SI – Introduction
The International System of Units (S.I.) was introduced in 1960 by the XI General Conference of Weights and Measures and modified by the following Conferences.The S.I. distinguishes by convention two kinds of quantities:
- base quantities, for which the measurement units are assumed as dimensionally independent;
- derived quantities, for which the measurement units are defined through analytical relations that connect them to the base units.
- complete: all considered physical quantities can be derived from the base quantities through analytical relations;
- coherent: the analytic relations that connect the units of the derived quantities don’t contain factors different from one;
- decimal (with the exception of the measurement of time interval): multiples and submultiples of the measurements units are powers of 10.
- the writing rules of names and symbols of the measurement units
- the use of multiplicative prefixes according to multiples of 1000.
Research Agencies and Normative Bodies
The B.I.P.M. operates under the supervision of the International Committee of Weights and Measures (C.I.P.M.), which has 18 members coming from different countries and which meets every year.
The C.I.P.M. comes under the authority of the General Conference of Weights and Measures (C.G.P.M.), which is attended by the delegates of all countries members of the Meter Convention (51 countries as of December 2005). The C.G.P.M. normally meets every four years ed emits resolutions about the S.I. of international relevance. The official language is French.
The C.I.P.M. is assisted by 9 international Consultive Committees, which are specialized in the different fields concerning metrology.
An international body important for the unification of scientific and technological rules and procedures, including rules concerning the S.I. is the International Organisation for Standardisation (I.S.O.).
In U.S.A. a similar task is performed by the National Institute of Standards and Technology (N.I.S.T.), known in the past as National Bureau of Standards (N.B.S.).
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Table of Contents |
SI – History
| 1790 | First attempt of the french government to establish a system of measurement units. |
| 1795 | The Decimal Metric System is
introduced by the french government. The meter is first defined as the fraction 1/107 of the arc of terrestrial meridian from the Pole to the Equator. This definition is modified in 1799. |
| 1799 | The natural standard of the meter (1/107 of
the arc of terrestrial meridian from the Pole to the Equator) is
substituted by an artificial standard made up by a platinum bar (legal
meter of Fortin). The standard is substituted in 1889. The platinum standard of the kilogram is built up. |
| 1832 | Gauss promotes the Metric System and adopts the second astronomically defined for the measurement of time. |
| 1874 | The British Association for the Advancement of Science (BAAS) introduces the c.g.s. system, a coherent system based on the three mechanical units centimeter, gram, second. |
| 1875 | The Meter Convention is
signed in Paris by the representatives of 17 countries. The Bureau International des Poids et Mesures is created. |
| 1880 | The British Association for the Advancement of Science (BAAS) introduces a coherent set practical units for the electromagnetism, including ohm, volt and ampere. |
| 1889 | The 1st C.G.P.M. introduces the new standards in
platinum-iridium of the meter and the kilogram. The three mechanical
units meter, kilogram and second form the M.K.S
system. The meter standard is substituted in 1960. |
| 1901 | Giovanni Giorgi demonstrates that it is possible to combine the three mechanical units of the M.K.S. system with the practical units of electromagnetism, so as to form a coherent system with 4 base units: three mechnical and one electromagnetic (Giorgi System). |
| 1948 | The 9th C.G.P.M. defines the ampere with reference to the law of electrodynamical action between two parallel conductors. |
| 1954 | The 10st C.G.P.M. introduces the kelvin and the candela. |
| 1960 | The artificial standard of the meter (platinum-iridium
bar) is substituted by a natural standard, the optical meter,
defined as a multiple of the wavelength of radiation emitted by the
isotope 86 of kripton. The standard is substituted in 1983. |
| 1961 | The 11th C.G.P.M. introduces the International System (S.I.) |
| 1967 | The 13th C.G.P.M. defines the second with
