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**The Units of measurement

The raison d’être of the SI and short history

Performing a measurement means comparing an unknown physical (or chemical) quantity with a quantity of the same type taken as reference using an instrument.

A measurement necessarily involves a reference frame and therefore units. In the not so distant past, there were numerous units, which had little in common with each other. The first coherent system of units only appeared with the French revolution: the metric system. This system was internationally ratified by the Metre Convention on 20 May 1875, a diplomatic treaty which set up the Bureau International des Poids et Mesures (BIPM).

In 1960, during the eleventh Conférence Générale des Poids et Mesures (CGPM), the International System of Units, the SI, was developed. It now includes two classes of units :

We must not believe, however, that once set up, this system is fixed. Progress made in science and technology and the new requirements from society and therefore the needs in terms of increased accuracy, will led the LNE and all national metrology institutes to continuously improve the practical realisation of all SI units. And this concern involves the references as well as the means for transfer to the users, to allow matching at best these new needs. Definitions of units sometimes need to be changed and new definitions added.

The base units and their definitions

To date, the International System of Units, the SI, is made up of seven base units (between brackets the sole/single symbol representing it) :

  • The metre (m)
  • The kilogram (kg)
  • The second (s)
  • The ampere (A)
  • The kelvin (K)
  • The candela (cd)
  • The mole (mol)

Units Définitions
metre (m) The metre is the length of the path travelled by light in vacuum during a  time interval of 1/299 792 458 of a second.
kilogram (kg) The kilogram is the mass of the platinum-iridium prototype which was  approved by the Conférence Générale des Poids et Mesures, held in Paris in  1889, and kept by the Bureau International des Poids et Mesures.
second (s) 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 caesium 133 atom.
ampere (A) The ampere is the intensity of a constant current which, if maintained in two straight  parallel conductors of infinite length, of negligible circular cross-section, and  placed 1 metre apart in vacuum, would produce between these conductors a  force equal to 2 x 10-7 newton per metre of length.
kelvin (K) The kelvin is the fraction 1/273,16 of the thermodynamic temperature of  the triple point of water.
candela (cd)  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
mole (mol) 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.

The derived units (including the dimensionless units)

There are numerous derived units that are complementary to the base units. They may have special names (e.g. hertz, pascal, becquerel, etc.) but can always be expressed in terms of the base units. There are also dimensionless derived units.

It should be noted that these units are linked together to form a consistent system.

These units are linked together to form a coherent system.

Lastly, each quantity may need to cover a vast range of values. To avoid the need for multiplying factors or values with a large number of zeros, prefixes are used. The prefixes cover a range extending from 1024 to 10-24 times the units.

  • Electricity and magnetism

Current intensity : The ampere (A)

Units Quantities
potential difference, U : volt (V = W/A)
electrical capacitance, C : farad (F = C/V)
electrical resistance, R : ohm (Ω = V/A)
inductance, L : henri (H = Wb/A)
quantity of electricity, Q : coulomb (C = A.s)
power, P : watt (W = J/s)
energy, W : joule (J = N.m)
magnetic induction, B : tesla (T = Wb/m2)
electric field, E : volt per metre (V/m)
magnetic field strength, H : ampère per metre (A/m)
electric conductance, G : siemens (S = A/V)
attenuation, η : decibel (dB)

  • Mass and related quantities

The mass : the kilogram (kg)

Units >Quantities
density : ρ kg.m-3
volume : V m3
force : F newton (N)
torque : M N.m
pressure : p pascal (Pa)
dynamic viscosity : η Pa.s
kinematic viscosity : υ m2.s-1
acoustic pressure : p pascal (Pa)
dynamic volume : v m3
mass flow-rate : qm kg.s-1
volume flow-rate : qv m3.s-1
air flow-rate : V m.s-1

  • Length and dimensional quantities

Length : the metre (m)

Unités Formules
wavelength : λ metre (m)
length of material standards : L metre (m)
lplane angle : α radian (rad)
form measurement : metre (m)

