of one oersted at the centre.^[9] ^IEC Interim (1946): The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10⁻⁷ newtons per metre of length. Current (2019): The flow of ¹⁄_{1.602176634×10⁻¹⁹} times the elementary charge e per second.
kelvin	K	Θ	thermodynamic temperature	Prior (1743): The centigrade scale is obtained by assigning 0 °C to the freezing point of water and 100 °C to the boiling point of water. Interim (1954): The triple point of water (0.01 °C) defined to be exactly 273.16 K.^{[n 3]} Previous (1967): ${\frac {1}{273.16}}$ of the thermodynamic temperature of the triple point of water. Current (2019): The kelvin is defined by setting the fixed numerical value of the Boltzmann constant k to 1.380649×10⁻²³ J⋅K⁻¹, (J = kg⋅m²⋅s⁻²), given the definition of the kilogram, the metre and the second.
mole	mol	N	amount of substance	Prior (1900): A stoichiometric quantity which is the equivalent mass in grams of Avogadro's number of molecules of a substance.^ICAW Interim (1967): The amount of substance of a system which contains as many elementary entities^{[n 4]} as there are atoms in 0.012 kilogram of carbon-12. Current (2019): The amount of substance of exactly 6.02214076×10²³ elementary entities. This number is the fixed numerical value of the Avogadro constant, N_A, when expressed in the unit mol⁻¹ and is called the Avogadro number.
candela	cd	J	luminous intensity	Prior (1946): The value of the new candle (early name for the candela) is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per square centimetre. Current (1979): The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.4×10¹⁴ hertz and that has a radiant intensity in that direction of ${683}$ watt per steradian. Note: both old and new definitions are approximately the luminous intensity of a whale blubber candle burning modestly bright, in the late 19th century called a "candlepower" or a "candle".
Notes ↑ Interim definitions are given here only when there has been a significant difference in the definition. ↑ Despite the prefix "kilo-", the kilogram is the coherent base unit of mass, and is used in the definitions of derived units. Nonetheless, prefixes for the unit of mass are determined as if the gram were the base unit. ↑ In 1954 the unit of thermodynamic temperature was known as the "degree Kelvin" (symbol °K; "Kelvin" spelt with an upper-case "K"). It was renamed the "kelvin" (symbol "K"; "kelvin" spelt with a lower-case "k") in 1967. ↑ When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. The Prior definitions of the various base units in the above table were made by the following authorities: FG = French Government IEC = International Electrotechnical Commission ICAW = International Committee on Atomic Weights All other definitions result from resolutions by either CGPM or the CIPM and are catalogued in the SI Brochure.

Derived units

Derived units are created by combining the base units. The base units can be divided, multiplied, or raised to powers. Some derived units have special names. Usually these were created to make calculations simpler.

Named units derived from SI base units
Name	Symbol	Quantity	Definition other units	Definition SI base units
radian	rad	plane angle		−
steradian	sr	solid angle		−
hertz	Hz	frequency		s⁻¹
newton	N	force, weight		m⋅kg⋅s⁻²
pascal	Pa	pressure, stress	N/m²	m⁻¹⋅kg⋅s⁻²
joule	J	energy, work, heat	N⋅m	m²⋅kg⋅s⁻²
watt	W	power, radiant flux	J/s	m²⋅kg⋅s⁻³
coulomb	C	electric charge		s⋅A
volt	V	voltage, electrical potential difference, electromotive force	W/A J/C	m²⋅kg⋅s⁻³⋅A⁻¹
farad	F	electrical capacitance	C/V	m⁻²⋅kg⁻¹⋅s⁴⋅A²
ohm	Ω	electrical resistance, impedance, reactance	V/A	m²⋅kg⋅s⁻³⋅A⁻²
siemens	S	electrical conductance	1/Ω	m⁻²⋅kg⁻¹⋅s³⋅A²
weber	Wb	magnetic flux	J/A	m²⋅kg⋅s⁻²⋅A⁻¹
tesla	T	magnetic field strength	Wb/m² V⋅s/m² N/(A⋅m)	kg⋅s⁻²⋅A⁻¹
henry	H	inductance	Wb/A V⋅s/A	m²⋅kg⋅s⁻²⋅A⁻²
degree Celsius	°C	temperature relative to 273.15 K	T_K − 273.15	K
lumen	lm	luminous flux	cd⋅sr	cd
lux	lx	illuminance	lm/m²	m⁻²⋅cd
becquerel	Bq	radioactivity (decays per unit time)		s⁻¹
gray	Gy	absorbed dose (of ionizing radiation)	J/kg	m²⋅s⁻²
sievert	Sv	equivalent dose (of ionizing radiation)	J/kg	m²⋅s⁻²
katal	kat	catalytic activity		s⁻¹⋅mol

Prefixes

Very large or very small measurements can be written using prefixes. Prefixes are added to the beginning of the unit to make a new unit. For example, the prefix kilo- means "1000" times the original unit and the prefix milli- means "0.001" times the original unit. So one kilometre is 1000 metres and one milligram is a 1000th of a gram.