reference to the frequency of radiation emitted by the isotope 133
of cesium (Cesium clock). The kelvin is defined as unit of temperature. |
| 1971 | The 14th C.G.P.M. defines the mole as the unit of the amount of substance. |
| 1979 | The 16th C.G.P.M. re-defines the candela as the unit of luminous intensity. |
| 1983 | The 17th C.G.P.M. rre-defines the meter as the length of the path traveled by the light in vacuum in a well defined time interval. The velocity of light in vacuum is assumed as an exact constant. |
| 2018 | The 26th C.G.P.M re-defines all the seven base units connecting their values to seven fundamental constants, which are assumed as exact constants. The new definitions are operative since May 2019. |
SI – Base Units
The S.I. is based on 7 base quantities and defines their units:
| Quantity | Unit | Symbol |
|---|---|---|
| Time interval | second | s |
| Length | meter | m |
| Mass | kilogram | kg |
| Temperature | kelvin | K |
| Amount of substance | mole | mol |
| Intensity of electrical current | ampere | A |
| Luminous intensity | candela | cd |
Since May 2019, the seven units are defined in connection with seven defining constants, whose value is assumed as exact:
| Defining constant | Symbol | Valori |
|---|---|---|
| Frequency of the hyperfine 133-cesium transition | ν Cs | 9 192 631 770 s-1 |
| Velocity of light in vacuum | c | 299 792 458 m s-1 |
| Planck constant | h | 6.626 070 15 x 10-34 kg m2 s-1 |
| Boltzmann constant | k | 1.380 649 x 10-23 kg m2 s-2 K-1 |
| Avogadro number | NA | 6.022 140 76 x 1023 mol-1 |
| Elementary electric charge | e | 1.602 176 634 x 10-19 A s |
| Luminous efficacy | Kcd | 683 cd kg-1 m-2 s3 sr |
Definition of the Base Units (since 2019)
| Time interval |
| The second is defined by attributing the exact value 9 192 631 770 s-1 to the frequency νCs of the radiation emitted by the isotope Cesio 133 in the transition between the two hyperfine levels (F=4, M=0) and (F=3, M=0) of the ground state 2S(1/2). |
As a consequence of the transition between two energy levels the atom emits electromagnetic waves of frequency ν=ΔE/h, corresponding to a wavelength λ=c/ν and to a period T=1/ν; h is the Planck constant and c is the velocity of electromagnetic waves in vacuum.
The radiation emitted by 133Cs during the considered transition has a frequency ν ≈ 1010 Hz and a wavelength λ ≈ 3 cm (range of microwaves). The second is thus defined as an integer multiple of the period T=1/ν of the considered radiation emitted by cesium.
The primary standard of the second is a cesium clock. The maximum relative error of a cesium clock is 1×10-12, corresponding to 1 ms in 12 days.
| Length |
| The meter is the length of the path traveled by the light in vacuum in a time interval of 1/299 792 458 seconds. |
| Mass |
| The kilogram is defined by attributing an exact value to the Planck constant h, to the velocity of light in vacuum c and to the frequency νCs of cesium. |
| Temperature |
| The kelvin is defined in relation with the exact value of the Boltzmann constant kB. |
The absolute thermodynamic temperature is defined with reference to the efficiency of an ideal thermodynamic cycle, the Carnot cycle; its measurement is traced back to the measurement of the ratio between two heath quantities or, more generally, to the measurement of the ratio between two values of a quantity which can be directly measured.
| Amount of substance |
| The mole is the amount of substance which contains exactly 6.022 140 76 x 1023 elementary entities. When the mole is used, one has to specify the nature of the elementary entities, which can be atoms, molecules, ions, electrons, other particles or specified groups of particles. |
| Intensity of electric
current |
| The ampere is the current corresponding to the flux of 1 C (electric charge unit) per second, say 1/e = 1/1.602 176 634 x 10-19 elementary charges per second. |
The standards of volt and ohm refer now to to quantum effects, the Josephson effect and the quantum Hall effect, respectively.
| Luminous intensity |
| The candela is the luminous intensity, in a given direction, of a source which emits a monochromaticradiation of frequency 540×1012 Hz and whose energetic intensity in that direction is 1/683 W/sr. |
The luminous intensity is the base quantity of photometry. The luminous intensity corresponds to the energy emitted by a source in the unit time and unit solid angle, weighted by the average sensitivity curve of the human eye.
