This SI Units Appendix sub-page of the SI Science Topics page is dedicated to the International System of Units, or SI Units.
IMPORTANT
The information in this appendix has been presented here for your convenience for rapid reference for our science related Blog posts. It is not intended to replace referencing of the OIML‘s original source information of the SI legal units of measurement for professional applications.
For professional and critical applications, please refer to the OIML‘s official website, or to your own country’s official SI units website (where this may exist).
SI Units – Summary
What follows is a summary of the SI Units.
The information contained in this summary was derived from OIML’s document: “OIML D 2, Legal units of measurement, Consolidated Edition 2007 (E)”.
This Appendix Last updated on 30/07/2023.
Base Units
| Measures: | Unit Name: | Unit Symbol: | Units Equation: | Definition: |
| length | metre | m | The metre is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second | |
| mass | kilogram | kg | The kilogram is the unit of mass; is equal to the mass of the international prototype of the kilogram | |
| time | 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 | |
| electric current | ampere | A | 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 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per metre of length. | |
| thermodynamic temperature | kelvin | K | The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. NOTE 1 | |
| amount of substance | 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. NOTE 2 | |
| luminous intensity | 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. |
NOTES
NOTE 1: In addition to the thermodynamic temperature (symbol T), expressed in kelvins, use is also made of Celsius temperature (symbol t) defined by the equation: t = T – T0 , where T0 = 273.15 K by definition. To express Celsius temperature, the unit “degree Celsius” (symbol: oC) which is equal to the unit “kelvin” is used; in this case , “degree Celsius” is a special name used in place of “kelvin”. An interval or difference of Celsius temperature can, however, be expressed in kelvins as well as in degrees Celsius.
NOTE 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.
Coherent Derived Units:
| Measures: | Unit Name: | Unit Symbol: | Units Equation: | Definition: |
| Space and Time | ||||
| length | metre | m | The metre is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second. | |
| plane angle | radian | rad | 1 rad = 1 m / 1 m = 1 | The radian is the plane angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius. |
| solid angle | steradian | sr | 1 sr = 1 m2 / 1 m2 = 1 | The steradian is the solid angle of a cone which, having its vertex in the center of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radiu7s of the sphere. |
| area | square metre | m2 | 1 m2 = 1 m . 1 m | The square metre is the area of a square of side 1 metre. |
| volume | cubic metre | m3 | 1 m3 = 1 m . 1 m . 1 m | The cubic metre is the volume of a cube of side 1 m. |
| time | 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 | |
| frequency | hertz | Hz | 1 Hz = 1 s-1 | The hertz is the frequency of a periodic phenomenon, the period of which is 1 second. |
| angular velocity | radian per second | rad/s or rad.s-1 | 1 rad/s = 1 rad / 1 s | The radian per second is the angular velocity of a body that rotates uniformly about a fixed axis through 1 radian in 1 second. |
| angular acceleration | radian per second squared | rad/s2 or rad.s-2 | 1 rad/s2 = 1 rad/s / 1 s | The radian per second squared is the angular acceleration of a body, rotating about a fixed axis with uniform acceleration, whose angular velocity changes by 1 radian per second in 1 second. |
| velocity | metre per second | m/s or m.s-1 | 1 m/s = 1 m / 1 s | The metre per second is the velocity of a point that moves through 1 metre in 1 second with uniform motion. |
| acceleration | metre per second squared | m/s2 or m.s-2 | 1 m/s2 = 1 m/s / 1 s | The metre per second squared is the acceleration of a body, animated by a uniformly varied movement whose velocity varies in 1 second by 1 metre per second. |
