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Units and Dimensional Formulas of Physical Quantities

Physical quantity Unit Dimensional formula
Acceleration or acceleration due to gravity ms–2 LT–2
Angle (arc/radius) rad MoLoTo
Angular displacement rad MoloTo
Angular frequency (angular displacement/time) rads–1 T–1
Angular impulse (torque x time) Nms ML2T–1
Angular momentum (Iω) kgm2s–1 ML2T–1
Angular velocity (angle/time) rads–1 T–1
Area (length x breadth) m2 L2
Boltzmann’s constant JK–1 ML2T–2θ–1
Bulk modulus (ΔP.VΔVΔPVV.) Nm–2, Pa M1L–1T–2
Calorific value Jkg–1 L2T–2
Coefficient of linear or areal or volume expansion oC–1 or K–1 θ–1
Coefficient of surface tension (force/length) Nm–1 or Jm–2 MT–2
Coefficient of thermal conductivity Wm–1K–1 MLT–3θ–1
Coefficient of viscosity (F =ηAdv/dx) poise ML–1T–1
Compressibility (1/bulk modulus) Pa–1, m2N–2 M–1LT2
Density (mass / volume) kgm–3 ML–3
Displacement, wavelength, focal length m L
Electric capacitance (charge/potential) CV–1, farad M–1L–2T4I2
Electric conductance (1/resistance) Ohm–1 or mho or siemen M–1L–2T3I2
Electric conductivity (1/resistivity) siemen/metre or Sm–1 M–1L–3T3I2
Electric charge or quantity of electric charge (current x time) coulomb IT
Electric current ampere I
Electric dipole moment (charge x distance) Cm LTI
Electric field strength or Intensity of electric field (force/charge) NC–1, Vm–1 MLT–3I–1
Electric resistance (potential differencecurrentcurrentpotential difference) ohm ML2T–3I–2
Emf (or) electric potential (work/charge) volt ML2T–3I–1
Energy (capacity to do work) joule ML2T–2
Energy density (energyvolumevolumeenergy) Jm–3 ML–1T–2
Entropy (ΔS=ΔQ/TΔSQ/T) Jθ–1 ML2T–2θ–1
Force (mass x acceleration) newton (N) MLT–2
Force constant or spring constant (force/extension) Nm–1 MT–2
Frequency (1/period) Hz T–1
Gravitational potential (work/mass) Jkg–1 L2T–2
Heat (energy) J or calorie ML2T–2
Illumination (Illuminance) lux (lumen/metre2) MT–3
Impulse (force x time) Ns or kgms–1 MLT–1
Inductance (L) (energy =12LI221LI2) or

coefficient of self-induction

henry (H) ML2T–2I–2
Intensity of gravitational field (F/m) Nkg–1 L1T–2
Intensity of magnetization (I) Am–1 L–1I
Joule’s constant or mechanical equivalent of heat Jcal–1 MoLoTo
Latent heat (Q = mL) Jkg–1 MoL2T–2
Linear density (mass per unit length) kgm–1 ML–1
Luminous flux lumen or (Js–1) ML2T–3
Magnetic dipole moment Am2 L2I
Magnetic flux (magnetic induction x area) weber (Wb) ML2T–2I–1
Magnetic induction (F = Bil) NI–1m–1 or T MT–2I–1
Magnetic pole strength (unit: ampere–meter) Am LI
Modulus of elasticity (stress/strain) Nm–2, Pa ML–1T–2
Moment of inertia (mass x radius2) kgm2 ML2
Momentum (mass x velocity) kgms–1 MLT–1
Permeability of free space (μo=4πFd2m1m2μo=m1m24πFd2) Hm–1 or NA–2 MLT–2I–2
Permittivity of free space (εo=Q1Q24πFd2εo=4πFd2Q1Q2.) Fm–1 or C2N–1m–2 M–1L–3T4I2
Planck’s constant (energy/frequency) Js ML2T–1
Poisson’s ratio (lateral strain/longitudinal strain) –– MoLoTo
Power (work/time) Js–1 or watt (W) ML2T–3
Pressure (force/area) Nm–2 or Pa ML–1T–2
Pressure coefficient or volume coefficient oC–1 or θ–1 θ–1
Pressure head m MoLTo
Radioactivity disintegrations per second MoLoT–1
Ratio of specific heats –– MoLoTo
Refractive index –– MoLoTo
Resistivity or specific resistance ΩΩ–m ML3T–3I–2
Specific conductance or conductivity (1/specific resistance) siemen/metre or Sm–1 M–1L–3T3I2
Specific entropy (1/entropy) KJ–1 M–1L–2T2θ
Specific gravity (density of the substance/density of water) –– MoLoTo
Specific heat (Q = mst) Jkg–1θ–1 MoL2T–2θ–1
Specific volume (1/density) m3kg–1 M–1L3
Speed (distance/time) ms–1 LT–1
Stefan’s constant(heat energyarea x time x temperature4)(area x time x temperature4heat energy). Wm–2θ–4 MLoT–3θ–4
Strain (change in dimension/original dimension) –– MoLoTo
Stress (restoring force/area) Nm–2 or Pa ML–1T–2
Surface energy density (energy/area) Jm–2 MT–2
Temperature oC or θ MoLoToθ
Temperature gradient (change in temperaturedistancedistancechange in temperature) oCm–1 or θm–1 MoL–1Toθ
Thermal capacity (mass x specific heat) Jθ–1 ML2T–2θ–1
Time period second T
Torque or moment of force (force x distance) Nm ML2T–2
Universal gas constant (work/temperature) Jmol–1θ–1 ML2T–2θ–1
Universal gravitational constant (F = G. m1m2d2d2m1m2) Nm2kg–2 M–1L3T–2
Velocity (displacement/time) ms–1 LT–1
Velocity gradient (dv/dx) s–1 T–1
Volume (length x breadth x height) m3 L3
Water equivalent kg MLoTo
Work (force x displacement) J ML2T–2

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