Dimensional formula with SI unit

Read dimensional formula of various physical quantity including their formula, their SI unit and denotation.
I hope, this post will help many students.

Please use Desktop mode or Rotate your device vertically to read comfortably In your MOBILE.

FUNDAMENTAL PHYSICAL QUANTITY	S.I. UNIT	DIMENSIONAL FORMULA
MASS(m)	Kg (Kilogram)	[M]
LENGTH(l)	m (metre)	[L]
TIME(t)	S (second)	[T]
TEMPERATURE(T)	K (kelvin)	[K]
ELECTRIC CURRENT(I)	A (ampere)	[A]
AMOUNT OF SUBSTANCE(n)	mol (mole)	[mol]
LUMINOUS INTENSITY	Cd (candela)	[cd]

DERIVED PHYSICAL QUANTIY	FORMULA	S.I. UNIT	DIMENSIONAL FORMULA
Area(A)	LENGTH*LENGTH	m2	[L2]
Volume(V)	L*L*L	m3	[L3]
Density(ρ, σ)	Mass/Volume	Kg/m3	[ML-3]
Angle(θ)	Arc/Radius	radian	Dimensionless
Distance(x)	LENGTH	m	[L]
Speed or velocity(v)	DISTANCE/TIME	m/s	[LT-1]
Acceleration(a)	VELOCITY/TIME	m/s2	[LT-2]
Force/thrust/tension(F)	MASS*ACCELERATION	N or Kg m/s2	[MLT-2]
Linear momentum(P)	MASS*VELOCITY	Kg m/s	[MLT-1]
Impulse(I)	FORCE*TIME	Ns	[MLT-1]
Pressure(P)	FORCE/AREA	Pa or N/m2	[ML-1T-2]
Frequency(ν)	1/TIME	Hz or PER SECOND	[T-1]
Angular velocity(ω)	ANGLE/TIME	Rad/S	[T-1]
Torqe(τ)	FORCE*LENGTH	Nm	[ML2T-2]
Angular momentum(L)	L mome.*DISTANCE	Kg m2/s	[ML2T-1]
Angular acceleration(α)	Ang. Velocity./TIME	rad/s2	[T-2]
Moment of inertia(I)	mr2	Kg m2	[ML2]
Velocity gradient	VELOCITY/DISTANCE	Per second	[T-1]
Pressure gradient	PRESSURE/DISTANCE	Kg /m2s2	[ML-2T-2]
Work(W,U)	FORCE*DISTANCE	J or Kg m2/s2	[ML2T-2]
Energy(E)	½mv2  , mgh	J (JOULE)	[ML2T-2]
Heat(Q)		J	[ML2T-2]
Power(P)	WORK/TIME, FORCE*VELOCITY	W(Watt),J/S, N m/s2	[ML2T-3]
Spring or force constant(K)	K=F/X	N/m	[MT-2]
Gravitational constant(G)	G=Fr2/m1*m2	N m2 / Kg2	[M-1L3T-2]
Acceleration due to gravity(g)	g=F/m	m/s2	[LT-2]
Gravitational field(I)	I=Gm/r2	N/Kg	[LT-2]
Gravitational potential(V)	-Gm/r	J/Kg	[L2T-2]
Friction(F)		N	[MLT-2]
Coefficient of friction(μ)	F/R	NO UNIT	DIMENSIONLESS
Coefficient of viscosity(η)	F dx/A dv	N s /m2 ,Decapoise	[ML-1T-1]
Reynold number(R)	VρD/η	NO UNIT	DIMENSIONLESS
Pressure(P)	Force/Area	Pa or N/m2	[ML-1T2]
Stress	Force/Area	Pa or N/m2	[ML-1T2]
Strain	Change in configuration/Original  configuration	NO UNIT	DIMENSIONLESS
Modulus of elasticity(E)	Stress/strain	Pa or N/m2	[ML-1T2]
Young’s modulus of elasticity(Y)	FL/A∆L	Pa or N/m2	[ML-1T2]
Bulk’s modulus of elasticity(B)	-PV/∆V	Pa or N/m2	[ML-1T2]
Compressibility(K)	1/B	m2/N	[M-1LT-2]
Shear modulus of elasticity or modulus of rigidity(G)	FL/A∆L	Pa or N/m2	[ML-1T2]
Poisson ratio(σ)	Lateral Strain/Longitudinal Strain	NO UNIT	DIMENSIONLESS
Surface tension(T)	F/L	N/m	[MT-2]
Surface energy()	E/A	J/m2	[MT-2]
Heat(Q)	Cm∆T	J	[ML2T-2]
Coefficient of linear expansion(α)	ΔL/LΔT	K-1	[K-1]
