# International System of Units (SI)

Source: NIST
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## Introduction

All systems of weights and measures, metric and non-metric, are linked through a network of international agreements supporting the International System of Units. The International System is called the SI, using the first two initials of its French name Système International d'Unités. The key agreement is the Treaty of the Meter (Convention du Mètre), signed in Paris on May 20, 1875. Forty-eight nations have now signed this treaty, including all the major industrialized countries. The United States is a charter member of this metric club, having signed the original document back in 1875.

The SI is maintained by a small agency in Paris, the International Bureau of Weights and Measures (BIPM, for Bureau International des Poids et Mesures), and it is updated every few years by an international conference, the General Conference on Weights and Measures (CGPM, for Conférence Générale des Poids et Mesures), attended by representatives of all the industrial countries and international scientific and engineering organizations.

## Some useful definitions

A quantity in the general sense is a property ascribed to phenomena, bodies, or substances that can be quantified for, or assigned to, a particular phenomenon, body, or substance. Examples are mass and electric charge.

A quantity in the particular sense is a quantifiable or assignable property ascribed to a particular phenomenon, body, or substance. Examples are the mass of the moon and the electric charge of the proton.

A physical quantity is a quantity that can be used in the mathematical equations of science and technology.

A unit is a particular physical quantity, defined and adopted by convention, with which other particular quantities of the same kind are compared to express their value.

The value of a physical quantity is the quantitative expression of a particular physical quantity as the product of a number and a unit, the number being its numerical value. Thus, the numerical value of a particular physical quantity depends on the unit in which it is expressed.

For example, the value of the height (hW) of the Washington Monument is hW = 169 m = 555 ft. Here hW is the physical quantity, its value expressed in the unit "meter," unit symbol m, is 169 m, and its numerical value when expressed in meters is 169. However, the value of hW expressed in the unit "foot," symbol ft, is 555 ft, and its numerical value when expressed in feet is 555.

## Base Units of the International System (SI)

The General Conference on Weights and Measures has replaced all but one of the definitions of its base (fundamental) units based on physical objects (such as standard meter sticks or standard kilogram bars) with physical descriptions of the units based on stable properties of the Universe.

Following are the official definitions of the seven base units, as given by BIPM.

 Unit of length meter The meter is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second. Unit of mass kilogram The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. Unit of time second The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. Unit of electric current ampere The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length. Unit of thermodynamic temperature kelvin The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. Unit of amount of substance mole 1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol."2. 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. Unit of luminous intensity candela The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

## SI derived units

Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units. Examples of such SI derived units are given in Table 2, where it should be noted that the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted.

SI derived units with special names and symbols
Derived quantity Name Symbol Expression in terms
of other SI units
Expression in terms
of SI base units
solid angle steradian(a) sr (c) - m2·m-2 = 1 (b)
frequency hertz Hz - s-1
force newton N - m·kg·s-2
pressure, stress pascal Pa N/m2 m-1·kg·s-2
energy, work, quantity of heat joule J N·m m2·kg·s-2
power, radiant flux watt W J/s m2·kg·s-3
electric charge, quantity of electricity coulomb C - s·A
electric potential difference, electromotive force volt V W/A m2·kg·s-3·A-1
electric resistance ohm ? V/A m2·kg·s-3·A-2
electric conductance siemens S A/V m-2·kg-1·s3·A2
magnetic flux weber Wb V·s m2·kg·s-2·A-1
magnetic flux density tesla T Wb/m2 kg·s-2·A-1
inductance henry H Wb/A m2·kg·s-2·A-2
Celsius temperature degree Celsius °C - K
luminous flux lumen lm cd·sr (c) m2·m-2·cd = cd
illuminance lux lx lm/m2 m2·m-4·cd = m-2·cd
activity (of a radionuclide) becquerel Bq - s-1
absorbed dose, specific energy (imparted), kerma gray Gy J/kg m2·s-2
dose equivalent (d) sievert Sv J/kg m2·s-2
catalytic activity katal kat - s-1·mol
(a) The radian and steradian may be used advantageously in expressions for derived units to distinguish between quantities of a different nature but of the same dimension.
(b) In practice, the symbols rad and sr are used where appropriate, but the derived unit "1" is generally omitted.
(c) In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units.
(d) Other quantities expressed in sieverts are ambient dose equivalent, directional dose equivalent, personal dose equivalent, and organ equivalent dose.

## History

In 1832, Johann Carl Friedrich Gauss strongly promoted the application of this Metric System, together with the second defined in astronomy, as a coherent system of units for the physical sciences. Gauss was the first to make absolute measurements of the Earth’s magnetic force in terms of a decimal system based on the three mechanical units millimeter, gram and second for, respectively, the quantities length, mass and time. In later years, Gauss and Wilhelm Eduard Weber extended these measurements to include electrical phenomena.

These applications in the field of electricity and magnetism were further developed in the 1860s under the active leadership of James Clerk Maxwell and Joseph John Thomson through the British Association for the Advancement of Science (BAAS). They formulated the requirement for a coherent system of units with base units and derived units. In 1874 the BAAS introduced the CGS system, a three-dimensional coherent unit system based on the three mechanical units centimeter, gram and second, using prefixes ranging from micro to mega to express decimal submultiples and multiples. The following development of physics as an experimental science was largely based on this system.

The sizes of the coherent CGS units in the fields of electricity and magnetism, proved to be inconvenient so, in the 1880s, the BAAS and the International Electrical Congress, predecessor of the International Electrotechnical Commission (IEC), approved a mutually coherent set of practical units. Among them were the ohm for electrical resistance, the volt for electromotive force, and the ampere for electric current.

After the establishment of the Meter Convention on May 20, 1875 the CIPM concentrated on the construction of new prototypes taking the meter and kilogram as the base units of length and mass. In 1889 the 1st CGPM sanctioned the international prototypes for the meter and the kilogram. Together with the astronomical second as unit of time, these units constituted a three-dimensional mechanical unit system similar to the CGS system, but with the base units meter, kilogram and second.

In 1901 Giovanni Giorgi showed that it is possible to combine the mechanical units of this meter–kilogram–second system with the practical electric units to form a single coherent four-dimensional system by adding to the three base units, a fourth base unit of an electrical nature, such as the ampere or the ohm, and rewriting the equations occurring in electromagnetism in the so-called rationalized form. Giorgi’s proposal opened the path to a number of new developments.

After the revision of the Meter Convention by the 6th CGPM in 1921, which extended the scope and responsibilities of the BIPM to other fields in physics, and the subsequent creation of the CCE (now CCEM) by the 7th CGPM in 1927, the Giorgi proposal was thoroughly discussed by the IEC and the IUPAP and other international organizations. This led the CCE to recommend, in 1939, the adoption of a four-dimensional system based on the meter, kilogram, second and ampere, a proposal approved by the ClPM in 1946.

Following an international inquiry by the BIPM, which began in 1948, the 10th CGPM, in 1954, approved the introduction of the ampere, the kelvin and the candela as base units, respectively, for electric current, thermodynamic temperature and luminous intensity. The name International System of Units (SI) was given to the system by the 11th CGPM in 1960. At the 14th CGPM in 1971 the current version of the SI was completed by adding the mole as base unit for amount of substance, bringing the total number of base units to seven.

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