Origin of the names of units
| second | Abbreviation of latin seconda pars minuta
(second diminished part) The minute is a sexagesimal unit for angles and for time (unit not authorized by S.I.). From latin minutum, past participle of minuere = reduce the size. One distinguishes:
|
| meter | From greek metron, latin metrum =
measure (in general, not specifically of length). The term meter
has various uses in the Middle Age and in the Renaissance. On 26-5-1791 the french Academy of Sciences proposes the term meter for the unit of length, defined as the fraction 1/10000000 of the arc of meridian from the Pole to the Equator. |
| kilogram | From kilo + gram = 1000 grams. The term gram (french gramme) was introduced with the present meaning by the french metric reform at the end of the XVIII century. Its origin is the latin gramma = 1/24 ounce. |
| kelvin | From the name of the enlish physicist William Thomson, lord Kelvin (Belfast 1824 – Neterhall 1907). Professor of Physics at the Glasgow University, president of the Royal Society, he made outstanding contributions to Thermodynamics. |
| ampere | From the name of the french physicist and mathematician André-Marie Ampère (Lion 1775 – Marseille 1836). Professor of Mathematics at the Ecole Polytechnique and of Physics at the Collège de France, he made outstanding contributions to Electrodynamics. |
| candela | From the latin candela = candle. |
SI – Derived Units
The units of derived quantities are obtained from the units of bse quantities by means of simple arithmetic operations. There are no conversion factors different from 1 (the S.I. is coherent).
The derived units with a proper name are listed below, grouped in different separate sets:.- Angles
- Units defined in Mechanics
- Temperature scales
- Units defined in Electromagnetism
- Units defined in Photometry
- Ionizing radiations and Dosimetric units
Angles
| Quantity | Unit | Symbol | Conversion | Notes |
|---|---|---|---|---|
| Plane angle | radian | rad | (1) (2) | |
| Solid angle | steradian | sr | (1) (3) |
- The 11th CGPM (1960) created a separate class of quantities, the supplementary quantities, for the plane and solid angles. The 20th CGPM (1995) suppressed the class of supplementary quantities and inserted the plane and solid angles in the class of derived quantities.
- The radian is the plane angle which subtends, on a circumference centered on its vertex, an arc of length equal to the radius.
- The steradian is the solid angle which subtends, on a sphere centered on its vertex, a part of spherical surface of area equal to the square of the radius.
Units defined in Mechanics
In the S.I. the base quantities of Mechanics are time, length and mass. The corresponding base units are second, meter and kilogram.By combining the base quantities and the corresponding base units through multiplications and divisions one obtains various derived quantities and the corresponding derived units. For example:
- The volume is the product of three lengths; its units is the cube meter (m3).
- The velocity is the ratio of length nd time; its unit is the meter per second (m s-1).
- The linear momentum is the product of mass and velocity; its unit is the kilogram times meter per second (kg m s-1).
| Quantity | Unit | Symbol | Conversion | Notes |
|---|---|---|---|---|
| Frequency | hertz | Hz | 1 Hz = 1 s-1 | 1, 2 |
| Force | newton | N | 1 N = 1 kg m s-2 | 3 |
| Pressure | pascal | Pa | 1 Pa = 1 N m-2 | 4, 5 |
| Work, energy, heat quantity | joule | J | 1 J = 1 N m | 6, 7 |
| Power | watt | W | 1 W = 1 J s-1 | 8 |
- The frequency ν of a periodic phenomenon is the inverse of
its period T: ν=1/T.
A given quantity G depends periodically on time, with period T, if, for whichever instant t, one has G(t)=G(t+T).
The frequency measures the number of repetition of a periodic phenomenon in one second. - Sinusoidal periodic quantities are analytically described by expressions like G(t)=A sin(ω t), where ω is the angular frequency, and is measured in rad s-1. The relation between angular frequency ω and frequency ν is: ω=2 π ν.
- The force of 1 N is the force which impresses to the mass of 1 kg the acceleration of 1 m s-2.
- The pressure of 1 Pa è is the pressure exerted on a surface of 1 m2 by the force of 1 N perpendicular to the surface.
- The pascal is a small unit for a large number of practical needs. It is thus customary to use a larger unit, the bar: 1 bar = 105 Pa. The bar is a non-S.I. unit accepted for use. The pressure of 1 bar is a good approximation to the atmospheric pressure (or better, to the standard atmospheric pressureThe101325 Pa = 1.01325 bar).
- The work of 1 J è is the forw of the force of 1 N times a displacement of 1 m in the direction of the force.
