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Measurement Units Standards & Services Department |
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Derived Units
Derived units are units which may be expressed in terms of base units by means of the mathematical symbols of multiplication and division. Certain derived units have been given special names and symbols, and these special names and symbols may themselves be used in combination with those for base and other derived units to express the units of other quantities.
(A). Derived units in relation to space and time
| Derived Quantity | Symbol |
Name |
Definition |
|---|---|---|---|
| surface area |
m²
|
square meter |
The surface of a square having a sides of one meter (1m² =1 m*1 m) |
| volume | m³ |
cubic meter |
The cubic meter is the volume of a cube having a side of one meter (1 m³ =1 m*1 m*1 m) |
| speed | m/s |
meter per second |
The meter per second is the speed of a body which, animated by a uniform movement, covers 1 meter in 1 second. (1 m/s = 1 m/1 s) |
| acceleration | m/s² |
meter per second squared |
The meter per second squared is the acceleration of a body, which animated by a uniformly varied movement whose speed various in 1 second by 1 meter per second (1 m/ s²= 1 m/s /1 s) |
| wave number | m¯¹ |
reciprocal meter |
1 per meter is the wave number of a monochromatic radiation whose wave length is equal to 1 meter ( 1 m¯¹ = 1 /1 m) |
| frequency | Hz |
hertz |
The Hertz is the frequency of a periodic phenomenon of which the periodic time is 1 second ( 1 Hz =1s¯¹ = 1 /1 s) |
| angular velocity | rad/s or rad. s¯¹ |
radian per second |
The radian per second is the angular velocity of a body which animated by a uniform rotation around a fixed axis, turns 1 radius in 1 second. (1 rad/s = 1 rad/ 1 s) |
| angular acceleration | rad/ s² or rad
.s¯² |
radian per second squared |
The radian per second squared is the angular acceleration of a body which is animated by a rotation varying uniformly around a fixed axis, and whose angular velocity varies 1 radiant per second in 1 second. (1 rad /s² = 1 rad/s/1 s) |
| rotational frequency | s¯¹ |
second raised to the power minus one (revolution per second) |
The second raised to the power minus one is the rotational frequency of a uniform rotatory movement which produces one complete revolution in one second. ( 1 s¯¹ = 1 / 1 s) |
| vergency of optical system | m¯¹ |
dioptre |
The dioptre is the vergency of an optical system, the focal distance of which is one meter in a medium having a refractive index of unity. ( 1 m¯¹ = 1/1 m) |
(B). The derived units in relation to mechanics
Derived Quantity |
Symbol |
Name |
Definition |
|---|---|---|---|
Liner density |
kg/m or kg.m¯¹ | kilogram per meter |
The kilogram per meter is the linear density of a homogeneous body of uniform section having a mass of 1 kilogram and a length of 1 metre. ( 1 kg/m = 1 kg /1 m) |
Surface density |
kg/m² or kg.m¯² |
kilogram per square meter |
The kilogram per square meter is the surface density of a homogeneous body of uniform thickness having a mass of 1 kilogram and an area of 1 square meter. (1 kg /m² = 1 kg/1m²) |
Density |
kg m³ /or kg. m¯³ |
kilogram per cubic meter |
The kilogram per cubic meter is the density of a homogeneous body having a mass of 1 kilograms and a volume of 1 cubic meter. ( 1 kg/m³ = 1 kg /1 m³) |
Concentration |
kg /m³or kg.m¯³ |
kilogramme per cubic meter |
The kilogram per cubic meter is the concentration of a homogeneous solution having a total volume of one cubic meter and containing a mass of one kilogram of a given substance ( 1 kg/m³ = 1 kg/1 m³) |
Force |
N |
newton |
The newton is the force which, when appiled to a body having a mass of 1 kilogram, gives it an acceleration of 1 meter per second squared. (1 N = 1 kg.1 m/ s² ) |
Moment of force |
Nm |
newton meter |
The newton meter is the moment of force produced in a body by a force of one newton acting at a perpendicular distance of one meter from the fixed axis around which the body turns ( 1 N.m. =1.N.1m) |