Coefficient of superficial expansion(β)	ΔA/AΔT	K-1	[K-1]
Coefficient of volume expansion(γ)	ΔV/VΔT	K-1	[K-1]
Specific heat capacity(C)	Q/m∆T	J/Kg k	[L2T-2K-1]
Molar specific heat capacity	MOLECULAR WEIGHT* SPECIFIC HEAT CAPACITY	J/mol k	[ML2T-2K-1mol-1]
Latent heat(L)	Q/M	J/Kg	[L2T-2]
Boltzmann constant	ENERGY/TEMPERATURE	J/K	[ML2T-2K-1]
Thermal conductivity(K)	-Q∆X/AT∆T	J/s m k	[MLT-3K-1]
Electric charge(Q,q)	CURRENT*TIME	COLOUMB	[AT]
Coulomb’s constant(K,1/4 π ε0r)	Fr2/q1q2	N m2/C2	[ML3T-4A-2]
Permittivity(ε)	εrε0  , 1/K	C2 / N m2	[M-1L-3T4A2]
Dipole moment(p)	CHARGE* 2 *LENGTH	C m	[LTA]
Linear charge density(λ)	CHARGE/LENGTH	C /m	[L-1TA]
Surface charge density(σ)	CHARGE/AREA	C /m2	[L-2TA]
Volume charge density(ρ)	CHARGE/VOLUME	C /m3	[L-3TA]
Electric field(E)	FORCE/CHARGE	N/C	[MLT-3A-1]
(Due to other charge)	Kq/r2	N/C	[MLT-3A-1]
(Due to dipole at axial)	2Kp/ r3	N/C	[MLT-3A-1]
(Due to dipole at equatorial)	Kp/ r3	N/C	[MLT-3A-1]
(Due to dipole at ANY POINT)	Kp√(3 Cos2θ +1)/ r3	N/C	[MLT-3A-1]
(Due to uniformly charged long wire)	2λ/4 π ε0r	N/C	[MLT-3A-1]
(Due to uniformly charged plane sheet)	σ/2 ε0	N/C	[MLT-3A-1]
Area vector(A)	ds	m2	[L2]
Electric flux(ϕ)	E*ds	N m2/C	[ML3T-3A-1]
ELECTRIC POTENTIAL(V)	WORK/CHARGE	V(VOLT) , J/C	[ML2T-3A-1]
(Due to other charge)	Kq/r	V	[ML2T-3A-1]
(Due to dipole at axial)	Kp/ r2	V	[ML2T-3A-1]
(Due to dipole at equatorial)	0	V	[ML2T-3A-1]
(Due to dipole at ANY POINT)	Kp Cosθ/ r2
ELECTRIC FIELD(E)	POTENTIAL/DISTANNCE	V/m	[MLT-3A-1]
POLARISATION(P)	DIPOLE MOMENT/VOLUME	p/V	[L-2TA]
SUSCEPTIBILITY(χ)	POLRISATION/ ε0 *E	NO UNIT	DIMENSIONLESS
POLARIZABILITY(P)	DIPOLE MOMENT/ ε0 *E	m3	[L3]
CAPACITANCE(C)	CHARGE/POTENTIAL	F(FARAD) , C/V	[M-1L-2T4A2]
(PARALLEL PLATE CAPACITOR)	A ε0/D	F	[M-1L-2T4A2]
(ISOLATED SPHERICAL CONDUCTOR)	4 π ε0r	F	[M-1L-2T4A2]
Energy Stored In Capacitors(U)	Q2/2C , CV2/2 , QV/2	J	[ML2T-2]
CHARGE(Q)	CAPACITANCE*POTENTIAL	C	[AT]
CURRENT(I)	Q/T , AneVd	A(Ampere), C/s	[A]
CHARGE(Q)	IT , ALne	C	[AT]
DRIFT VELOCITY(Vd)	Eet/m,	m/s	[LT-1]
ELECTRIC FIELD(E)	J ρ , J/ σ	N/C	[MLT-3A-1]
CURRENT DENSITY(J)	I/A , σ  E , E/ρ ,neVd	A/m2	[AL-2]
POTENTIAL DIFFERENCE(V)	I*R	V(VOLT) , J/C	[ML2T-3A-1]
RESISTANCE(R)	V/I , ρ l/A	Ω(Ohm)	[ML2T-3A-2]
RESISTIVITY(ρ)	RA/L	Ωm	[ML3T-3A-1]
CONDUCTANCE(G)	1/R	Ω-1,mho ,simen	[M-1L-2T3A2]
CONDUCTIVITY(σ)	1/ ρ	Ω-1m-1	[M-1L-3T3A2]
COOFICIENT OF RESISTANCE(α)	[R2-R1]/[R1(T2-T1)]	K-1	[K-1]
ELECTRICAL ENERGY	I2RT , VIT, V2T/R	J(JOULE)	[ML2T-2]
ELECTRICAL POWER	I2R , VI, V2/R	W(WATT)	[ML2T-3]

  If want more dimension formula of various physical quantities,then comment below..

Read my other interesting blog.

Thanks
Rahul Kumar

For any confusion or information
Write your queries.
Mail us
Iamriamrahulkr13@gmail