| Mechanics | ||||
| mass | kilogram | kg | The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. | |
| lineic mass, linear density | kilogram per metre | kg/m or kg.m-1 | 1 kg/m = 1 kg / 1 m | The kilogram per metre is the lineic mass of a homogeneous body of uniform section having a mass of 1 kilogram and a length of 1 metre. |
| areic mass, surface density | kilogram per square metre | kg/m2 or kg.m-2 | 1 kg/m2 = 1 kg / 1 m2 | The kilogram per square metre is the areic mass of a homogeneous body of uniform thickness having a mass of 1 kilogram and an area of 1 square metre. |
| density (mass density) | kilogram per cubic metre | kg/m3 or kg.m-3 | 1 kg/m3 = 1 kg / 1 m3 | The kilogram per cubic metre is the density of a homogeneous body having a mass of 1 kilogram and a volume of 1 cubic metre. |
| force | newton | N | 1 N = 1 kg . 1m / s2 | The newton is the force which gives to a mass of 1 kilogram an acceleration of 1 metre per second, per second. |
| moment of force | newton metre | N.m | 1 N.m = 1 kg.m2/s2 | The moment of a force about a point is equal to the vector product of any radius vector from this point to a point on the line of action of the force, and the force. |
| pressure, stress | pascal | Pa | 1 Pa = 1 N / 1 m2 | The pascal is the uniform pressure that, when acting on a plane surface of 1 square metre, exerts perpendicularly to that surface a total force of 1 newton. It is also the uniform stress that, when acting on a plane surface of 1 square metre, exerts on that surface a total force of 1 newton. |
| dynamic viscosity | pascal second | Pa.s | 1 Pa.s = ( 1 Pa . 1 m ) / 1 m/s | The pascal second is the dynamic viscosity of a homogeneous fluid in which the velocity varies uniformly in a direction normal to that of the flow with a variation of 1 metre per second over a distance of 1 metre, and in which there is a shear stress of 1 pascal. |
| kinematic viscosity | metre squared per second | m2/s or m2.s-1 | 1 m2/s = 1 Pa.s / 1 kg/m3 | The metre squared per second is the kinematic viscosity of a fluid whose dynamic viscosity is 1 pascal second and whose density is 1 kilogram per cubic metre. |
| work, energy, quantity of heat | joule | J | 1 J = 1 N . 1 m | The joule is the work done when the point of application of 1 newton moves a distance of 1 metre in the direction of the force. |
| energy flow rate, heat flow rate, power | watt | W | 1 W = 1 J / 1 s | The watt is the power which in 1 second gives rise to energy of 1 joule. |
| volume flow rate | cubic metre per second | m3/s or m3.s-1 | 1 m3/s = 1 m3 / 1 s | The cubic metre per second is the volume flow rate such that a substance having a volume of 1 cubic metre passes through the cross section considered in 1 second. |
| mass flow rate | kilogram per second | kg/s or kg.s-1 | 1 kg/s = 1 kg / 1 s | The kilogram per second is the mass flow rate of a uniform flow such that a substance having a mass of 1 kilogram passes through the cross section considered in a time of 1 second. |
| Heat | ||||
| thermodynamic temperature, interval of temperature | kelvin | K | The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. See NOTE 3 below. | |
| entropy | joule per kelvin | J/K or J.K-1 | 1 J/K = 1 J / 1 K | The joule per kelvin is the increase in the entropy of a system receiving a quantity of heat of 1 joule at the constant thermodynamic temperature of 1 kelvin, provided that no irreversible change takes place in the system. |
| massic heat capacity, specific heat capacity | joule per kilogram kelvin | J/(kg.K) or J.kg-1.K-1 | 1 J/(kg.K) = 1 J / (1 kg . 1 K) | The joule per kilogram kelvin is the massic heat capacity of a homogeneous body at constant pressure or constant volume having a mass of 1 kilogram in which the addition of a quantity of heat of 1 joule produces a rise in temperature of 1 kelvin. |
| thermal conductivity | watt per metre kelvin | W/(m.K) or W.m-1.K-1 | 1 W/(m.K) = (1 W/m2) / (1 K/m) | The watt per metre kelvin is the thermal conductivity of a homogeneous body in which a difference of temperature of 1 kelvin between two parallel planes having a surface of 1 square metre and which are 1 metre apart produces a heat flow rate of 1 watt between these planes. |