- The experiments of J. Joule in the middle of the XIX century demonstrated the equivalence of heat and work. Heat and work are different forms by which two physical systems can exchange energy. The joule is thus a unit also for the heat amounts. The old unit calorie (in its different definitions) is not admitted by S.I. and shouldn’t be used anymore.
- The power of 1 W corresponds to the work of 1 J performed in the time interval of 1 s.
There exists different physical quantities which share the same units; for example:
a) the mechanical work, product of a force times a displacement parallel to the force
b) the torque (moment of a force), product of a force times a distance perpendicular to the forceTemperature scales
Temperature is a base quantity of
S.I. Its unit is the kelvin.
In practical use the empirical scale Celsius is largely employed. The Celsius
degree has been thus assumed as derived S.I. unit.
The Celsius scale is defined so that the values 0 and 100 correspond to
the fusion and ebullition points of water at atmospheric pressure,
respectively.
The Celsius scale exactly corresponds to the kelvin scale to within ad
additive term of 273.15.
Both Kelvin and Celsius scales are centigrade scales, since the
interval between the fusion and ebullition points of water is divided into
100 equal parts.
| Quantity | Unit | Symbol | Conversion |
| Celsius temperature | Celsius degree | °C | T(°C) = T(K) – 273.15 |
Temperature scales different from the Kelvin and Celsius ones have been
used in the past; some of them are still in use in some country. The
following table allows a comparison between different scales.
The Kelvin and Rankine scales are absolute scales.
The Rankine and Réaumur scales are no more used.
| |
|
Absolute zero | Water fusion (at 1 bar) |
Water ebullition (at 1 bar) |
| Centigrade scales | Celsius | -273.15 | 0 | 100 |
| Kelvin | 0 | 273.15 | 373.15 | |
| English scales | Fahrenheit | -459.67 | 32 | 212 |
| Rankine | 0 | 491.67 | 671.67 | |
| Other scales | Réaumur | -218.52 | 0 | 80 |
- The Fahrenheit scale, still in use in anglo-saxon countries, was introduced in fu introdotta nel 1724 by the physicist Gabriel Fahrenheit (Dantzig 1686 – the Hague 1736). Born in Poland, Fahrenheit worked in U.K. and in Holland; in 1714 he built the first mercury thermometer.
- The Réaumur scale, today out of use, was introduced in 1732 by the French scientist René-Antoine Ferchault de Réaumur (1683-1757). Physicist, naturalist, technologist, Réaumur invented the alcohol thermometer around 1730.
- The Celsius scale was introduced in 1742 by the Swedish physicist and astronomer e Anders Celsius (1701-1744).
- The Kelvin absolute scale was introduced in 1847 by the British physicist of Scottish origin William Thomson, Lord Kelvin, author of outstanding contributions to Thermodynamics.
- The Rankine absolute scale, today out of use, was introduced around 1860 by William John Macquorn Rankine (1820-1872), fScottish physicist and engineer.
Units defined in Elettromagnetism
| Quantity | Unit | Symbol | Conversion | Notes |
| Electric charge | coulomb | C | 1 | |
| Difference of electric potential |
volt | V | 2 | |
| Electric capacity | farad | F | F = 1 C V -1 | 3 |
| Electric resistance | ohm | Ω | 1 Ω = 1 V A -1 | 4 |
| Electric conductance | siemens | S | 1 S = 1 Ω-1 | 5 |
| Flux of magnetic induction | weber | Wb | 1 Wb = 1 V s | 6 |
| Magnetic induction | tesla | T | 1 T = 1 Wb m-2 | 7 |
| Inductance | henry | H | 1 H = 1 Wb A-1 | 8 |
- 1 C is the electric charge transported in 1 s by the current of 1 A.
- 1 V is the difference of electric potential between two points of a conductor which, traversed by a current of 1 A, dissipates the power of 1 W by Joule effect.
- 1 F is thecapacity of a capacitor on which the charge of 1 C induces a potential difference of 1 V.
- 1 Ω is the electric resistance between two points of a conductor to which the potential difference of 1 V is applied when traversed by a current of 1 A.
- 1 S is the conductance of a conductor whose resistance is 1 Ω.
- 1 Wb = 1 V s is the magnetic flux which, traversing a closed circuit, induces an electromotive force of 1 V, when it goes to zero in 1 s at constant speed.
