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International System of Units

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The International System of Units (French Système International or SI for short) is the agreed-upon system for measurement as adopted by periodic meetings of the forty-six-member, Conférence Générale des Poids et Mesures (General Conference on Weights and Measures) or abbreviated as CGPM. It was developed in 1960 from the meter-kilogram-second (mks) system and replaces the centimeter-gram-second (cgs) system.

Definitions have been subject to change through the years and generally depend on assumptions that the CGPM makes about what is permanent and what is not.

The Base Units

SI depends on seven base units of measurement from which all other units derive. They are:


The second (abbreviated s or sec) is the unit of time, defined as
the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom (13th CGPM, 1967).

Historically the second was without definition, until 1820, when it was defined as 1/86,400 of the mean solar day. In 1956 the CGPM adopted the ephemeris second definition of 1/31 556 925.9747 of the tropical year 1900. The present definition dates from 1963.


The meter (abbreviated m) is the unit of length. Originally (see Metric system) it had a definition depending on the dimensions of the earth. It later had a definition dependent on a particular type of radiation. Today its definition depends upon the second and on the speed of light in a vacuum--which the CGPM now assumes to be constant. Thus a meter is 1⁄299,792,458th of a light-second. (Therefore the speed of light is exactly 299,792,458 meters per second.)


The kilogram (abbreviated kg) (and not the Metric gram) is the unit of mass. It is defined as an amount of mass equal to that of the standard prototype kilogram kept at the International Bureau of Weights and Measures at Sèvres, France. It is the only unit of measure based on a physical artifact. This is the same artifact that has provided the definition of grams and kilograms for over a century. It is also the only base SI unit to retain its decimal prefix, kilo-, which comes from the Greek word for "thousand."


The ampere (abbreviated A) is the unit of electric current. (Strangely, electric charge is not the base quantity.) The definition is as follows:

One 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 a vacuum, would produce between these conductors a force equal to 2 × 10−7 newtons per meter of length.

For the definition of a newton, see below under "derived units."


The kelvin (abbreviated K, named for Lord Kelvin) is the unit of temperature, and specifically of absolute temperature. It is 1/273.16 of the absolute temperature of the triple point of water. The size of the kelvin is the same as the size of the Celsius degree, and thus to convert from degrees Celsius to kelvins, one adds 273.15. (The zero of the Celsius scale, which is the melting point of water ice under standard atmospheric pressure, happens to be 273.15 kelvins.)


The mole (abbreviated mol) is the unit of amount of substance. Its definition depends on that of the kilogram. It is that mass of any substance having as many elementary entities of that substance as are to be counted in 0.012 kilogram of carbon-12. An elementary entity is either an atom or a molecule--but for an ionic compound, the number of elementary entities is the total number of cations and anions required to make the compound electrically neutral.

Effectively, one mole of any substance is its formula mass in grams.


The candela (abbreviated cd) is the unit of luminous intensity. Its definition is
the luminous intensity, in a given direction, of a [light] source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1⁄683 watt per steradian.

The term hertz means "vibrations, transitions, or other events per second." For the definitions of the terms watt and steradian, see below. Light having the stated frequency is generally perceived as red.

Supplementary Units

SI originally had the two units of plane angle and solid angle. CGPM decided not to retain them in the SI definition. However, their definitions, deriving as they do from geometry, are still valid.


The radian (abbreviated rad) is the plane angle unit. It is the measure of a central angle (one having its origin as the center of a circle) that subtends an arc of the circle having a length equal to that of the radius. By convention, the circumference of the unit circle (a circle having a radius of one) is 2π, and therefore the maximum "major angle" of any circle is 2π radians.


The steradian (abbreviated sr) is the solid angle unit. A solid angle is actually one nappe of a right circular conical surface. One steradian is the measure of a solid angle that subtends a portion of the surface of a sphere having an area equal to that of a square having sides equal in length to the radius. By convention, the surface area of a sphere is 4πr2, where r is the length of the radius, and thus the maximum "major solid angle" of any sphere is 4π steradians.