Pressure |
Pa |
pascal |
The pascal is the uniform pressure which, when acting on a plane surface of 1 square meter, exercises perpendicularly to that surface a total force of 1 newton. It is also the stress which, when acting on a plane surface of 1 squaremetre, exercises on that surface a total force of 1 newton. ( 1 Pa = 1 N/1m² ) |
Dynamic viscosity |
Pa.s |
pascal second |
The pascal second is the dynamic viscosity of a homogeneous fluid in which the uniform linear movement of a plane surface of 1 square meter leads to a retarding force of 1 newton, when there is a difference in velocity between two parallel planes separated by a distance of 1 meter. ( 1 Pa.s = 1 Pa. 1m / 1 m/s) |
Kinematic viscosity |
m²/s or m².s¯¹ |
square meter per second |
The meter 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 meter. ( 1 m²/s = 1 Pa.s/1 kg / m²) |
Surface tension |
N/m or N.m¯¹ |
newton per meter |
The newton per meter is the surface tension produced when a force of one newton sets over a length of one meter on the surface of liquid separating that liquid from the material surrounding it. ( 1N/m = 1N/1m) |
Work, energy, quantity of heat |
J |
joule |
The Joule is the work done when the point of application of a force of 1 newton is displaced through a distance of 1 meter in the direction of the force. ( 1 J = 1 N. 1 m) |
Power, energy, flow rate, heat flow rate, |
W |
watt |
The Watt is the power which gives rise to a production of energy equal to 1 Joule per second ( 1 W = 1 J/ 1 s) |
Volume flow rate |
m³ /s or m³.s¯¹ |
cubic meter per second |
The cubic meter per second is the volume flow rate of a uniform flow such that a substance having a volume of 1 cubic meter passes through the cross section considered in 1 second. ( 1 m³ /s = 1 m³ / 1 s) |
Mass flow rate |
Kg/s or kg.s ¯¹ |
kilogram per second |
The kg 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 1 second. ( 1 kg/s = 1 kg/1 s) |
Specific volume
|
m ³ /kg orm ³ .kg ¯¹ |
cubic meter per kilogramme |
The cubic meter per kilogramme is the specific volume of a homogeneous body having a volume of one cubic meter and a mass of one kilogram. ( 1 m ³ /kg = 1 m ³ /1 kg)
|
(C). The derived units in relation to heat
Derived Quantity |
Symbol |
Name |
Definition |
|---|---|---|---|
Entropy |
J/K or J.K ¯¹ |
joule per Kelvin |
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. ( 1 J/K = 1 J /1 K) |
Specific entropy |
J / kg.K or J kg¯¹.K¯¹ |
joule per kilogram Kelvin |
The Joule per kilogram Kelvin is the specific entropy of a system of homogeneous mass of 1 kilogram receiving a quantity of heat equal to one Joule at the constant thermodynamic temperature of one Kelvin, provided that no irreversible change takes place in the system. ( 1 J /kg.K = 1 J /1 kg. 1 K ) |
Heat capacity |
J / K or J.K¯¹ |
joule per Kelvin |
The Joule per Kelvin is the heat capacity of a homogeneous body in which a quantity of heat equal to one joule produces as increases of one Kelvin in the thermodynamic temperature. ( 1 J / K = 1 J/ 1 K) |
Specific heat capacity |
J / kg . K or J kg¯¹.K¯¹ |
joule per kilogram Kelvin |
The Joule per kilogram Kelvin is the specific heat capacity of a homogeneous body 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. ( 1 J / kg.K = 1 J / 1 kg.1 K ) |
Latent heat |
J / kg or J.kg¯¹ |
joule per kilogram |
The Joule per kilogram is the heat exchanged by 1 kg of substances to change one phase to another at the temperature of its changing phase. ( 1 J / kg = 1 J / 1 kg ) |
| Thermal conductivity | W/m K or W.m¯¹ .K ¯¹ |
watt per meter kelvin |
The watt per meter kelvin is the thermal conductivity of a homogeneous body in which a difference of temperature of 1 Kelvin produces a heat flow rate of 1 watt between two parallel planes having a surface of 1 square meter which are 1 meter apart. ( 1 W /m.K = (1 W/m) /(1 K/1 m) ) |
(D). The derived units in relation to electricity and magnetism
Derived Quantity |
Symbol |
Name |
Definition |
|---|---|---|---|
Quantity of electricity |
C |
coulomb |