- 1 T is the magnetic induction which, traversing a plane surface of 1 m2, gives rise to a magnetic flux of 1 Wb s.
- 1 H is the inductance of a closed circuit in which the uniform
variation of the current intensity of 1 A/s gives rise to an
electromotive force of 1 V.
Units defined in Photometry
Photometry measures the properties of electromagetic radiation within
the sensitivity range of the human eye (say the properties of visible
light). lThe average human eye is sensitive to electromagnetic radiation with wavelengths included between about 400 nm and about 750 nm (violet and red, respectively). The maximum sensitivity corresponds to a wavelength of about 556 nm.
The luminous flux is the flux of radiated energy (energy per unit time), weighted by the average curve of the eye sensitivity.
Base quantity of Photometry in the S.I. is the luminous intensity, say the luminous flux emitted in the unit solid angle. The unit of luminous intensity is the candela (cd).
There are two derived quantities to which a proper name is assigned by the S.I.:
| Quantity | Unit | Symbol | Conversion |
| Luminous flux | lumen | lm | 1 lm = 1 cd sr |
| Illuminance | lux | lx | 1 lx = 1 lm m-2 |
The following Table presents a comparison between the relevant quantities of Photometry and the corresponding quantities of Radiometry. (Radiometry measures the absolute energetic properties of electromagnetic radiation, Photometry measures the same properties weighted by the sensitivity curve of the human eye).
| RADIOMETRY | PHOTOMETRY | |||
| Quantity | Unit | Quantity | Unit | |
| Radiant energy | J | Quantity of light | lm s | |
| Radiant flux | W | Luminous flux | lm | |
| Energetic intensitya | W sr-1 | Luminous intensity | cd | |
| Radiant intensity | W sr-1 m-2 | Luminance | cd m-2 | |
| Irradiance | W m-2 | Illuminance | lux | |
Ionizing radiations and dosimetric units
By the term ionizing radiations one means electromagnetic radiation
and particles (electrons, neutrons, alpha particles, etc) which can cause a
significant ionization of the traversed material. Ionization is the removal of one or more electrons from an atom or a molecule. In living tissues ionization can damage the DNA and give rise to mutations.
In order to give rise to ionization, the single particles or photons
must posses an energy sufficient to extract an electron from the atome or
the molecule. The amount of energy necessary for ionization differs
according to the atomic or molecular species.
- for gamma rays and X rays the photon energy is larger than 1000 eV; they are strongly ionizing
- the visible light is ionizing only for somef number of molecules
- or microwaves and radiowaves the photon energy is lower than 0.001 eV; they are non ionizing
One considers as ionizing radiations: electromagnetic radiations of small wavelength and high photon energy (ultraviolet, X rays, gamma rays), alpha particles (He nuclei), swift electrons, swift neutrons, cosmic rays, …
Typically, ionizing radiations are produced:- during radioactive decays, both natural and artificial
| Alpha rays |
= He nuclei = 2 protons + 2 neutrons |
| Beta rays |
= Electrons |
| Gamma rays |
= High-energy electromagnetic
radiation |
- in collisions between high-energy particles (in cosmic space, in particle accelerators, in nuclear reactors)
| Cosmic rays |
Protons (87%), alpha rays (12%),
gamma rays, electrons |
| Elementary particles |
|
| Neutrons |
- when swift electrons are accelerated or decelerated (X rays generated in laboratory tubes and in synchrotrons)
| X rays |
Generated in laboratory tubes, for
research activity or for medical uses |
| Ultraviolet, X-rays |
Generated in synchrotron radiation
sources |
Aim of dosimetry sis to measure the effects of ionizing radiation on traversed materials, in particular on biological tissues.
The base quantity of dosimetry is the dose absorbed by a material, say the energy transferred by the ionizing radiation on the unit mass.For radiations produced during radioactive decays, it is important to measure the activity of the radionuclide, say of the atomic nucleus that undergoes the decay.
Dosimetric Units
| Quantity | Unit | Symbol | Conversion | Notes |
| Activity (of a radionuclide) | becquerel | Bq | 1 Bq = 1 s-1 | 1,2 |
| Absorbed dose | gray | Gy | 1 Gy = 1 J kg-1 | 3,4 |
| Equivalent dose | sievert | Sv | 1 Sv = 1 J kg-1 | 5,6 |
- The term ‘radionuclide’ indicates the nucleus of a radioactive atom. The activity of a radioactive sample is the number of decays per unit time. The activity of 1 Bq 1 corresponds thus to one radioactive decay per second.
