All Dimensional Formula List PDF Download

All Dimensional Formula List PDF


All Dimensional Formula List




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All Dimensional Formula List PDF Download

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Dimensional Formulas

All physical quantities can be expressed in terms of seven fundamental (base) quantities such as mass, length, time, temperature, electric current, luminous intensity, and amount of substance. These seven quantities are called the seven dimensions of the physical world.


The dimensional formula is a compound expression showing how and which of the fundamental quantities are involved in making that physical quantity.

We can use symbols instead of the names of the base quantities. M, L, and T are used to represent the dimensions of the three mechanical quantities mass, length, and time respectively. 

Dimensional Formula List

Here is a list of all the Dimensional Formulas of Physical Quantities.

Sr. NoPhysical QuantityFormulaDimensional FormulaS.I Unit
1Area (A)Length x Breadth[M0L2T0]m2
2Volume (V)Length x Breadth x Height[M0L3T0]m3
3Density (d)Mass / Volume[M1L-3T0]kgm-3
4Speed (s)Distance / Time[M0L1T-1]ms-1
5Velocity (v)Displacement / Time[M0L1T-1]ms-1
6Acceleration (a)Change in velocity / Time[M0L1T-2]ms-2
7Acceleration due to gravity (g)Change in velocity / Time[M0L1T-2]ms-2
8Specific gravityDensity of body/density of water at 4oCNo dimensions [M0L0T-0]No units
9Linear momentum (p)Mass x Velocity[M1L1T-1]kgms-1
10Force (F)Mass x Acceleration[M1L1T-2]N
11Work (W)Force x Distance[M1L2T-2]J (Joule)
12Energy (E)Work[M1L2T-2]J
13Impulse (I)Force x Time[M1L1T-1]Ns
14Pressure (P)Force / Area[M1L-1T-2]Nm-2
15Power (P)Work / Time[M1L2T-3]W
16A Universal constant of gravitation (G)[M-1L3T-2]Nm2kg-2
17Moment of inertia (I)Mass x (distance)2[M1L2T0]kgm2
18Moment of force, moment of coupleForce x distance[M1L2T-2]Nm
19Surface tension (T)Force / Length[M1L0T-2]Nm-1
20Surface energy (E)Energy/unit area[M1L0T-2]Nm-1
21Force constant (x)Force / Displacement[M1L0T-2]Nm-1
22Coefficient of viscosity ( η )[M1L-1T-1]Nsm-2
23Thrust (F)Force[M1L1T-2]N
24Tension (T)Force[M1L1T-2]N
25StressForce / Area[M1L-1T-2]Nm-2
26StrainChange in dimension / Original dimensionNo dimensions [M0L0T-0]No unit
27Modulus of Elasticity (E)Stress/strain[M1L-1T-2]Nm-2
28Radius of gyration (k)Distance[M0L1T0]m
29Angle ( θ), Angular displacementArc length / RadiusNo dimensions [M0L0T-0]rad
30Trigonometric ratio ( sin θ, cos θ, tan θ, etc)Length/lengthNo dimensions [M0L0T-0No unit
31Angular velocity( ω )Angle / Time[M0L0T-1]rad s-1
32Angular acceleration( α )Angular velocity / Time[M0L0T-2]rad s-2
33Angular momentum (J)Moment of inertia x Angular velocity[M1L2T-1]kgm2s-1
34Torque (𝞽)Moment of inertia x Angular acceleration[M1L2T-2]Nm
35Velocity gradient Velocity / Distance[M0L0T-1]s-1
36Rate flowVolume / Time[M0L3T-1]m3s-1
37Wavelength( 𝛌 )Length of a wavelet[M0L1T0]m
38Frequency(\large \begin{aligned} \nu \end{aligned})Number of vibrations/second or 1/time period[M0L0T-1]Hz or s-1
39Angular frequency (ω)2π x frequency[M0L0T-1]
40Planck’s constant (h)Energy / Frequency[M1L2T-1]Js
41Buoyant forceForce[M1L1T-2]N
42Relative densityDensity of substance/ density of water at 4oCNo dimensions [M0L0T-0]No unit
43Pressure gradientPressure / Distance[M1L-2T-2]Nm-3
44Pressure energyPressure x Volume[M1L2T-2]J
46Heat (Q)Energy[M1L2T-2]J
47Latent heat (L)Heat / Mass[M0L2T-2]Jkg-1
48Specific heat (S)[M0L2T-2K-1]Jkg-1K-1
49Thermal expansion coefficient or thermal expansivity[M0L0T0K-1]K-1
