Dimensional Formula for Different Physical Quantities

The dimensional formula for different physical quantities and dimensional analysis are the major topics of this article. Before diving into the dimensions and dimensional formulas, you should first brush up on the fundamentals of measurement, which you can learn about in my earlier essay on measuring and different systems of units. Each and every physical quantity is known until day can be expressed in terms of seven fundamental quantities by calculations and relationships.  

Seven Fundamental Quantities

There are seven fundamental underived physical quantities: length, mass, electric current, time, luminous intensity, amount of substance, and temperature. These seven fundamental quantities are also termed the seven dimensions of the physical world. Instead of using the names of the base quantities, we can utilize symbols. The dimensions of the three mechanical quantities mass, length, and time are represented by M, L, and T.

The brackets [M], [L], and [T] can also be used to indicate them. Other dimensions are denoted by K (for temperature), I (for electric current), cd (for luminous intensity) and mol (for the amount of substance).  A physical quantity’s dimensions and its unit’s dimensions are the same. The letters [M], [L], [T], and so on merely indicate the unit’s type, not its size.

What Are Dimensional Formulas For Different Physical Quantities?

Each derived quantity requires the appropriate power for fundamental quantities to be represented. Dimensions are the powers of fundamental quantities used to increase them to represent unit derived quantities. In other words, a physical quantity’s dimensions are the powers to which the base quantities (basic quantities) are elevated to express that quantity.

1. The Dimensional Formula for Length is [L].
2. The Dimensional Formula for Mass is [M].
3. The Dimensional Formula for Time is [T].
4. The Dimensional Formula for Acceleration is [LT-2].
5. Dimensional Formula for Angle (arc/radius) is [MoLoT]o.
6. Dimensional Formula for Angular displacement is [MoLoT]o.
7. Dimensional Formula for Angular frequency is [T-1].
8. Dimensional Formula for the Angular impulse is [ML2T–1].
9. Dimensional Formula for Angular momentum is [ML2T-1].
10. Dimensional Formula for Angular velocity is [T-1].
11. Dimensional Formula for Area is [L2].
12. Dimensional Formula for Boltzmann’s constant is [ML2T–2θ–1].
13. Dimensional Formula for Bulk modulus is [M1L–1T–2].
14. Dimensional Formula for Calorific value is [L2T-2].
15. Dimensional Formula for the coefficient of linear or areal or volume expansion is [θ–1].
16. Dimensional Formula for the coefficient of surface tension is [MT–2].
17. Dimensional Formula for the coefficient of thermal conductivity is [MLT–3θ–1].
18. Dimensional Formula for the coefficient of viscosity is [ML–1T–1].
19. Dimensional Formula for Compressibility is [M–1LT2].
20. Dimensional Formula for Density is [ML–3].
21. Dimensional Formula for wavelength, focal length, displacement is [L].
22. Dimensional Formula for Electric capacitance is [M–1L–2T4I2].
23. Dimensional Formula for Electric conductance is [M–1L–2T3I2].
24. Dimensional Formula for Electric conductivity is [M–1L–3T3I2].
25. Dimensional Formula for Charge is [IT].
26. Dimensional Formula for Electric current is [I].
27. Dimensional Formula for Electric dipole moment is [LTI].
28. Dimensional Formula for Electric field intensity is [MLT–3I–1].
29. Dimensional Formula for Electric resistance is [ML2T–3I–2].
30. Dimensional Formula for Electric potential is [ML2T–3I–1].
31. Dimensional Formula for Energy is [ML2T–2]. 
32. Dimensional Formula for Energy density is [ML–1T–2].
33. Dimensional Formula for Entropy is [ML2T–2θ–1].
34. Dimensional Formula for Force is [MLT-2].
35. Dimensional Formula for the Spring constant is [MT-2].
36. Dimensional Formula for Frequency is [T-1].
37. Dimensional Formula for Gravitational potential is [L2T-2].
38. Dimensional Formula for Illuminance is [MT-3].
39. Dimensional Formula for Impulse is [MLT-1].
40. Dimensional Formula for Inductance is [ML2T–2I–2].
41. Dimensional Formula for gravitational field intensity is [L1T-2].
42. Dimensional Formula for Intensity of magnetisation is [L-1I].
43. Dimensional Formula for Joule’s constant is [M0L0T0].
44. Dimensional Formula for Latent heat is [MoL2T–2].
45. Dimensional Formula for Linear density is [ML-1].
46. Dimensional Formula for Luminous flux is [ML2T–3].
47. Dimensional Formula for Magnetic dipole moment is [L2I].
48. Dimensional Formula for Magnetic flux is [ML2T–2I–1].
49. Dimensional Formula for Magnetic induction is [MT–2I–1].
50. Dimensional Formula for modulus of elasticity is [ML–1T–2].
51. Dimensional Formula for Moment of inertia is [ML2].
52. Dimensional Formula for Momentum is [MLT–1].
53. Dimensional Formula for Permeability of free space is [MLT–2I–2].
54. Dimensional Formula for the Permittivity of free space is [M–1L–3T4I2].
55. Dimensional Formula for Planck’s constant is [ML2T–1].
56. Dimensional Formula for Poisson’s ratio is [M0L0T0].
57. Dimensional Formula for Power is [ML2T-3].
58. Dimensional Formula for Pressure is [ML–1T–2].
59. Dimensional Formula for the Refractive index is  [M0L0T0].
60. Dimensional Formula for Resistivity is [ML3T–3I–2].
61. Dimensional Formula for Conductivity is [M–1L–3T3I2].
62. Dimensional Formula for Specific entropy is [M–1L–2T2θ].
63. Dimensional Formula for Specific gravity is [M0L0T0].
64. Dimensional Formula for Specific heat is [MoL2T–2θ–1].
65. Dimensional Formula for Specific volume is [M–1L3].
66. Dimensional Formula for Speed is [LT-1].
67. Dimensional Formula for Stefan’s constant is [MLoT–3θ–4].
68. Dimensional Formula for Strain is [M0L0T0].
69. Dimensional Formula for Surface energy density is [MT–2].
70. Dimensional Formula for Temperature gradient is [MoL–1Toθ].
71. Dimensional Formula for Thermal capacity is [ML2T–2θ–1].
72. Dimensional Formula for Torque is [ML2T–2].
73. Dimensional Formula for the Universal gas constant is [ML2T–2θ–1].
74. Dimensional Formula for Universal gravitational constant is [M–1L3T–2].
75. Dimensional Formula for Velocity gradient is [T-1].
76. Dimensional Formula for Water equivalent is [M].

Conclusion

The dimensional formula for different physical quantities is somehow connected to the seven fundamental physical quantities. Any dimensional formula such as the dimensional formula for force, dimensional formula for velocity, the dimensional formula for charge, etc., can be derived by following specific rules and laws of homogeneity. These physical quantities will help you derive the ultimate unit combination made from dimensional formulas of other pre-known physical quantities. Any numerical value shall be ignored and can’t be retrieved to obtain or calculate the formula for mathematical calculations.