Table of Units and Dimensions of Physical quantities.

Units & Dimensions of Physical quantities in S.I system.
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Fundamental Physical Quantities:

S.No Fundamental Physical Quantity Formula Dimensional Formula S.I Unit of physical quantity
1. Mass Amount of matter in the object M kg
2. Length L meter
3. Time T sec
4. Electric current I or A ampere
5. Amount of substance N mole(mol
6. Luminous intensity J candela(cd)
7. Temperature K or \theta Kelvin

Derived Physical Quantities:

S.No Derived Physical Quantity Formula Dimensional Formula S.I Unit of physical quantity
1. Area l\times b [M^0L^2T^o] m^2
2. Volume l\times b\times h [M^0L^3T^o] m^3
3. Density \frac{M}{V} [M^1L^{-3}T^0] kg/m^3
4. Specific Gravity \frac{Density of Substance}{Density of Water} [M^0L^0T^0] No units
5. Frequency \frac{no of vibrations}{Time} [M^0L^0T^{-1}] hertz
6. Angle \frac{Arc}{radius} M^0L^oT^o No units
7. Velocity \frac{Displacement}{time} M^0L^1T^{-1} m/sec
8. Speed \frac{Distance}{time} M^0L^1T^{-1} m/sec
9. Areal velocity \frac{Area}{time} M^0L^2T^{-1} m^2sec^{-1}
10. Acceleration \frac{Change in velocity }{time} M^0L^1T^{-2} m/sec^2
11. Linear momentum M\times V M^1L^1T^{-1} kg m/sec
12. Force mass\times acceleration M^1L^1T^{-2} kg-m/sec^2 or Newton
13. Weight w=mg M^1L^1T^{-2} kg-m/sec^2 or Newton
14. Moment of force/Torque/Couple Force\times arm M^1L^2T^{-2} kgm^2sec^{-2}
15. Impulse Force\times time M^1L^1T^{-1} kg m/sec or Ns
16. Pressure \frac{Force}{Area} M^1L^{-1}T^{-2} N/m^2 or Pa
17. Work Force\times Distance M^1L^2T^{-2} Nm or Joule
18. Kinetic Energy \frac{1}{2} mv^2 M^1L^2T^{-2} joule
19. Potential Energy mgh M^1L^2T^{-2} joule
20. Gravitational constant \frac{Force\times (Length)^2}{(mass)^2} M^{-1}L^3T^{-2} kg^{-1}m^3sec^{-2}
21. Gravitational field strength \frac{Force}{mass} M^0L^1T^{-2} N kg^{-1}
22. Gravitational Potential \frac{Work}{mass} M^0L^2T^{-2} J kg^{-1}
23. Force constant (k) \frac{F}{L} M^1L^0T^{-2} N m^{-1}
24. Power \frac{Work}{time} M^1L^2T^{-3} W or J/sec
25. Moment of Inertia ( I ) Mass\times Distance^2 M^1L^2T^{0} kgm^2
26. Stress \frac{Force}{Area} M^1L^{-1}T^{-2} N/m^2 or Pa
27. Strain \frac{Change in length}{Origional length} M^0L^0T^0 No units
28. Modulus of Elasticity \frac{Stress}{Strain} M^1L^{-1}T^{-2} N/m^2 or Pa
29. Poission’s Ratio σ =\frac{Y}{2n}-1 M^0L^0T^0 No units
30. Velocity gradient \frac{Change in velocity}{Distance} M^0L^0T^{-1} sec^{-1}
31. Coefficient of dynamic viscosity \frac{Tangential stress}{Velocity Gradient} M^1L^{-1}T^{-1} kgm^{-1}sec^{-1}(or) N-sec/$latex  \m^2$ (or)pascal-sec (or)poiseuille
32. Surface Tension \frac{Force}{Length} M^1L^0T^{-2} kg sec^2,N/m
33. Angular displacement (\theta) \frac{Arc}{radius} M^0L^oT^o no Units
34. Angular velocity(ω) \frac{Angular displacement}{Time} M^0L^oT^{-1} rad/sec
35. Angular acceleration(α) \frac{Change in angular velocity}{Time} M^0L^oT^{-2} rad/sec^{-2}
