Dimensions of few quantities

Dimensional formulae 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 ($\Delta P.\frac{V}{\Delta V}$.)	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 =$\eta A\frac{dv}{dx}$)	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 ($\frac{potential\text{ difference}}{current}$)	ohm	ML2T–3I–2
Emf (or) electric potential (work/charge)	volt	ML2T–3I–1
Energy (capacity to do work)	joule	ML2T–2
Energy density ($\frac{energy}{volume}$)	Jm–3	ML–1T–2
Entropy ($\Delta S=\Delta Q/T$)	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 =$\frac{1}{2}L{{I}^{2}}$) 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 ($\mu_o = \frac{4\pi Fd^{2}}{m_1m_2}$)	Hm–1 or NA–2	MLT–2I–2
Permittivity of free space (${{\varepsilon }_{o}}=\frac{{{Q}_{1}}{{Q}_{2}}}{4\pi F{{d}^{2}}}$​.)	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	$\Omega$–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$\left( \frac{heat\ energy}{area\ x\ time\ x\ temperatur{{e}^{4}}} \right)$).	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 ($\frac{change\text{ in temperature}}{\text{distance}}$)	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. $\frac{{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$​)	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