The coulomb is the quantity of electricity carried in 1 second by current of 1 ampere. ( 1 C = 1 A .1 s = 1 As ) |
electric potential, electric tension, electromotive force |
V |
volt |
The volt is the difference of electric potential between two points of a conducting wire carrying a constant current of 1 ampere, when the power dissipated between these two points is equal to 1 watt. ( 1 V= 1 W/ 1 A ) |
Electric field strength |
V/m |
volt per meter |
The volt per meter is the strength of the electric field which exercises a force of a Newton on a body charged with a quantity of electricity of 1 coulomb. ( 1 V/m = 1 N/ 1 C ) |
Electric charge density |
C/m³or C. m¯³ |
coulomb per cubic meter |
The coulomb per cubic meter is the electric charge density of a homogeneous mass or system of volume of one cubic meter and having a charge of one coulomb. ( 1 C / m³ = 1C/ 1 m³) |
| Electric flux density |
|
coulomb per square meter |
The coulomb per square meter is the electric flux density when a condenser, having plates of infinite length parallel to each other, is charged in vacuum with a quantity of electricity equal to one coulomb per one square meter of area of the plate. ( 1 C/m²= 1C / 1 m²) |
| Electric resistance |
|
ohm |
The ohm is the electric resistance between two points of a conductor when a constant potential difference of 1 volt, applied to these points. produces in the conductor & current of 1 ampere , the conductor not being the source of any electromotive force. ( 1 ohm= 1 V/1 A) |
| Conductance | S |
siemens |
The siemens is the conductance of a conductor having an electric resistance of 1 ohm. ( 1 S = 1 ohm¯¹ = 1 /1ohm ) |
| Electric capacitance | F |
farad |
The farad is the capacitance of a capacitor between the plates of which there appere a difference of electric potential of 1 volt, when it is charged by a quantity of electricity of 1 coulomb. ( 1 F = 1 C / 1 V ) |
| Permittivity | F/m or F.m¯¹ |
farad per meter |
The farad per meter is the permittivity of the medium which give a capacitance of one farad per square meter of area of two parallel plates separates by a distance of one meter. ( 1 F/m = 1 F / 1 m) |
| Inductance | H |
henry |
The henry is the electric inductance of a closed circuit in which an electromotive force of a volt is produced when the electric current in the circuit varies uniformly at the rate of 1 ampere per second ( 1 H = 1 V. 1s/ 1A ) |
Permeability |
H / m or H.m¯¹ |
henry per meter |
The henry per meter is the permeability of a material surrounded by a single turn of a flat sheet conductor including an area of one square meter and length one meter which gives an inductance of one henry. ( 1 H / m = 1 H / 1 m ) |
| Magnetic flux | Wb |
weber |
The weber is the magnetic flux which linking a circuit of 1 turn would produce in it an electromotive force of 1 volt, if it were reduced to zero at a uniform rate in 1 second. ( 1 Wb = 1 V. 1 s ) |
| Magnetic inductance | T |
tesla |
The tesler is the uniform magnetic induction which, distributed normally over a surface of 1 square meter , produces across the surface a total magnetic flux of 1 weber ( 1 T = 1 Wb / 1 m² ) |
Magnetomotive force
|
A |
ampere |
The ampere is the magnetomotive force along any closed curve which surrounds, once only, an electric conductor through which an electric current of 1 ampere passes. |
| Magnetic field strength | A/m or A.m¯¹ |
ampere per meter |
The ampere per meter is the strength of the magnetic field produced in vacuum along the circumference of a circle of 1 meter 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. ( 1 A.m¯¹ = 1 A / 1 m ) |
| Current density | A/m² or A.m¯² |
ampere per square meter |
The ampere per square meter is the current density in a linear, conductor when a current of intensity one ampere flows uniformly through a cross section of the conductor equal to one square meter, perpendicular to the direction of flow of the current. ( 1 A /m² = 1 A/ 1 m² ) |
(E). The derived units in relation to electromagnetic radiation and light
Derived Quantity |
Symbol |
Name |
Definition |
|---|---|---|---|
