Dimensional Formula of Physical Quantities : Dimensional Formula of Physical Quantities: In this post,we are sharing most important dimensional formula of physical quantities. Download PDF now. The first table lists the base quantities used in the International System of Units to define the physical dimension of physical quantities for dimensional analysis. The second table lists the derived physical quantities. Derived quantities can be mentioned in terms of the base quantities. Note that neither the names nor the symbols used for the physical quantities are international standards. Some quantities are known as several different names such as the magnetic B-field which known as the magnetic flux density, the magnetic induction or simply as the magnetic field depending on the context. Similarly, surface tension can be denoted by either σ, γ or T. The table usually lists only one name and symbol. The final column lists some special properties that some of the quantities have, such as their scaling behavior (i.e. whether the quantity is intensive or extensive), their transformation properties (i.e. whether the quantity is a scalar, vector or tensor) or whether the quantity is conserved.Dimensional Formula of Physical Quantities

Dimensional Formula of Physical Quantities

Derived quantityDescriptionSI derived unitDimensionComments
AbsementMeasure of sustained displacement: the first integral of displacementm sL Tvector
Absorbed dose rateAbsorbed dose received per unit of timeGy s−1L2 T−3
AccelerationChange of the speed or velocity per unit timem s−2L T−2vector
Angular accelerationChange in angular speed or velocity per unit timerad s−2T−2
Angular momentumMeasure of the extent and direction an object rotates about a reference pointkg m2 s−1M L2 T−1conserved quantity, pseudovector
Angular speed (or angular velocity)The angle incremented in a plane by a segment connecting an object and a reference point per unit timerad s−1T−1scalar or pseudovector
AreaExtent of a surfacem2L2scalar
Area densityMass per unit areakg m−2M L−2
CapacitanceStored charge per unit electric potentialfarad (F = A2 s4 kg−1 m−2)M−1 L−2 T4 I2scalar
Catalytic activityChange in reaction rate due to presence of a catalystkatal (kat = mol s−1)T−1 N
Catalytic activity concentrationChange in reaction rate due to presence of a catalystper unit volume of the systemkat m−3L−3 T−1 N
Chemical potentialEnergy per unit change in amount of substanceJ mol−1M L2 T−2 N−1intensive
CrackleChange of jounce per unit time: the fifth time derivative of positionm s−5L T−5vector
Current densityElectric current per unit cross-section areaA m−2L−2 Ivector
Dose equivalentReceived radiation adjusted for the effect on biological tissuesievert (Sv = m2 s−2)L2 T−2
Dynamic viscosityMeasure for the resistance of an incompressible fluid to stressPa sM L−1 T−1
Electric chargeThe force per unit electric field strengthcoulomb (C = A s)T Iextensive, conserved quantity
Electric charge densityElectric charge per unit volumeC m−3L−3 T Iintensive
Electric displacementStrength of the electric displacementC m−2L−2 T Ivector field
Electric field strengthStrength of the electric fieldV m−1M L T−3 I−1vector field
Electrical conductanceMeasure for how easily current flows through a materialsiemens (S = A2 s3 kg−1 m−2)M−1 L−2 T3 I2scalar
Electrical conductivityMeasure of a material’s ability to conduct an electric currentS m−1M−1 L−3 T3 I2scalar
Electric potentialEnergy required to move a unit charge through an electric field from a reference pointvolt (V = kg m2 A−1 s−3)M L2 T−3 I−1extensive, scalar
Electrical resistanceElectric potential per unit electric currentohm (Ω = kg m2 A−2 s−3)M L2 T−3 I−2extensive, scalar, assumes linearity
Electrical resistivityBulk property equivalent of electrical resistanceohm metre (Ω⋅m = kg m3 A−2 s−3)M L3 T−3 I−2intensive, scalar
EnergyCapacity of a body or system to do workjoule (J = kg m2 s−2)M L2 T−2extensive, scalar, conserved quantity
Energy densityEnergy per unit volumeJ m−3M L−1 T−2intensive
EntropyLogarithmic measure of the number of available states of a systemJ K−1M L2 T−2 Θ−1extensive, scalar
ForceTransfer of momentum per unit timenewton (N = kg m s−2)M L T−2extensive, vector
FrequencyNumber of (periodic) occurrences per unit timehertz (Hz = s−1)T−1scalar
Fuel efficiencyDistance traveled per unit volume of fuelm m-3 ( = m/m3)L−2scalar
Half-lifeTime for a quantity to decay to half its initial valuesT
HeatThermal energyjoule (J)M L2 T−2
Heat capacityEnergy per unit temperature changeJ K−1M L2 T−2 Θ−1extensive
Heat flux densityHeat flow per unit time per unit surface areaW m−2M T−3
IlluminanceLuminous flux per unit surface arealux (lx = cd sr m−2)L−2 J
ImpedanceResistance to an alternating current of a given frequency, including effect on phaseohm (Ω = kg m2 A−2 s−3)M L2 T−3 I−2complex scalar
ImpulseTransferred momentumnewton second (N⋅s = kg m s−1)M L T−1vector
InductanceMagnetic flux generated per unit current through a circuithenry (H = kg m2 A−2 s−2)M L2 T−2 I−2scalar