| Electricity and Magnetism | ||||
| electric current | ampere | A | 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 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per metre of length. | |
| quantity of electricity, electric charge | coulomb | C | 1 C = 1 A . 1 s | The coulomb is the quantity of electricity carried in 1 second by a current of 1 ampere. |
| electric potential, electric tension, electromotive force | volt | V | 1 V = 1 W / 1 A | The volt is the potential difference between two points of a conducting wire carrying a constant current of 1 ampere, when the power dissipated between these points is equal to 1 watt. |
| electric field strength | volt per metre | V/m | 1 V/m = 1 N / 1 C | The volt per metre is the strength of the electric field which exercises a force of 1 newton on a body charged with a quantity of electricity of 1 coulomb. |
| electric resistance | ohm | Ω | 1 Ω = 1 V / 1 A | The ohm is the electrical resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points, produces in the conductor a current of 1 ampere, the conductor not being the seat of any electromotive force. |
| conductance | siemens | S | 1 S = 1 Ω-1 | The siemens is the conductance of a conductor having an electrical resistance of 1 ohm. |
| electric capacitance | farad | F | 1 F = 1 C / 1 V | The farad is the capacitance of a capacitor between the plates of which there appears a potential difference of 1 volt when it is charged by a quantity of electricity of 1 coulomb. |
| inductance | henry | H | 1 H = ( 1 V . 1 s) / 1 A | The henry is the inductance of a closed circuit in which an electromotive force of 1 volt is produced when the electric current in the circuit varies uniformly at the rate of 1 ampere per second. |
| magnetic flux | weber | Wb | 1 Wb = 1 V . 1 s | The 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. |
| magnetic flux density, magnetic induction | tesla | T | 1 T = 1 Wb / 1 m2 | The tesla is the magnetic flux density produced within a surface of 1 square metre by a uniform magnetic flux of 1 weber perpendicular to this surface. |
| magnetomotive force | ampere | A | The magnetomotive force of 1 ampere is caused along any closed curve that passes once around an electric conductor through which an electric current of 1 ampere is passing. | |
| magnetic field strength | ampere per metre | A/m or A.m-1 | 1 A/m = 1 A / 1 m | The ampere per metre is the strength of the magnetic field produced in a vacuum along the circumference of a circle of 1 metre in circumference by an electric current of 1 ampere, maintained in a straight conductor of infinite length, of negligible circular cross section, forming the axis of the circle mentioned. |
| Physical chemistry and Molecular physics | ||||
| amount of a substance | mole | mol | The mole is the amount of a substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. 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. | |
| catalytic activity | katal | kat | 1 kat = 1 mol / 1 s | The katal is the activity of a catalyst which causes a catalysed conversion rate of one mole of substrate per second. It is recommended that when the katal is used, the measurand be specified by reference to the measurement procedure; the measurement procedure must identify the indicator reaction. |
| Radiation and Light | ||||
| radiant intensity | watt per steradian | W/sr or W.sr-1 | 1 W/sr = 1 W / 1 sr | The watt per steradian is the radiant intensity of a point source emitting uniformly a radiant flux of 1 watt in a solid angle of 1 steradian. |
| luminous intensity | 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. | |
| luminance | candela per square metre | cd/m2 or cd.m-2 | 1 cd/m2 = 1 cd / 1 m2 | The candela per square metre is the luminance perpendicular to the plane surface of 1 square metre of a source of which the luminous intensity perpendicular to that surface is 1 candela. |
| luminous flux | lumen | lm | 1 lm = 1 cd . 1 sr | The lumen is the luminous flux emitted in a unit solid angle of 1 steradian by a uniform point source having a luminous intensity of 1 candela. |