36. Angular momentum ML^2T^{-1} kg-m^2 sec^{-1}
37. Angular Impulse ML^2T^{-1} kg-m^2 sec^{-1}
38. Temperature \theta or K kelvin or degree Celsius
39. Coefficient of linear expansion(α) \frac{l_2-l_1}{l_1\times Temp(t_2-t_1)} M^0L^0T^0K^{-1} /kelvin
40. Specific heat \frac{Energy}{Mass\times Temp} M^0L^2T^{-2}K^{-1}
41. Latent heat \frac{Energy}{Mass} M^0L^2T^{-2} joule-kg^{-1}
42. Entropy \frac{Q}\theta M^1L^2T^{-2}K^{-1} J K^{-1}
43. Thermal capacity \frac{H}\theta M^1L^2T^{-2}K^{-1} J K^{-1}
44. Gas constant \frac{PV}{m T} M^0L^2T^{-2}K^{-1} joule-K^{-1}
45. coefficient of thermal conductivity \frac{Qd}{A(\theta_2-\Theta_1)t} M^1L^1T^{-3}K^{-1} W m^{-1}K^{-1}
46. Pole strength Ampere\times meter M^0L^1T^0I Am
47. Magnetic Moment M^0L^2T^0I^1 Amp-m^2
48. Magnetic flux \phi ML^2T^{-2}I^{-1} weber ;T-m^{2} ;J/Amp
49. Magnetic field,magnetic flux density (B) MT^{-2}I^{-1} Tesla;J/A-m^{2}
50. Permeability of free space \frac{\mu}{\mu_r} MLT^{-2}I^{-2} NA^{-2}
51. Magnetic susceptibilty also called volumetric or bulk susceptibility χm χm = μr − 1 M^0L^oT^o no units
52. Electric Charge I\times T M^0L^0T^1I^1 Amp sec , coul
53. Electric potential \frac{Work}{Charge} M^1L^2T^{-3}I^{-1} Volt
54. E.M.F \frac{Work}{Charge} M^1L^2T^{-3}I^{-1} Volt
55. Electric Capacity \frac{q}{V} M^{-1}L^{-2}T^4I^2 Farad
56. Electric Resistance \frac{V}{i} M^1L^2T^{-3}I^{-2} Ohm (Ω) or volt/amp
57. Resistivity \rho \frac{R A}{L} M^1L^3T^{-3}I^{-1} Ohm mt (Ω-m)
58. Conductivity \sigma 1/\rho M^{-1}L^{-3}T^3I Siemens/m
59. Permittivity \varepsilon
\varepsilon = \varepsilon_r \varepsilon_0 = (1+\chi)\varepsilon_0
M^{-1}L^{-3}T^4I^2 farad/m
60. Electric conductance \frac{1}{R} M^{-1}L^{-2}T^3I^2 Siemens (or) mhos
61. Electric power V\times I M^1L^2T^{-3}I^{-1} Watt
62. Electrical Impedance(Z) \frac{V}{i} M^1L^2T^{-3}I^{-2} Ohm (Ω) or volt/amp
63. Electrical admittance 1/Z(Reciprocal of electric impedance) M^{-1}L^{-2}T^3I^3 Siemens (or) mhos
64. Self Inductance(L) \displaystyle v=L\frac{di}{dt} ML^2T^{-2}I{-2} weber/amp or Henry
65. Boltzmann’s constant \frac{Energy}{Temp} M^1L^2T^{-2}K^{-1} J/kelvin
66. Stefan’s constant \frac{E}{At \theta^4} M^1L^0T^{-3}K^{-4} W m^{-2}K^{-4}
67. Co-efficient of friction \mu \mu=\frac{F}{N},N=Normal reaction dimension less scalar no units
68. Dielectric constant \varepsilon_r It is also called relative permittivity dimension less no
units
69. Planck’s constant E=h\nu ML^2T^{-1} J.sec (or) eV.sec
70. Refractive index μ M^0L^oT^o no units
71. Focal length(f) Distance between center of the lens(mirror) to its focus L meter
72. Power of a lens (P) The reciprocal of the focal length of a lens in meters is called power of a lens; p=1/f L^{-1} diaptors
73. Wave number No.of waves/distance L^{-1} m^{-1}
74. Wave length Length of a wave L meter
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112 thoughts on “Table of Units and Dimensions of Physical quantities.