Derived Units

SI has multiple derived units that measure quantities in several areas of measurement and inquiry. The following is a comprehensive list, grouped by category.



The newton (abbreviated N, named for Sir Isaac Newton) is the SI unit of force. One newton is that amount of force required to accelerate a one-kilogram mass one meter per second per second. To calculate, multiply mass by acceleration.


The pascal (abbreviated Pa) is that amount of pressure that exerts a force of one newton in every square meter of area.

Work and Power


The joule (abbreviated J, named for James Joule) is that amount of energy required to do the work of exerting a force of one newton over a distance of one meter. To calculate, multiply force by distance.


The watt (abbreviated W, named for James Watt) is the power required to do one Joule of work in one second. To calculate, divide work by time.

Electricity and Magnetism


The coulomb (abbreviated coul, for C. A. Coulomb) is that amount of electric charge that passes through a conductor in one second at a current of one ampere. To calculate, multiply current by time.


The volt (abbreviated V) is the electric potential difference between two conductors having a current flow of one ampere from one to another, and dissipating one watt of power. Most people find the phrase "electric potential" hard to understand and the alternative "electromotive force" to be hard to pronounce. They therefore use the word "voltage" for this quantity. To calculate, divide power by current--or divide work (or energy) by electric charge.


The ohm (abbreviated Ω, for Georg Simon Ohm) is that amount of electric resistance that requires an electric potential difference of one volt to push a current of one ampere through it. To calculate, divide electrical potential by current.


The siemens (abbreviated S, for Werner von Siemens) is the unit of electric conductance, which is merely the reciprocal of resistance. In essence, the siemens is that level of conductance required to allow a current of one ampere to flow through a load after an electric potential of one volt is applied. To calculate it, divide current by electric potential or "voltage," rather than dividing voltage by current.


The farad (abbreviated F, for Michael Faraday) is that amount of capacitance that exists in a capacitor (essentially a pair or collection of metal plates that store charge) if a charge of one coulomb increases the electrical potential by one volt. To calculate, divide charge by electrical potential.


The weber (abbreviated Wb, for W. E. Weber) is
the magnetic flux which, linking a circuit of one turn, would produce in it an electromotive force of 1 volt if it were reduced to zero at a uniform rate in 1 second.
To calculate, multiply electric potential (or electromotive force) by time.


The henry (abbreviated H) is that inductance in a closed loop or coil that produces a magnetic flux of one weber given a current of one ampere. To calculate, divide magnetic flux by current.


The tesla (abbreviated T, for Nicola Tesla) is the magnetic flux density required to produce one weber of magnetic flux in one square meter of surface area. To calculate, divide flux by area.



The lumen (abbreviated lm) is that amount of luminous flux emitted in a solid-angle region of one steradian that produces one candela of intensity. To calculate, multiply luminous intensity by solid angle.


The lux (abbreviated lx) is that illuminance that represents one lumen in one square meter. To calculate, divide luminous flux by area.

Radioactivity, Radiation, Health Physics, and Radiation Safety


The becquerel (abbreviated Bq, for Henri Becquerel) is that amount of activity of a radioactive substance represented by one decaying atom per second.


The curie (abbreviated Ci, for Marie Curie) is obsolete today. Its original definition was "the amount of radioactivity in one gram of radium-226." Madame Curie, of course, is most famous as the discoverer of radium. One curie is equal to 3.7 * 1010 becquerel.

Gray (Unit)

The gray (abbreviated Gy) is that absorbed dose of radiation that imparts one joule of energy to one kilogram of target mass. To calculate, divide imparted energy by mass.


The sievert (abbreviated Sv) is the unit of dose equivalent. It is that dose of any given form of ionizing radiation that would cause a human being or an animal as much injury as would a one-gray dose of X rays.

Related Reference

  • SI
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