| illuminance | lux | lx | 1 lx = 1 lm / 1 m2 | The lux is the illuminance of a surface receiving a luminous flux of 1 lumen, uniformly distributed over 1 square metre of the surface. |
| Ionizing radiation | ||||
| activity (of a radiation source) | becquerel | Bq | 1 Bq = 1 / 1 s | The becquerel is the activity of a radioactive source in which the quotient of the expectation value of a number of spontaneous nuclear transitions or isomeric transitions and the time interval in which these transitions take place tends to the limit 1/s. |
| absorbed dose, kerma | gray | Gy | 1 Gy = 1 J / 1 kg | The gray is the absorbed dose or the kerma in an element of matter of 1 kilogram mass to which the energy of 1 joule is imparted by ionizing radiations (absorbed dose), or in which the sum of the initial kinetic energies of 1 joule is liberated by charged ionizing particles (kerma), each under a condition of constant energy fluence. |
| dose equivalent | sievert | Sv | 1 Sv = 1 J / 1 kg | The sievert is the dose equivalent in an element of tissue of 1 kilogram mass to which the energy of 1 joule is imparted by ionizing radiations whose value of the quality factor, which weights the absorbed dose for the biological effectiveness of the charged particles producing the absorbed dose, is 1 and whose energy fluence is constant. |
| exposure | coulomb per kilogram | C/kg or C.kg-1 | 1 C/kg = 1 C / 1 kg | The coulomb per kilogram is the exposure of photonic ionizing radiation that can produce, in a quantity of air of 1 kilogram mass, ions of one sign carrying a total electric charge of 1 coulomb when all the electrons (negatrons and positrons) liberated by photons in the air are completely stopped in air, the energy fluence being uniform in the quantity of air. |
NOTES Continued
NOTE 3: regarding Celsius temperature (symbol t) and “degree Celsius” (oC), and the thermodynamic temperature (symbol T) and the unit kelvin, K:
In addition to the thermodynamic temperature (symbol T), expressed in kelvins, use is also made of Celsius temperature (symbol t) defined by the equation:
t = T – T0
where T0 = 273.15 K by definition. To express Celsius temperature, the unit “degree Celsius” (symbol: 0C) which is equal to the unit “kelvin” is used; in this case, “degree Celsius” is a special name used in place of “kelvin”. An interval or difference of Celsius temperature can, however, be expressed in kelvins as well as degrees Celsius.
Decimal multiples and sub-multiples of the coherent SI units
The names for the decimal multiples and sub-multiples of the SI units are formed by means of SI prefixes designating the decimal numerical factors:
| Factor | SI-Prefix | Symbol |
| 1 000 000 000 000 000 000 000 000 = 1024 | yotta | Y |
| 1 000 000 000 000 000 000 000 = 1021 | zetta | Z |
| 1 000 000 000 000 000 000 = 1018 | exa | E |
| 1 000 000 000 000 000 = 1015 | peta | P |
| 1 000 000 000 000 = 1012 | tera | T |
| 1 000 000 000 = 109 | giga | G |
| 1 000 000 = 106 | mega | M |
| 1 000 = 103 | kilo | k |
| 100 = 102 | hecto | h |
| 10 = 101 | deca | da |
| 0.1 = 10-1 | deci | d |
| 0.01 = 10-2 | centi | c |
| 0.001 = 10-3 | milli | m |
| 0.000 001 = 10-6 | micro | μ |
| 0,000 000 001 = 10-9 | nano | n |
| 0.000 000 000 001 = 10-12 | pico | p |
| 0.000 000 000 000 001 = 10-15 | femto | f |
| 0.000 000 000 000 000 001 = 10-18 | atto | a |
| 0.000 000 000 000 000 000 001 = 10-21 | zepto | z |
| 0.000 000 000 000 000 000 000 001 = 10-24 | yocto | y |
A prefix is considered to be combined with the name of the unit to which it is directly attached. (E.g. megawatt).
The symbol of the prefix must be placed before the symbol of the unit without an intermediate space; the whole forms the symbol of the multiple or sub-multiple of the unit. The symbol of the prefix is therefore considered to be combined with the symbol of the unit to which it is directly attached, forming with it a new unit symbol which can be raised to a positive or negative power and which can be combined with other unit symbols to form the symbols for compound units.
Compound prefixes, formed by the juxtaposition of several SI prefixes, are not allowed.