| Radiant intensity | W/sr or W.sr¯¹ |
watt per steradian |
The watt per steradian is the radiant intensity of a point source sending uniformly a radiant flux of 1 watt in a soild angle of 1 steradian. ( 1 W/sr = 1W/ 1 sr) |
| Irradiance | W/m² or W.m¯² |
watt per square meter |
The watt per square meter is the irradiance produced by radiant flux of one watt, distributed uniformly over an element having a surface of one square meter, and containing the point source. ( W/m² = 1 W / 1m² ) |
| Radiance | W/m².sr or W.m¯².sr¯¹ | watt per square meter steradian |
The watt per square meter steradian is the radiance of a source radiating one watt per steradian per square meter of projected area. (1 W/m².sr = 1 W/ 1m².1sr ) |
| Luminance | cd/m² or cd.m¯² |
candela per square meter |
The candela per square metre is the luminance perpendiculer to the plane surface of 1 square meter of a source of which the luminous intensity perpendicular to that surface is 1 candela ( 1 cd/m² = 1 cd / 1m² ) |
| Luminous flux | lm |
lumen |
The lumen is the luminous flux emitted in the solid angle of 1 steradian by a uniform point source having a luminous intensity of 1 candela. ( 1 lm = 1 sd. 1 sr) |
| Illuminance | lx |
lux |
The lux is the illuminance of a surface receiving a luminous flux of 1 lumen, uniformaly distributed over 1 square meter of the surface. ( 1 lx = 1 lm / 1m²) |
(F). The derived units in relation to ionizing radiation
Derived Quantity |
Symbol |
Name |
Definition |
|---|---|---|---|
| Activity (of a radiocative source) | Bq |
becqueral |
The becqueral is the activity of a radioactive source in which a molecular transformation or transition occurs per second ( 1 Bq = 1/ 1s ) |
| Absorbed dose | Gy |
gray |
The gray is the dose absorbed in an element of matter of 1 kilogramme mass to which the energy of 1 joule is communicated by ionizing radiation whose energy fluence to constant. ( 1 Gy = 1J / 1 kg) |
| Exposure | C/kg or C.kg¯¹ |
coulomb per kilogramme |
The coulomb per kilogramme is the exposure of a photonic ionizing radiation which can produce in a quantity of air of 1 kilogramme mass, ions of one sign carrying a total electric charge of 1 coulomb. the energy fluence being uniform in the quantity of air considered. ( 1 C/kg = 1 C/ 1 kg) |
(G). The derived units in relation to Physical chemistry and Molecular physics
Derived Quantity |
Symbol |
Name |
Definition |
|---|---|---|---|
| Concentration( of amount of substances) | mol / m³ or mol.m¯ ³ |
mole per cubic meter |
The mole per cubic meter is the concentration of a homogeneous solution having a total volume of one cubic meter and containing one mole of the given substance. ( 1 mol/ m³ = 1 mol / 1 m³) |
| Molar Energy | J/mol or J.mol¯¹ |
joule per mole |
The joule per mole is the molar energy of one mole of substance having the energy of one joule. ( 1 J/ mol = 1 J / 1 mol) |
| Molar Entropy | J /mol .K or J.mol¯¹ .K¯¹ |
joule per mole kelvin |
The joule per mole kelvin is the molar entropy of a system of homogeneous mass having a substance equal to one mole receiving a quantity of heat equal to one joule at the constant thermodynamic temperature of one kelvin, provided that no irreversible change takes place in the system. ( 1 J/mol.K = 1J/1 mol.1 K) |
Names, Magnitudes and symbols of SI prefixes and principles of use of SI prefixes
The decimal multiples and sub-multiples of SI units are formed by means of the decimal numerical factors set out in the following article, by which the SI unit concerned is multiplied.
The names of the decimal multiples and sub- multiples of the SI units are formed by means of SI prefixes designating the decimal numerical factories.
| Factor | Name |
Symbol |
|---|---|---|
10E18 |
exa |
E |
10E15 |
peta |
p |
| 10E12 | tera |
T |
| 10E9 | giga |
G |
| 10E6 | mega |
M |
| 10E3 | kilo |
k |
| 10E2 | hecto |
h |
| 10E1 | deca |
da |
| 10E-1 | deci |
d |
10E-2 |
centi |
c |
| 10E-3 | milli |
m |
| 10E-6 | micro |
µ |
| 10E-9 | nano |
n |
| 10E-12 | pico |
p |
| 10E-15 | femto |
f |
| 10E-18 | atto |
a |