IrradianceElectromagnetic radiation power per unit surface areaW m−2M T−3
IntensityPower per unit cross sectional areaW m−2M T−3
JerkChange of acceleration per unit time: the third time derivative of positionm s−3L T−3vector
Jounce (or snap)Change of jerk per unit time: the fourth time derivative of positionm s−4L T−4vector
Kinematic viscosityDynamic viscosity/densitym2 s−1L2 T−1scalar
Linear densityMass per unit lengthkg m−1M L−1
Luminous flux (or luminous power)Perceived power of a light sourcelumen (lm = cd sr)J
Mach number (or mach)Ratio of flow velocity to the local speed of soundunitless1
Magnetic field strengthStrength of a magnetic fieldA m−1L−1 Ivector field
Magnetic fluxMeasure of magnetism, taking account of the strength and the extent of a magnetic fieldweber (Wb = kg m2 A−1 s−2)M L2 T−2 I−1scalar
Magnetic flux densityMeasure for the strength of the magnetic fieldtesla (T = kg A−1 s−2)M T−2 I−1pseudovector field
MagnetizationAmount of magnetic moment per unit volumeA m−1L−1 Ivector field
Mass fractionMass of a substance as a fraction of the total masskg/kg1intensive
(Mass) Density (or volume density)Mass per unit volumekg m−3M L−3intensive
Mean lifetimeAverage time for a particle of a substance to decaysTintensive
Molar concentrationAmount of substance per unit volumemol m−3L−3 Nintensive
Molar energyAmount of energy present in a system per unit amount of substanceJ mol−1M L2 T−2 N−1intensive
Molar entropyEntropy per unit amount of substanceJ K−1 mol−1M L2 T−2 Θ−1N−1intensive
Molar heat capacityHeat capacity of a material per unit amount of substanceJ K−1 mol−1M L2 T−2 Θ−1N−1intensive
Moment of inertiaInertia of an object with respect to angular accelerationkg m2M L2tensor, scalar
MomentumProduct of an object’s mass and velocityN sM L T−1vector, extensive
PermeabilityMeasure for how the magnetization of material is affected by the application of an external magnetic fieldH m−1M L T−2 I−2intensive
PermittivityMeasure for how the polarization of a material is affected by the application of an external electric fieldF m−1M−1 L−3 T4 I2intensive
Plane angleRatio of circular arc length to radiusradian (rad)1
PowerRate of transfer of energy per unit timewatt (W)M L2 T−3extensive, scalar
PressureForce per unit areapascal (Pa = kg m−1 s−2)M L−1 T−2intensive, scalar
PopRate of change of crackle per unit time: the sixth time derivative of positionm s−6L T−6vector
(Radioactive) ActivityNumber of particles decaying per unit timebecquerel (Bq = s−1)T−1extensive, scalar
(Radioactive) DoseIonizing radiation energy absorbed by biological tissue per unit massgray (Gy = m2 s−2)L2 T−2
RadiancePower of emitted electromagnetic radiation per unit solid angle per emitting source areaW m−2 sr−1M T−3
Radiant intensityPower of emitted electromagnetic radiation per unit solid angleW sr−1M L2 T−3scalar
Reaction rateRate of a chemical reaction for unit timemol m−3 s−1N L−3 T−1intensive, scalar
Refractive indexFactor by which the phase velocity of light is reduced in a mediumunitless1intensive, scalar
Reluctanceresistance to the flow of magnetic fluxH−1M-1 L-2 T2 I2scalar
Solid angleRatio of area on a sphere to its radius squaredsteradian (sr)1
SpeedMoved distance per unit time: the first time derivative of positionm s−1L T−1scalar
Specific energyEnergy density per unit massJ kg−1L2 T−2intensive
Specific heat capacityHeat capacity per unit massJ kg−1 K−1L2 T−2 Θ−1intensive
Specific volumeVolume per unit mass (reciprocal of density)m3 kg−1M−1 L3intensive
SpinQuantum-mechanically defined angular momentumof a particlekg m2 s−1M L2 T−1
StrainExtension per unit lengthunitless1
StressForce per unit oriented surface areaPaM L−1 T−2order 2 tensor
Surface tensionEnergy change per unit change in surface areaN m−1 or J m−2M T−2
Temperature gradientsteepest rate of temperature change at a particular locationK m−1Θ L−1vector
Thermal conductivityMeasure for the ease with which a material conducts heatW m−1 K−1M L T−3 Θ−1intensive
TorqueProduct of a force and the perpendicular distance of the force from the point about which it is exertednewton metre (N m)M L2 T−2bivector (or pseudovector in 3D)
VelocitySpeed and direction of an objectm s−1L T−1vector
VolumeThree dimensional extent of an objectm3L3extensive, scalar
Volumetric flowRate of change of volume per unit timem3 s-1L3 T-1extensive, scalar
WavelengthPerpendicular distance between repeating units of a wavemL
WavenumberRepetency or spacial frequency: the number of cycles per unit distancem−1L−1scalar
WavevectorRepetency or spacial frequency vector: the number of cycles per unit distancem−1 with directionL−1vector
WeightGravitational force on an objectnewton (N = kg m s−2)M L T−2vector
WorkTransferred energyjoule (J = kg m2 s−2)M L2 T−2scalar
Young’s modulusRatio of stress to strainpascal (Pa = kg m−1 s−2)M L−1 T−2scalar; assumes isotropic linear material
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