All Dimensional Formula List PDF

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All-Dimensional Formula List With SI Unit

What do you mean by dimensions of physical quantity?

Each derived quantity requires proper power for fundamental quantities to represent it. The powers of fundamental quantities, through which they are to be raised to represent unit-derived quantity, are called dimensions. In other words, the dimensions of a physical quantity are the powers to which the base quantities (fundamental quantities) are raised to represent that quantity.

For example:

  • The area is the product of two lengths.
    Area = Length X breadth = [L] x [L] = [L2]
    Therefore, [A] = [L2] That is, the dimension of the area is 2 dimensions in length and zero dimensions in mass and time.
    Or [A] = [M0L2T0]
  • Similarly, the volume is the product of three lengths.
    Volume = Length X breadth X height = [L] x [L] x [L] = [L3]
    Therefore, [V] = [L3] That is, the dimension of volume is 3 dimensions in length and zero in mass and time.
    Or [V] = [M0L3T0]
  • Similarly, acceleration is the rate of change of velocity per unit of time.
Sl. 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]gms-1
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]The universal constant of gravitation (G)
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
16Energy/unit area\large\begin{aligned}\frac{Force \times (distance)^{2}}{(mass)^{2}}\end{aligned}[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)Stress/strain[M1L0T-2]Nm-1
21Force constant (x)Force / Displacement[M1L0T-2]Nm-1
22Coefficient of viscosity ( η )\large\begin{aligned}\frac{Force}{area\times velocity\;gradient}\end{aligned}[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)Length/length[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)Density of substance/density of water at 4oCNo 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 (????)Moment of inertia x Angular acceleration[M1L2T-2]Nm
35Velocity gradient \large \begin{aligned} \left ( \frac{dv}{dx} \right ) \end{aligned}Velocity / Distance[M0L0T-1]s-1
36Rate flowVolume / Time[M0L3T-1]m3s-1
37Wavelength( ???? )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 densityPressure / DistanceNo dimensions [M0L0T-0]No unit
43Pressure gradientEnergy/temperature[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)\begin{aligned} \frac{Heat}{Mass\times temperature}\end{aligned}[M0L2T-2K-1]Jkg-1K-1
49Thermal expansion coefficient or thermal expansivity\begin{aligned}\frac{Change\;in\;dimension}{original\;dimension\times temperature}\end{aligned}[M0L0T0K-1]K-1
50Thermal conductivity\begin{aligned}\frac{Heat\;energy\times thickness}{Area\times temperature\times time}\end{aligned}[M1L1T-3K-1]Wm-1K-1
51Bulk modulus or (compressibility)-1\begin{aligned}\frac{Volume\times (change\;in\;pressure)}{(change\;in\;volume)}\end{aligned}[M1L-1T-2]Nm-2 or Pascals
52Centripetal acceleration\begin{aligned}\frac{(velocity)^2}{radius}\end{aligned}[M0L1T-2]
53Stefan constant (σ)\begin{aligned}\frac{(Energy / area \times time)}{(temperature)^4}\end{aligned}[M1L0T-3K-4]Wm−2K−4 
54Wien constantWavelength X temperature[M0L1T0K1]mK
55Gas constant (R)\begin{aligned} \frac{Pressure \times Volume}{Temperature}\end{aligned}[M1L2T-2K-1]JK-1
56Boltzmann constant (K)Potential difference/distance[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\begin{aligned}\frac{Resistance \times area}{length}\end{aligned}[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 intensityMagnetic flux/current[M1L1T-3A-1]NC-1