  1. I am with an I.Com background and now is studing IT Physics and facing a lot of problems in first semester.I was in need of Dimentions of SI units for average learning but reading the table above I have knewed extra ordinary information about dimentions.Thank you very much for this help!!!

  2. sir plz check about the dimensional formula of angular momentum and angular impulse, i hav a doubt wid d gvn infrmtn.

  3. here the dimensional formula of density is incorrect as it should be l-3……………..kindly make the changes …..

  4. It was really very helpful, but i don’t understand the Planck’s constant, can you tell the derivation, I always end up with [M L^2 T^-3]… how does it become T^-1 ? I have a test on monday, please help ! Also I have the same problem with Coefficient of Viscocity, I get M^1 L^-1 T^-3 ! instead of T^-1. Is there some specific reason for this ? :(

  5. We can derive dimensional formulas of physical quantities from their units also.Hence, the unit of plank’s constant is Joule-sec ,Joule(Unit of Energy) – D.F is ML^2T^-2 and sec(Unit of time) – D.F is T . If we multiply these two (ML^2T^-2)(T)= ML^2T^-1.Similarly Coefficient of viscosity = . D.F of Stress is M L ^-1 T^-2 and D.F of Velocity is reciprocal of time i.e T^-1.Therefore D.F Of Coefficient of viscosity=(M L ^-1 T^-2)/( T^-1)=M L ^-1 T^-1.Hope this clarifies your doubt.

  6. yeah its very helpful but i think explanation should be there……………..:-)

  7. [L][M][T-2][A-2] IS DIMENSION FOR PERMEABILITY OF FREE SPACE
    HERE
    T-2 =PER TIME SQUARE AND SAME FOR A

  8. EXCELLENT CLLECTION OF UNITS ,,,,,,,,,,,,,,,,,,,,,,,,,,,AND THE GOOD THING IS THAT THE ORGANISER OF THIS TABLE LISTENS TO SHORTCOMINGS AND IMPROVES THIS TABLE

  9. it is nicely arranged but some of the formulaes are missing but these formulaes are enough for +1

  10. areee….kitni sari..formules hai……….adhi toh tappi bhi nai padti.any easy way 4 tis?2 rembr??????????????????????????????

  11. i want the dimension formula of surface tension and citical velocity plz reply as earliar as possible….

  12. yr its good but i want more dimensional formula , but i thanks to it becose with the help of table i done my home work ……… Thanks to the formulas

  13. Thanks to all who gives these physics material and helps to all in solving the problem:::::::fantastic miss u shaz:::

  14. Mr.Shoib ,Tesla is the unit of flux density and weber is the unit of flux.As desired by you I added these physical quantities to the table as 49& 48 entries respectively.

  15. its very help full…..
    but i can’t understand dimension of stefan constant i think its [M^1L^0T^-3K^-4] not [M1^L^0T^3K^-4] Plz explain……

  16. nice work done .i need some more dimrensions as i am preparing for entry test mcat

  17. Can anyone explain me relationship between accleration,radius and velocity using dimensional formulaes?

  18. l like this but some thing is less comfortable and this dimention should also express in electrostatic system of unit . And also in eletromegnetic system of unit.

  19. hai myself n.nithin from new delhi this was very nice but somemore amendments like adding more stuff like increasing formulae number but anyway itwas fabulous (nithin nagulakonda b.tech)

  20. Thanks…………. with the help of this table i have done my asignment…………………….need more…….

  21. hahahahahaha, but muje in sub ki zaroorat nahi hai, sab k sub nalayak ho. .bladdyyyy FOOLS. .lol

  22. I like this way of formula seeing. i want it more in several branches scinces.

  23. And diminsion of e=mc^2 is [ML^2T^-2] and also energy diminsion is [ML^2T^-2]

  24. Many thanks for the good work its help us a lot, but kindly elevate some of the dimensional quantities

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