  • Radiometry – Photometry


Luminous intensity : the candela (cd) (m)

Units Quantities
luminous flux : Φ lumen (lm)
illuminance : E lux (lx)
luminance : L cd.m-2

Radiometry of detectors

Units Quantities
spectral responsivity : S(λ) A.W-1

Radiometry of sources

Units Quanntities
 energy flow : Φe watt (W)
radiance : Le W.m-2.sr-1
irradiance : Ee W.m-2
laser source power : P watt (W)
laser source energy : Q joule (J)

Radiometry of materials

Units Quanntities
regular spectral transmittance : t(Φ) flux ratio
diffuse spectral reflectance : R(λ) flux ratio

Fibre optics

Units Quanntities
energy flow : P watt (W)
wavelength : λ metre (m)
propagation time : t second (s)
fibre length metre (m)
linear attenuation factor : dB.m-1
reflectance dB
detector (or fibre) passband hertz (Hz) (ou Hz.m-1)

  • Temperature and thermal quantities

Thermometry and radiation thermometry

Units Quanntities
temperature in the ITS-90 or in the PLTS-2000 : T kelvin (K)
or t degree Celsius (°C)

Metrology of thermal quantities

Units Definitions Quantities
thermal conductivity : λ = α.ρ.Cp (ρ = density) W.m-1.K-1
 thermal diffusivity : α =λ/ρ.Cp (ρ = density) m2.s-1
specific heat capacity : Cp = (∂H/∂T)p (H = enthalpy) J.kg-1.K-1
spectral directional emissivity : ελ dimensionless ratio
normal spectral emissivity : ελ dimensionless ratio
total hemispherical emissivity : ελ dimensionless ratio


Units Definitions Quantities
temperature dew point : Td
frost point : Tf
degree Celsius (°C)
degree Celsius (°C)
l’humidité relative with respect to water : Uw
with respect to ice : Ui
percentage (%)
percentage (%)

  • Amount of Substance - Chemical analysis

The two main SI units used in amount of substance are the mole and the kilogram. From the definition of the mole (amount of substance of a system which contains as many elementary entities as there are atoms in 0,012 kilogram of carbon 12) there is a ratio between them; consequently, they are both used. More precisely, the measurement of an amount of substance is expressed either in mole or in kilogram, or as concentrations (ratio of two quantities: mass / mass, mole / mole, mole /mass, etc.).

  • Ionizing radiation


Quantities Units
activity : A Bq
activity per mass unit : Am Bq.kg-1
activity per volume unit : Av Bq.m-3
emission rate : N s-1
emission rate per solid angle unit : s-1.sr-1
neutron fluence rate : m-2.s-1
with Bq : becquerel

Dosimetry : (photons, electrons, protons)

Quantities Units
air kerma normal : kn Gy.m2
air kerma rate : Kair Gy.s-1
absorbed dose rate to water : Dwater Gy.s-1
absorbed dose rate to graphite : Dg Gy.s-1
absorbed dose rate to tissure : Dtissus Gy.s-1
directional dose equivalent rate : H'(0,07 ; α) Sv.s-1
ambient dose equivalent rate : H*(10) Sv.s-1
with : Gy = gray, Sv = sievert

Neutron Dosimetry

Quantities Units
neutron fluence rate : m2.s-1
kerma rate to tissue : Ktissus Gy.s-1
ambient dose equivalent rate : H*(10) Sv.s-1
individual dose equivalent rate : Hp(d) Sv.s-1

  • Time and frequency

Time : the second (s)

Quantities Units
frequency : υ hertz (Hz)
 time interval : second (s)
phase fluctuation spectral density : (dBc/Hz)
rotation speed (tr/min)

  • Dimensionless derived units

Quantities Units
Plane angle radian (rad) = m.m-1
Solid steradian angle stéradian (sr) = m2.m-2

The SI prefixe

Factor Prefixe Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 péta P
1012 téra T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 déca da
10-1 déci d
10-2 centi c
10-3 milli m
10-6 micro µ
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y