The names and the symbols of the decimal multiples and sub-multiples of the unit of mass are formed by the addition of the SI prefixes to the word “gram” (symbol: g).
1 g = 0,001 kg = 10-3 kg
To designate the decimal multiples and sub-multiples of a derived unit which is expressed in the form of a fraction, a prefix can be attached indifferently to the units which appear either in the numerator, or in the denominator, or in both of these. In standardization the general advice is not to use prefixes in the denominator.
Other Units
| Name | Symbol | Definition |
| Time | ||
| minute | min | 1 min = 60 s |
| hour | h | 1 h = 60 min = 3 600 s |
| day | d, (see NOTE 4 below) | 1 d = 24 h = 86 400 s |
| Plane angle | ||
| degree | 0 | 10 = (ℼ / 180) rad |
| minute | ‘ | 1′ = (1/60)0 = (ℼ / 10 800) rad |
| second | “ | 1″ = (1/60)’ = (ℼ / 648 000) rad |
| gon | gon | 1 gon = (ℼ / 200) rad |
| Volume | ||
| litre | l or L | 1 l = 1 L = 1 dm3 = 10-3 m3 |
| Mass | ||
| tonne | t | – and the multiples of the tonne formed according to the above table of described decimal multiples. 1 t = 1 Mg = 103 kg |
| unified atomic mass unit | u | – is equal to the fraction 1/12 of the mass of an atom of the nuclide carbon 12. Approximate value: 1 u ≈ 1.660 540 yg = 1.660 540 x 10-27 kg Its use is authorized only in chemistry and physics. |
| Work, energy, quantity of heat | ||
| watt hour | W.h | – and the multiples of the watt hour formed according to the above table of described decimal multiples. 1 W.h = 3,6 kJ = 3.6 x 103 J |
| electronvolt | eV | – is equal to the kinetic energy acquired by an electron in passing through a potential difference of 1 volt in vacuum, and the multiples and sub-multiples of the electronvolt formed according to the above table of described decimal multiples. Approximate value: 1 eV ≈ 160.217 7 zJ = 1.602 177 x 10-19 J Its use is authorized only in specialized fields. |
| Logarithmic quantities | ||
| field level, e.g. sound pressure level and logarithmic decrement: | LF | LF = ln(F/F0) = ln(F/F0) Np = 2 lg(F/F0) B |
| neper | Np | The neper is the level of a field quantity F when F/F0 = e, where F0 is a reference quantity of the same kind, i.e.: 1 Np = ln (F/F0) = ln e = 1 |
| bel | B | The bel is the level of a field quantity F when F/F0 = 101/2, where F0 is a reference quantity of the same kind, i.e.: 1 B = ln (F/F0) = ln 101/2 Np = (1/2) ln 10 Np = 2 lg 101/2 B |
| power level, e.g. power attenuation | LP | LP = (1/2) ln (P/P0) = (1/2) ln (P/P0) Np = lg (P/P0) B |
| neper | Np | The neper is the level of a power quantity P when P/P0 = e2, where P0 is a reference power, i.e.: 1 Np = (1/2) ln(P/P0) = (1/2) ln e2 = 1 |
| bel | B | The bel is the level of a power quantity P when P/P0 = 10, where P0 is a reference power, i.e.: 1 B = (1/2) ln (P/P0) = (1/2) ln 10 Np = lg 10 B |
NOTES Continued
NOTE 4: Gregorian Calendar annual adjustments
According to the Gregorian Calendar established in 1582 the year (a) consists of 365 days with a leap-year of 366 days every 4th year, whereas of the centenary years only those exactly divisible by 400 should be counted as leap-years.
Annex’s to OIML D 2: 2007 (E)
Please note that there are two Annex to the OIML D 2 document which list other older SI units of measurement and denominations whose status have changed. Please refer to the document for these particular changes of status.
Disclaimer:
E & O E:
All care has been taken in preparing the above SI units summary tables and notes with information derived from the OIML’s source documents. However for professional and critical applications, you may wish to consult directly with the source information available from the OIML’s website, or from your own country‘s official SI units and standards website.
End.