[PDF] All Dimensional Formula List PDF

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All Dimensional Formula List PDF Free Download

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.

\large\begin{aligned}\frac{Force \times (distance)^{2}}{(mass)^{2}}\end{aligned}

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All Dimensional Formula List PDF Free Download

Sl. No	Physical Quantity	Formula	Dimensional Formula	S.I Unit
1	Area (A)	Length x Breadth	[M⁰L²T⁰]	m²
2	Volume (V)	Length x Breadth x Height	[M⁰L³T⁰]	m³
3	Density (d)	Mass / Volume	[M¹L^-3T⁰]	gms^-1
4	Speed (s)	Distance / Time	[M⁰L¹T^-1]	ms^-1
5	Velocity (v)	Displacement / Time	[M⁰L¹T^-1]	ms^-1
6	Acceleration (a)	Change in velocity / Time	[M⁰L¹T^-2]	ms^-2
7	Acceleration due to gravity (g)	Change in velocity / Time	[M⁰L¹T^-2]	ms^-2
8	Specific gravity	Density of body/density of water at 4^oC	No dimensions [M⁰L⁰T^-0]	No units
9	Linear momentum (p)	Mass x Velocity	[M¹L¹T^-1]	The universal constant of gravitation (G)
10	Force (F)	Mass x Acceleration	[M¹L¹T^-2]	N
11	Work (W)	Force x Distance	[M¹L²T^-2]	J (Joule)
12	Energy (E)	Work	[M¹L²T^-2]	J
13	Impulse (I)	Force x Time	[M¹L¹T^-1]	Ns
14	Pressure (P)	Force / Area	[M¹L^-1T^-2]	Nm^-2
15	Power (P)	Work / Time	[M¹L²T^-3]	W
16	Energy/unit area	$\large\begin{aligned}\frac{Force \times (distance)^{2}}{(mass)^{2}}\end{aligned}$	[M^-1L³T^-2]	Nm²kg^-2
17	Moment of inertia (I)	Mass x (distance)²	[M¹L²T⁰]	kgm²
18	Moment of force, moment of couple	Force x distance	[M¹L²T^-2]	Nm
19	Surface tension (T)	Force / Length	[M¹L⁰T^-2]	Nm^-1
20	Surface energy (E)	Stress/strain	[M¹L⁰T^-2]	Nm^-1
21	Force constant (x)	Force / Displacement	[M¹L⁰T^-2]	Nm^-1
22	Coefficient of viscosity ( η )	$\large\begin{aligned}\frac{Force}{area\times velocity\;gradient}\end{aligned}$	[M¹L^-1T^-1]	Nsm^-2
23	Thrust (F)	Force	[M¹L¹T^-2]	N
24	Tension (T)	Force	[M¹L¹T^-2]	N
25	Stress	Force / Area	[M¹L^-1T^-2]	Nm^-2
26	Strain	Change in dimension / Original dimension	No dimensions [M⁰L⁰T^-0]	No unit
27	Modulus of Elasticity (E)	Length/length	[M¹L^-1T^-2]	Nm^-2
28	Radius of gyration (k)	Distance	[M⁰L¹T⁰]	m
29	Angle ( θ), Angular displacement	Arc length / Radius	No dimensions [M⁰L⁰T^-0]	rad
30	Trigonometric ratio ( sin θ, cos θ, tan θ, etc)	Density of substance/density of water at 4^oC	No dimensions [M⁰L⁰T^-0	No unit
31	Angular velocity( ω )	Angle / Time	[M⁰L⁰T^-1]	rad s^-1
32	Angular acceleration( α )	Angular velocity / Time	[M⁰L⁰T^-2]	rad s^-2
33	Angular momentum (J)	Moment of inertia x Angular velocity	[M¹L²T^-1]	kgm²s^-1
34	Torque (????)	Moment of inertia x Angular acceleration	[M¹L²T^-2]	Nm
35	Velocity gradient $\large \begin{aligned} \left ( \frac{dv}{dx} \right ) \end{aligned}$	Velocity / Distance	[M⁰L⁰T^-1]	s^-1
36	Rate flow	Volume / Time	[M⁰L³T^-1]	m³s^-1
37	Wavelength( ???? )	Length of a wavelet	[M⁰L¹T⁰]	m
38	Frequency( $\large \begin{aligned} \nu \end{aligned}$ )	Number of vibrations/second or 1/time period	[M⁰L⁰T^-1]	Hz or s^-1
39	Angular frequency (ω)	2π x frequency	[M⁰L⁰T^-1]
40	Planck’s constant (h)	Energy / Frequency	[M¹L²T^-1]	Js
