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 so as 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 area is 2 dimension in length and zero dimension 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 dimension 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. 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] | kgm-3 |
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 4oC | No dimensions [M0L0T-0] | No units |
9 | Linear momentum (p) | Mass x Velocity | [M1L1T-1] | kgms-1 |
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 | Universal constant of gravitation (G) | [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) | Energy / unit area | [M1L0T-2] | Nm-1 |
21 | Force constant (x) | Force / Displacement | [M1L0T-2] | Nm-1 |
22 | Coefficient of viscosity ( η ) | [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) | Stress / strain | [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) | Length / length | 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 | 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( | 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 | Density of substance / density of water at 4oC | No dimensions [M0L0T-0] | No unit |
43 | Pressure gradient | Pressure / Dstance | [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) | [M0L2T-2K-1] | Jkg-1K-1 | |
49 | Thermal expansion coefficient or thermal expansivity | [M0L0T0K-1] | K-1 | |
50 | Thermal conductivity | [M1L1T-3K-1] | Wm-1K-1 | |
51 | Bulk modulus or (compressibility)-1 | [M1L-1T-2] | Nm-2 or Pascals | |
52 | Centripetal acceleration | [M0L1T-2] | ||
53 | Stefan constant (σ) | [M1L0T-3K-4] | Wm−2K−4 | |
54 | Wien constant | Wavelength X temperature | [M0L1T0K1] | mK |
55 | Gas constant (R) | [M1L2T-2K-1] | JK-1 | |
56 | Boltzmann constant (K) | Energy / temperature | [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 | [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 | Potential difference / distance | [M1L1T-3A-1] | NC-1 |
67 | Magnetic field (B), magnetic flux density, magnetic induction | [M1L0T-2A-1] | T (Tesla) | |
68 | Magnetic flux (Φ) | Magnetic field X area | [M1L2T-2A-1] | Wb (Weber) |
69 | Inductance | Magnetic flux / current | [M1L2T-2A-2] | H (Henry) |
70 | Magnetic dipole moment | Torque /field or current X area | [M0L2T0A1] | Am2 |
71 | Magnetic field strength (H), magnetic intensity or magnetic moment density | Magnetic moment / volume | [M0L-1T0A1] | Am-1 |
72 | Hubble constant | Recession speed / distance | [M0L0T-1] | s-1 |
73 | Intensity of wave | (Energy/time)/area | [M1L0T-3] | Wm-2 |
74 | Radiation pressure | Intensity of wave / speed of light | [M1L–1T-2] | |
75 | Energy density | Energy / volume | [M1L-1T-2] | Jm-3 |
76 | Critical velocity | [M0L1T-1] | ms-1 | |
77 | Escape velocity | [M0L1T-1] | ms-1 | |
78 | Heat energy, internal energy | Work ( = Force X distance) | [M1L2T-2] | J |
79 | Kinetic energy | [M1L2T-2] | J | |
80 | Potential energy | Mass X acceleration due to gravity X height | [M1L2T-2] | J |
81 | Rotational kinetic energy | [M1L2T-2] | J | |
82 | Efficiency | No dimensions [M0L0T0] | No unit | |
83 | Angular impulse | Torque X time | [M1L2T-1] | Js (Joule second) |
84 | Permitivity constant (of free space) | [M-1L-3T4A2] | F m-1 | |
85 | Permeability constant (of free space) | [M1L1T-2A-2] | NA-2 | |
86 | Refractive index | No dimensions [M0L0T0] | No unit | |
87 | Faraday constant (F) | Avogadro constant X elementary charge | [M0L0T1A1 mol-1] | C mol-1 |
88 | Wave number | [M0L-1T0] | ||
89 | Radiant flux, Radiant power | Energy emitted / time | [M1L2T-3] | W(Watt) |
90 | Luminosity of radiant flux or radiant intensity | [M1L2T-3] | W sr-1 (Watt/steradian) | |
91 | Luminous power or luminous flux of source | [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 (Lv) | [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 | [M1L2T-2] | ||
99 | Decay constant | 0.693 / half-life | [M0L0T-1] | |
100 | Resonant frequency | [M0L0T-1A0] | ||
101 | Quality factor or Q-factor of coil | No dimensions [M0L0T0] | No unit | |
102 | Power of lens | [M0L-1T0] | D (dioptre) | |
103 | Magnification | Image distance / Object distance | No dimensions [M0L0T0] | No unit |
104 | Fluid flow rate | [M0L3T-1] | m3s-1 | |
105 | Capacitive reactance (Xc) | (Angular frequency X capacitance)-1 | [M1L2T-3A-2] | ohms (Ω) |
106 | Inductive reactance (XL) | (Angular frequency X inductance) | [M1L2T-3A-2] | ohms (Ω) |
Author | – |
Language | English |
No. of Pages | 5 |
PDF Size | 0.1 MB |
Category | Education |
All Dimensional Formula List PDF Free Download