- A non-S.I. unit of activity is the curie (symbol: Ci), corresponding to the activity og 1 gram of pure Radium. The conversion Curie-becquerel is: 1 Ci = 3.70×1010 Bq.
- The absorbed dose is the energy absorbed from radiation by the unit mass. The unit gray corresponds to the unit energy (1 J) ddivided by the unit mass (kg).
- In the c.g.s. system (centimeter-gram-second) the unit of absorbed dose was the rad (acronym of radiation absorbed dose). The conversion rad-gray is: 1 rad = 0.01 Gy.
- The equivalent dose is the absorbed dose multiplied by a weighing factor WR that takes into account the biological effectiveness (RBE) of the given considered radiation [see Table below]. 1 Sv is the dose absorbed from whichever radiation which has the same biological effectiveness of 1 Gy of X rays.
- In the c.g.s. system (centimeter-gram-second) the equivalent dose is measured in REM (acronym of roentgen equivalent man ), corresponding to the dose measured in rad moltiplicata by the factor that accounts for the RBE.
| X rays of energy 200 keV | 1 |
| Gamma rays (high energy photons) | 1 |
| Beta rays (electrons) | 1 |
| Protons | 10 |
| Alpha particles (He nuclei) | 10-20 |
| Slow neutrons | 2 |
| Swift neutrons | 10 |
Exposure
The exposure measure the ionization produced by X or gamma rays (high-energy electromagnetic radiation) in air at standard temperature and pressure in terms of the electric charge generated in the unit mass.In S.I. the exposure is measured in C/kg (coulomb per kilogram), with no specific name.
A non-SI unit often used is the roentgen: 1 R corresponds to an exposure to X or gamma rays which produces positive and negative charges corresponding to one unit of electrostatic charge per cm3 of air at standardtemperature and pressure.
Conversion S.I.: 1 R = 2.58×10-4 C/kg.
Origin of the names of the derived units
| becquerel | From the French physicist Antoine Henri Becquerel (1852-1908), who discovered radioactivity (1896). Nobel Prize for Physics in 1903 (together with Pierre and Marie Curie). |
| celsius | From the Swedish physicist and astronomer Anders Celsius (1701-1744), who in 1742 proposed the temperature scale now known as Celsius. |
| coulomb | From the French physicist Charles Augustin de Coulomb (1736-1806), who performed fundamental experiments on the interaction between electric charges and stated the law now known as Coulomb law. |
| farad | From the English chemist and physicist Michael Faraday (1791-1867), author of fundamental studies on electromagnetism and electrochemistry. |
| gray | From the English physicist Louis Harold Gray (1905-1965), who decisively contributed to understanding the absorption of ionizing radiations from matter and biological tissues. |
| henry | From the American physicist Joseph Henry (1797-1878), who discovered the phenomenon of electromagnetic auto-induction. |
| hertz | From the German physicist Heinrich Rudolf Hertz (1857-1894), who experimentally verified the existence of electromagnetic waves (1887), theoretically anticipated by J.K. Maxwell 16 years before. |
| joule | From the English physicist James Prescott Joule (1818-1889), who experimentally studied the thermal effects of electrical current (Joule affect) and measured the mechanical equivalent of the calorie, contributing to the assessment of the First Law of Thermodynamics. |
| lumen | From latin. |
| lux | From latin. |
| newton | From the Enlish scientist Isaac Newton (1643-1727), who stated the laws of dynamics and the law of universal gravitation. Newton contributed also to the development of differential calculus. |
| ohm | From the German physicist Georg Simon Ohm (1789-1854), who discovered the direct proportionality between potential difference and intensity of current in conducting materials (Ohm law). |
| pascal | From the French philosopher and scientist Blaise Pascal (1623-1662), who contributed to define the fluid pressure and to measure the atmospheric pressure. |
| radiante | From talin “radius” = radius. |
| siemens | From the German inventor and industrialist Ernst Werner von Siemens (1816-1892), author of important contributions to electrical engineering and establisher of the Siemens Society. |
| sievert | From the Swedish physician Rolf Maximilian Sievert (1896-1966), who decisively contributed to the study of biological effects of ionizing radiations. |
| steradiante | From ste(reo) + radian. The prefix “stereo”, of greek origin, means three-dimensional. |
| tesla | From Nikola Tesla (1856-1943), physicist and engineer of Serb origin, naturalized U.S. citizen in s1891, author of a number of studies on electromagnetism. |
| volt | From the Italian physicist Alessandro Volta (1745-1827), who invented the first electrical pile. |
| watt | From the English engineeer and inventor James Watt (1736-1819), who performed significant modifications of the vapor engine, obtaining a relevant increase of efficiency. |
| weber | From the German physicist Wilhelm Eduard Weber (1804-1891), inventor, with C.F. Gauss, of the first electromagnetic telegraph. |
SI – Prefixes
The S.I. codifies the use of multiplication prefixes according to powers of 1000.There are also the prefixes for factors 10, 100 and 1/10 , 1/100.