41	Buoyant force	Force	[M¹L¹T^-2]	N
42	Relative density	Pressure / Distance	No dimensions [M⁰L⁰T^-0]	No unit
43	Pressure gradient	Energy/temperature	[M¹L^-2T^-2]	Nm^-3
44	Pressure energy	Pressure x Volume	[M¹L²T^-2]	J
45	Temperature	——	[M⁰L⁰T⁰K¹]	K
46	Heat (Q)	Energy	[M¹L²T^-2]	J
47	Latent heat (L)	Heat / Mass	[M⁰L²T^-2]	Jkg^-1
48	Specific heat (S)	$\begin{aligned} \frac{Heat}{Mass\times temperature}\end{aligned}$	[M⁰L²T^-2K^-1]	Jkg^-1K^-1
49	Thermal expansion coefficient or thermal expansivity	$\begin{aligned}\frac{Change\;in\;dimension}{original\;dimension\times temperature}\end{aligned}$	[M⁰L⁰T⁰K^-1]	K^-1
50	Thermal conductivity	$\begin{aligned}\frac{Heat\;energy\times thickness}{Area\times temperature\times time}\end{aligned}$	[M¹L¹T^-3K^-1]	Wm^-1K^-1
51	Bulk modulus or (compressibility)^-1	$\begin{aligned}\frac{Volume\times (change\;in\;pressure)}{(change\;in\;volume)}\end{aligned}$	[M¹L^-1T^-2]	Nm^-2 or Pascals
52	Centripetal acceleration	$\begin{aligned}\frac{(velocity)^2}{radius}\end{aligned}$	[M⁰L¹T^-2]
53	Stefan constant (σ)	$\begin{aligned}\frac{(Energy / area \times time)}{(temperature)^4}\end{aligned}$	[M¹L⁰T^-3K^-4]	Wm⁻²K⁻⁴
54	Wien constant	Wavelength X temperature	[M⁰L¹T⁰K¹]	mK
55	Gas constant (R)	$\begin{aligned} \frac{Pressure \times Volume}{Temperature}\end{aligned}$	[M¹L²T^-2K^-1]	JK^-1
56	Boltzmann constant (K)	Potential difference/distance	[M¹L²T^-2K^-1]	JK^-1
57	Charge (q)	Current x time	[M⁰L⁰T¹A¹]	C
58	Current density	Current / area	[M⁰L^-2T⁰A¹]	A m⁻²
59	Electric potential (V), voltage, electromotive force	Work / Charge	[M¹L²T^–3A^-1]	V
60	Resistance (R)	Potential difference / Current	[M¹L²T^–3A^-2]	ohms (Ω)
61	Capacitance	Charge / potential difference	[M^–¹L^–²T⁴A²]	F (Farad)
62	Electrical resistivity or (electrical conductivity)^-1	$\begin{aligned}\frac{Resistance \times area}{length}\end{aligned}$	[M¹L³T^-3A^–²]	Ωm ( resistivity)
63	Electric field (E)	Force / Charge	[M¹L¹T^-3A^-1]	NC^-1
64	Electric flux	Electric field X area	[M¹L³T^–³A^-1]	Nm²C^-1
65	Electric dipole moment	Torque / electric field	[M⁰L¹T¹A¹]	C m
66	Electric field strength or electric intensity	Magnetic flux/current	[M¹L¹T^-3A^-1]	NC^-1
67	Magnetic field (B), magnetic flux density, magnetic induction	$\begin{aligned}\frac{Force}{current \times length}\end{aligned}$	[M¹L⁰T^-2A^-1]	T (Tesla)
68	Magnetic flux (Φ)	Magnetic field X area	[M¹L²T^-2A^-1]	Wb (Weber)
69	Inductance	Magnetic field strength (H), magnetic intensity, or magnetic moment density	[M¹L²T^-2A^-2]	H (Henry)
70	Magnetic dipole moment	Torque /field or current X area	[M⁰L²T⁰A¹]	Am²
71	Magnetic moment/volume	Recession speed/distance	[M⁰L^-1T⁰A¹]	Am^-1
72	Hubble constant	Intensity of wave/speed of light	[M⁰L⁰T^-1]	s^-1
73	Intensity of wave	(Energy/time)/area	[M¹L⁰T^-3]	Wm^-2
74	Radiation pressure	Energy/volume	[M¹L^–¹T^-2]
75	Energy density	Permittivity constant (of free space)	[M¹L^-1T^-2]	Jm^-3
76	Critical velocity	$\begin{aligned}\frac{Reynold's\;number \times coefficient\;of\;viscocity}{Mass\; density \times radius}\end{aligned}$	[M⁰L¹T^-1]	ms^-1