67Magnetic field (B), magnetic flux density, magnetic induction\begin{aligned}\frac{Force}{current \times length}\end{aligned}[M1L0T-2A-1]T (Tesla)
68Magnetic flux (Φ)Magnetic field X area[M1L2T-2A-1]Wb (Weber)
69InductanceMagnetic field strength (H), magnetic intensity, or magnetic moment density[M1L2T-2A-2]H (Henry)
70Magnetic dipole momentTorque /field
current X area
71Magnetic moment/volumeRecession speed/distance[M0L-1T0A1]Am-1
72Hubble constantIntensity of wave/speed of light[M0L0T-1]s-1
73Intensity of wave(Energy/time)/area[M1L0T-3]Wm-2
74Radiation pressureEnergy/volume[M1L1T-2]
75Energy densityPermittivity constant (of free space)[M1L-1T-2]Jm-3
76Critical velocity\begin{aligned}\frac{Reynold's\;number \times coefficient\;of\;viscocity}{Mass\; density \times radius}\end{aligned}[M0L1T-1]ms-1
77Escape velocity\begin{aligned}(2 \times acceleration\;due\;to\;gravity\times earth's\;radius)^{1/2}\end{aligned}[M0L1T-1]ms-1
78Heat energy, internal energyWork ( = Force X distance)[M1L2T-2]J
79Kinetic energy\begin{aligned}\frac{1}{2}mass \times (velocity)^{2}\end{aligned}[M1L2T-2]J
80Potential energyMass X acceleration due to gravity X height[M1L2T-2]J
81Rotational kinetic energy\begin{aligned}\frac{1}{2}\times moment\;of\;inertia\times (angular\;velocity)^{2}\end{aligned}[M1L2T-2]J
82Efficiency\begin{aligned}\frac{output\;work\;or\;energy}{input\;work\;or\;energy}\end{aligned}No dimensions [M0L0T0]No unit
83Angular impulseTorque X time[M1L2T-1]Js (Joule second)
84The energy emitted / time\begin{aligned}\frac{Charge \times charge}{4\pi\times electric\;force\times (distance)^{2} }\end{aligned}[M-1L-3T4A2]F m-1
85Permeability constant (of free space)\begin{aligned}\frac{2\pi \times force\times distance}{current\times current\times length}\end{aligned}[M1L1T-2A-2]NA-2
86Refractive index\begin{aligned}\frac{Speed\;of\;light\;in\;vacuum}{Speed\;of\;light\;in\;medium}\end{aligned}No  dimensions [M0L0T0]No unit
87Faraday constant (F)Avogadro constant X elementary charge[M0L0T1Amol-1]C mol-1
88Wave number\begin{aligned}\frac{2\pi }{wavelength}\end{aligned}[M0L-1T0]
89Radiant flux, Radiant powerBinding energy of the nucleus[M1L2T-3]W(Watt)
90Luminosity of radiant flux or radiant intensity\begin{aligned}\frac{Radiant\;power\;or\;radiant\;flux\;of\;source}{Solid\;angle}\end{aligned}[M1L2T-3]W sr-1 (Watt/steradian)
91Luminous power or luminous flux of source\begin{aligned}\frac{Luminous\;energy\;emitted}{time}\end{aligned}[M1L2T-3]lm (lumen)
92Luminous intensity or illuminating power of sourceLuminous flux / Solid angle[M1L2T-3]cd (candela)
93Intensity of illumination or luminance (Lv)\begin{aligned}\frac{Luminous\;intensity}{(distance)^{2}}\end{aligned}[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]
98Binding energy of nucleus\begin{aligned}Mass\;defect\times (Speed\;of\;light\;in\;vacuum)^{2}\end{aligned}[M1L2T-2]
99Decay constant0.693 / half-life[M0L0T-1]
100Resonant frequency\begin{aligned}(Inductance\times capacitance)^{-1/2}\end{aligned}[M0L0T-1A0]
101Quality factor or Q-factor of coil\begin{aligned}\frac{Resonant\;frequency \times inductance}{Resistance}\end{aligned}No dimensions [M0L0T0]No unit
102Power of lens\begin{aligned}\frac{1}{focal\;length}\end{aligned}[M0L-1T0]D (dioptre)
103MagnificationImage distance / Object distanceNo dimensions [M0L0T0]No unit
104Fluid flow rate\begin{aligned}\frac{(\pi /8)(pressure)\times (radius)^{4}}{Viscosity\;coefficient\times length}\end{aligned}[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)
Language English
No. of Pages5
PDF Size0.1 MB

All Dimensional Formula List PDF Free Download

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