| Factor | Prefix | Symbol | Factor | Prefix | Symbol | |
|---|---|---|---|---|---|---|
| 1024 | yotta- | Y- | 10-24 | yocto- | y- | |
| 1021 | zetta- | Z- | 10-21 | zepto- | z- | |
| 1018 | exa- | E- | 10-18 | atto- | a- | |
| 1015 | peta- | P- | 10-15 | femto- | f- | |
| 1012 | tera- | T- | 10-12 | pico- | p- | |
| 109 | giga- | G- | 10-9 | nano- | n- | |
| 106 | mega- | M- | 10-6 | micro- | µ- | |
| 103 | chilo- | k- | 10-3 | milli- | m- | |
| 102 | etto- | h- | 10-2 | centi- | c- | |
| 10 | deca- | da- | 10-1 | deci- | d- |
The prefixes precede the name of the unit.
Examples: 1 km = 103 m; 1 µF = 10-6 F.
As an exception to the general rule, the multiples and submultiples
of the mass unit (kilogram, kg) are formed by adding the prefixes to the
term “gram” and to the symbol “g”.
Example: 1 mg = 10-3 g = 10-6 kg.
SI – Writing rules
The S.I. codifies the rules for writing the names and the symbols of the units.The most important are given below.
| The names of the units must always be written
lowercase, without accents. Example: ampere, not Ampère. |
| The first character of the unit symbols is always
lowercase, with the exception of the symbols derived from people
names. Examples: mol for the mole, K for the kelvin. |
| The symbols are not followed by a period (except at the end of a sentence). |
| Symbols always follow the numerical values. Example: 1 kg, not kg 1. |
| The multiplication of two or more units is indicated
by a half-height dot or by a space. Example: N·m or N m. |
| The division of two units is
indicated by a bar or with negative exponents. Example: J/s or J s-1). |
Non-SI units accepted for use
Some non-SI units are largely used in scientific, technological and commercial fields as well as in everyday life.The use of these units is admitted, although not encouraged.
| Quantity | Unit | Symbol | Conversion | Notes |
|---|---|---|---|---|
| Time | minute | min | 1 min = 60 s | |
| hour | h | 1 h = 3600 s | ||
| day | d | 1 d = 86400 s | ||
| Length | astronomical unit | au | 1 au = 149 597 870 700 m | 1 |
| Area |
hectare | ha | 1 ha = 104 m2 | 2 |
| Volum | liter | L | 1 L = 10-3 m3 | 3 |
| Energy | electronvolt | eV | 1.602 176 634 x 10-19 J |
4 |
| Mass | tonne | t | 1 t = 103 kg | 5 |
| Dalton [atomic mass unit] | Da [u] | 1 Da = 1.660539 06660(50) 10-27 kg | 6 |
|
| Plane angle | degree | ° | 1 °= (π/180)rad | |
| minute | ‘ | 1′ = (Ï€/10800) rad | |
|
| second | ” | 1” = (Ï€/648000) rad | |
|
| Ratio of quantities | neper | Np | 1 Np = 1 | |
| bel | B | 1 B = (1/2) ln 10 (Np) | ||
| decibel | dB | 1 dB = 1/10 B |
- The astronomical unit rougly corresponds to the Earth-Sun distance. In 2012, the International Astronomical (IAU) decide to assign to the astronomical unit the exact value listed in the previous table.