Prefix		Base 1000	Base 10	Decimal	English word		Adoption^{[nb 1]}
Name	Symbol	Base 1000	Base 10	Decimal	Short scale	Long scale	Adoption^{[nb 1]}
quetta	Q	1000¹⁰	10³⁰	1000000000000000000000000000000	nonillion	quintillion	2022
ronna	R	1000⁹	10²⁷	1000000000000000000000000000	octillion	quadrilliard	2022
yotta	Y	1000⁸	10²⁴	1000000000000000000000000	septillion	quadrillion	1991
zetta	Z	1000⁷	10²¹	1000000000000000000000	sextillion	trilliard	1991
exa	E	1000⁶	10¹⁸	1000000000000000000	quintillion	trillion	1975
peta	P	1000⁵	10¹⁵	1000000000000000	quadrillion	billiard	1975
tera	T	1000⁴	10¹²	1000000000000	trillion	billion	1960
giga	G	1000³	10⁹	1000000000	billion	milliard	1960
mega	M	1000²	10⁶	1000000	million		1873
kilo	k	1000¹	10³	1000	thousand		1795
hecto	h	1000^2/3	10²	100	hundred		1795
deca	da	1000^1/3	10¹	10	ten		1795
		1000⁰	10⁰	1	one		–
deci	d	1000^−1/3	10⁻¹	0.1	tenth		1795
centi	c	1000^−2/3	10⁻²	0.01	hundredth		1795
milli	m	1000⁻¹	10⁻³	0.001	thousandth		1795
micro	μ	1000⁻²	10⁻⁶	0.000001	millionth		1873
nano	n	1000⁻³	10⁻⁹	0.000000001	billionth	milliardth	1960
pico	p	1000⁻⁴	10⁻¹²	0.000000000001	trillionth	billionth	1960
femto	f	1000⁻⁵	10⁻¹⁵	0.000000000000001	quadrillionth	billiardth	1964
atto	a	1000⁻⁶	10⁻¹⁸	0.000000000000000001	quintillionth	trillionth	1964
zepto	z	1000⁻⁷	10⁻²¹	0.000000000000000000001	sextillionth	trilliardth	1991
yocto	y	1000⁻⁸	10⁻²⁴	0.000000000000000000000001	septillionth	quadrillionth	1991
ronto	r	1000⁻⁹	10⁻²⁷	0.000000000000000000000000001	octillionth	quadrilliardth	2022
quecto	q	1000⁻¹⁰	10⁻³⁰	0.000000000000000000000000000001	nonillionth	quintillionth	2022

↑ Prefixes adopted before 1960 already existed before SI. 1873 was the introduction of the CGS system.

References

↑ "Appendix G: Weights and Measures". The World Facebook. Central Intelligence Agency. 2013. Archived from the original on 6 April 2011. Retrieved 5 April 2013.
↑ International Bureau of Weights and Measures (1954), Système pratique d'unités de mesure (Practical system of units). 9^th session, Resolution 6.
↑ International Bureau of Weights and Measures (1971), Unité SI de quantité de matière (SI unit of amount of substance). 14^th session, Resolution 3.
↑ Taylor, Barry N.; Thompson, Ambler (2008). The International System of Units (SI) (Special publication 330) (PDF). Gaithersburg, MD: National Institute of Standards and Technology. Archived from the original (PDF) on 2017-11-20. Retrieved 2017-08-04.
↑ Quantities Units and Symbols in Physical Chemistry, IUPAC
↑ Page, Chester Hall; Vigoureux, Paul (1975-05-20). Page, Chester H.; Vigoureux, Paul (eds.). The International Bureau of Weights and Measures 1875–1975: NBS Special Publication 420. Washington, D.C.: National Bureau of Standards. pp. 238–244.
↑ Secula, Erik M. (7 October 2014). "Redefining the Kilogram, The Past". Nist.gov. Retrieved 22 August 2017.
↑ Materese, Robin (2018-11-16). "Historic Vote Ties Kilogram and Other Units to Natural Constants". NIST. Retrieved 2018-11-16.
↑ McKenzie, A. E. E. (1961). Magnetism and Electricity. Cambridge University Press. p. 322.

[7] Interim definitions are given here only when there has been a significant difference in the definition.

[8] Despite the prefix "kilo-", the kilogram is the coherent base unit of mass, and is used in the definitions of derived units. Nonetheless, prefixes for the unit of mass are determined as if the gram were the base unit.

[12] In 1954 the unit of thermodynamic temperature was known as the "degree Kelvin" (symbol °K; "Kelvin" spelt with an upper-case "K"). It was renamed the "kelvin" (symbol "K"; "kelvin" spelt with a lower-case "k") in 1967.

[13] When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

[14] Prefixes adopted before 1960 already existed before SI. 1873 was the introduction of the CGS system.

[ciawf-1] "Appendix G: Weights and Measures". The World Facebook. Central Intelligence Agency. 2013. Archived from the original on 6 April 2011. Retrieved 5 April 2013.

[9cgpm-2] International Bureau of Weights and Measures (1954), Système pratique d'unités de mesure (Practical system of units). 9^th session, Resolution 6.

[14cgpm-3] International Bureau of Weights and Measures (1971), Unité SI de quantité de matière (SI unit of amount of substance). 14^th session, Resolution 3.

[NIST330-4] Taylor, Barry N.; Thompson, Ambler (2008). The International System of Units (SI) (Special publication 330) (PDF). Gaithersburg, MD: National Institute of Standards and Technology. Archived from the original (PDF) on 2017-11-20. Retrieved 2017-08-04.

[BIPM1975-5] Quantities Units and Symbols in Physical Chemistry, IUPAC

[6] Page, Chester Hall; Vigoureux, Paul (1975-05-20). Page, Chester H.; Vigoureux, Paul (eds.). The International Bureau of Weights and Measures 1875–1975: NBS Special Publication 420. Washington, D.C.: National Bureau of Standards. pp. 238–244.

[9] Secula, Erik M. (7 October 2014). "Redefining the Kilogram, The Past". Nist.gov. Retrieved 22 August 2017.

[NIST_2018-11-10] Materese, Robin (2018-11-16). "Historic Vote Ties Kilogram and Other Units to Natural Constants". NIST. Retrieved 2018-11-16.

[11] McKenzie, A. E. E. (1961). Magnetism and Electricity. Cambridge University Press. p. 322.

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