50Thermal conductivity[M1L1T-3K-1]Wm-1K-1
51Bulk modulus or (compressibility)-1[M1L-1T-2]Nm-2 or Pascals
52Centripetal acceleration[M0L1T-2]
53Stefan constant (σ)[M1L0T-3K-4]Wm−2K−4 
54Wien constantWavelength X temperature[M0L1T0K1]mK
55Gas constant (R)[M1L2T-2K-1]JK-1
56Boltzmann constant (K)Energy/temperature[M1L2T-2K-1]JK-1
57Charge (q)Current x time[M0L0T1A1]C
58Current densityCurrent / area[M0L-2T0A1]A m−2
59Electric potential (V), voltage, electromotive forceWork / Charge[M1L2T–3A-1]V
60Resistance (R)Potential difference / Current[M1L2T–3A-2]ohms (Ω)
61CapacitanceCharge / potential difference[M1L2T4A2]F (Farad)
62Electrical resistivity or (electrical conductivity)-1[M1L3T-3A2]Ωm ( resistivity)
63Electric field (E)Force / Charge[M1L1T-3A-1]NC-1
64Electric fluxElectric field X area[M1L3T3A-1]Nm2C-1
65Electric dipole momentTorque / electric field[M0L1T1A1]C m
66Electric field strength or electric intensityPotential difference/ distance[M1L1T-3A-1]NC-1
67Magnetic field (B), magnetic flux density, magnetic induction[M1L0T-2A-1]T (Tesla)
68Magnetic flux (Φ)Magnetic field X area[M1L2T-2A-1]Wb (Weber)
69InductanceMagnetic flux/current[M1L2T-2A-2]H (Henry)
70Magnetic dipole momentTorque /field
current X area
71Magnetic field strength (H), magnetic intensity, or magnetic moment densityMagnetic moment/volume[M0L-1T0A1]Am-1
72Hubble constantRecession speed/distance[M0L0T-1]s-1
73Intensity of wave(Energy/time)/area[M1L0T-3]Wm-2
74Radiation pressureIntensity of wave/speed of light[M1L1T-2]
75Energy densityEnergy/volume[M1L-1T-2]Jm-3
76Critical velocity[M0L1T-1]ms-1
77Escape velocity[M0L1T-1]ms-1
78Heat energy, internal energyWork ( = Force X distance)[M1L2T-2]J
79Kinetic energy[M1L2T-2]J
80Potential energyMass X acceleration due to gravity X height[M1L2T-2]J
81Rotational kinetic energy[M1L2T-2]J
82EfficiencyNo dimensions [M0L0T0]No unit
83Angular impulseTorque X time[M1L2T-1]Js (Joule second)
84Permittivity constant (of free space)[M-1L-3T4A2]F m-1
85Permeability constant (of free space)[M1L1T-2A-2]NA-2
86Refractive indexNo  dimensions [M0L0T0]No unit
87Faraday constant (F)Avogadro constant X elementary charge[M0L0T1Amol-1]C mol-1
88Wave number[M0L-1T0]
89Radiant flux, Radiant powerThe energy emitted / time[M1L2T-3]W(Watt)
90Luminosity of radiant flux or radiant intensity[M1L2T-3]W sr-1 (Watt/steradian)
91Luminous power or luminous flux of source[M1L2T-3]lm (lumen)
92Luminous intensity or illuminating power of sourceLuminous flux / Solid angle[M1L2T-3]cd (candela)
93Intensity of illumination or luminance (Lv)[M1L0T-3]cd m-2
94Relative luminosityLuminous flux of a source of given wavelength / luminous flux of peak sensitivity wavelength(555 nm) source of the same powerNo dimensions [M0L0T0]No unit
95Luminous efficiencyTotal luminous flux / Total radiant fluxNo dimensions [M0L0T0]No unit
96Illuminance or illuminationLuminous flux incident / Area[M1L0T-3]lx (lux)
97Mass defect(Sum of masses of nucleons) – (mass of the nucleus)[M1L0T0]
98The Binding energy of a nucleus[M1L2T-2]
99Decay constant0.693 / half-life[M0L0T-1]
100Resonant frequency[M0L0T-1A0]
101Quality factor or Q-factor of coilNo dimensions [M0L0T0]No unit
102Power of lens[M0L-1T0]D (dioptre)
103MagnificationImage distance / Object distanceNo dimensions [M0L0T0]No unit
104Fluid flow rate[M0L3T-1]m3s-1
105Capacitive reactance (Xc)(Angular frequency X capacitance)-1[M1L2T-3A-2]ohms (Ω)
106Inductive reactance (XL)(Angular frequency X inductance)[M1L2T-3A-2]ohms (Ω)


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