77	Escape velocity	$\begin{aligned}(2 \times acceleration\;due\;to\;gravity\times earth's\;radius)^{1/2}\end{aligned}$	[M⁰L¹T^-1]	ms^-1
78	Heat energy, internal energy	Work ( = Force X distance)	[M¹L²T^-2]	J
79	Kinetic energy	$\begin{aligned}\frac{1}{2}mass \times (velocity)^{2}\end{aligned}$	[M¹L²T^-2]	J
80	Potential energy	Mass X acceleration due to gravity X height	[M¹L²T^-2]	J
81	Rotational kinetic energy	$\begin{aligned}\frac{1}{2}\times moment\;of\;inertia\times (angular\;velocity)^{2}\end{aligned}$	[M¹L²T^-2]	J
82	Efficiency	$\begin{aligned}\frac{output\;work\;or\;energy}{input\;work\;or\;energy}\end{aligned}$	No dimensions [M⁰L⁰T⁰]	No unit
83	Angular impulse	Torque X time	[M¹L²T^-1]	Js (Joule second)
84	The 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
85	Permeability 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
86	Refractive index	$\begin{aligned}\frac{Speed\;of\;light\;in\;vacuum}{Speed\;of\;light\;in\;medium}\end{aligned}$	No dimensions [M⁰L⁰T⁰]	No unit
87	Faraday constant (F)	Avogadro constant X elementary charge	[M⁰L⁰T¹A¹mol^-1]	C mol^-1
88	Wave number	$\begin{aligned}\frac{2\pi }{wavelength}\end{aligned}$	[M⁰L^-1T⁰]
89	Radiant flux, Radiant power	Binding energy of the nucleus	[M¹L²T^-3]	W(Watt)
90	Luminosity 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)
91	Luminous power or luminous flux of source	$\begin{aligned}\frac{Luminous\;energy\;emitted}{time}\end{aligned}$	[M¹L²T^-3]	lm (lumen)
92	Luminous intensity or illuminating power of source	Luminous flux / Solid angle	[M¹L²T^-3]	cd (candela)
93	Intensity of illumination or luminance (`L`_v)	$\begin{aligned}\frac{Luminous\;intensity}{(distance)^{2}}\end{aligned}$	[M¹L⁰T^-3]	cd m^-2
94	Relative luminosity	Luminous flux of a source of given wavelength / luminous flux of peak sensitivity wavelength(555 nm) source of the same power	No dimensions [M⁰L⁰T⁰]	No unit
95	Luminous efficiency	Total luminous flux / Total radiant flux	No dimensions [M⁰L⁰T⁰]	No unit
96	Illuminance or illumination	Luminous flux incident / Area	[M¹L⁰T^-3]	lx (lux)
97	Mass defect	(Sum of masses of nucleons) – (mass of the nucleus)	[M¹L⁰T⁰]
98	Binding energy of nucleus	$\begin{aligned}Mass\;defect\times (Speed\;of\;light\;in\;vacuum)^{2}\end{aligned}$	[M¹L²T^-2]
99	Decay constant	0.693 / half-life	[M⁰L⁰T^-1]
100	Resonant frequency	$\begin{aligned}(Inductance\times capacitance)^{-1/2}\end{aligned}$	[M⁰L⁰T^-1A⁰]
101	Quality factor or Q-factor of coil	$\begin{aligned}\frac{Resonant\;frequency \times inductance}{Resistance}\end{aligned}$	No dimensions [M⁰L⁰T⁰]	No unit
102	Power of lens	$\begin{aligned}\frac{1}{focal\;length}\end{aligned}$	[M⁰L^-1T⁰]	D (dioptre)
103	Magnification	Image distance / Object distance	No dimensions [M⁰L⁰T⁰]	No unit
104	Fluid flow rate	$\begin{aligned}\frac{(\pi /8)(pressure)\times (radius)^{4}}{Viscosity\;coefficient\times length}\end{aligned}$	[M⁰L³T^-1]	m³s^-1
105	Capacitive reactance (X_c)	(Angular frequency X capacitance)^-1	[M¹L²T^-3A^-2]	ohms (Ω)
106	Inductive reactance (X_L)	(Angular frequency X inductance)	[M¹L²T^-3A^-2]	ohms (Ω)

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