- The hectare is used to express land areas.
- The 16a CGPM in 1979 proposed to substitute the symbol of the liter “l” (lowercase) iwith the symbol “L” (uppercase) to avoid the possible mistake between the lowercase “l” and the number “1”.
- The electronvolt is the kinetic energy acquired by an electron when traversing the potential difference of 1 V in vacuum. Its value is connected to the value of the electron charge. Since the electron charge is assumed as a defining quantity of SI and its value is exact, also the conversion electronvolt-joule is exact.
- Don’t mistake the tonne (mass unit, also called metric ton) with the register ton, unit of volume of mercantile navy, corresponding to 2.83168 m3 (100 ft3 in imperial units).
- The Dalton is equivalent to the atomic mass unit, defined as 1/12 of the mass of an atom of Carbon 12, at rest in its ground state.
Non-SI units not recommended for use
Some non-SI units, not recommended but still used in practice are listed in the following tables.| Quantity | Unit | Symbol | Conversion | Notes |
|---|---|---|---|---|
| Length | ångström | Å | 1 Å = 10-10 m | 1 |
| nautical mile | NM |
1 NM = 1852 m | 2 | |
| Velocity | knot | 1 knot = 0.514 m/s | 3 | |
| Area | are | a | 1 a = 102 m2 | 4 |
| barn | b | 1 b = 10-28 m2 | 5 | |
| Pressure | bar | bar | 1 bar = 105 Pa |
- The ångström is used in Physics and Chemistry to measure distances at the atomic level.
- The nautical mile roughly corresponds to the length of equatorial arc subtended by a longitude angle of one minute. The nautical mile is used in maritime and aerial navigation.
- One knot corresponds to the speed of one mile per hour.
- The are is used in land areas measurement.
- The barn is used in Physics to measure the cross sections in elementari particle collisions.
| Quantity | Unit | Symbol | Conversion | Notes |
|---|---|---|---|---|
| Linear density (textile fibers) | tex | tex | 1 tex = 10-6 kg/m | |
| Optical power of a lens | diopter | m-1 | |
|
| Mass (of gems) | metric carat | 0.2 g | 1,2 | |
| Blood pressure | mercury millimiters | mm Hg | 1 mm Hg = 133.322 Pa |
- In Imperial systems, 1 carat = 4 grains = 0.259 g
- In the alloys of precious metals, carats measure the purity expressed as numerator of a fraction whose denominator is 24. For example, an 18 carats gold means an alloy containing 18/24 of gold.
| Quantity | Unit | Symbol | Conversion |
|---|---|---|---|
| Volume | stere | st | 1 m3 |
| Force | kilogram-force | kgf | 9.80665 N |
| Pressure | torr | torr | 33.322 Pa |
| Pressure | atmosphere | atm | 101325 Pa |
| Energy | calorie at 15 C international calorie thermochem. calorie |
cal15 calit caltc |
4.1855 J 4.1868 J 4.1840 J |
| Power | horse power | HP | 735.499 W |
| Electric dipole | debye | D | 3.336 x 10-30 C m |
| Luminance | stilb | sb | 104 nt |
| Kinematic viscosity | stokes | St | 10-4 m2 s-1 |
| Dynamic viscosity | poise | P | 10-1 Pa s |
| Activity | curie | Ci | 3.7×1010 Bq |
| Adsorbed dose | rad | rd | 10-2 Gy |
| Equivalent dose | rem | rem | 10-2 Sv |
| Exposure | röntgen | R | 2.58×10-4 C kg-1 |
Bibliography
- J.D. Jackson: Classical Electrodynamics, Wiley (1998).[The appendix on measurement units is useful to clarify the relation between the Gauss c.g.s. and the S.I. systems.]
- R.A. Nelson: Foundations of the international system of units (SI), The Physics Teacher, December 1981, pag. 596. [Short history of the development of S.I., updated to 1981.]
- Bureau International des poids et mesures: The International System of Units, 1998.
- Ken Alder: The measure of all things. Free Press (2003) [The history of two French scientists, Delambre e Méchain, who measured the length of the meridian from Dunkerque and Barcelon between 1792 and 1798.]
- Bureau International des poids et mesures: The International System of Units, 2019.
Paolo Fornasini 