Dimensional Formulae of Physical Quantities
S.No Physical Quantity Relationship with other Remark Dimensional
physical quantities Formula
1. Area Length × breadth 0 2 0
[M L T ]
2. Volume Length × breadth × height [M L3 T0]
3. Mass density Mass/volume [M L–3 T0]
4. Frequency 1/time period [M0 L0 T–1]
5. Velocity, speed Displacement/time [M0 L T–1]
6. Acceleration Velocity/time [M0 L T–2]
7. Force Mass × Acceleration [M L T–2]
8. Impulse Force × Time [M L T–1]
9. Work, Energy Force × Distance [M L2 T–2]
10 Power Work/Time [M L2 T–3]
.
11 Momentum Mass × Velocity [M L T–1]
.
12 Pressure, stress Force/Area [M L–1 T2]
.
13 Strain change in dimension [M0 L0 T0]
. Original dimension
14 Modulus of elasticity Stress/Strain [M L–1 T–2]
.
15 Surface tension Force/Length [M L0 T–2]
.
16 Surface energy Energy/Area [M L0 T–2]
.
17 Velocity gradient Velocity/distance [M0 L0 T–1]
.
18 Pressure gradient Pressure/distance [M L–2 T–2]
.
19 Pressure energy Pressure × volume [M L2 T–2]
.
20 Coefficient of Force/area × velocity [M L–1 T–1]
. viscosity gradient
21 Angle, Angular Arc/radius [M0 L0 T0]
. displacement
22 Trigonometric ratio Length/length [M0 L0 T0]
. (sinθ, cosθ, tanθ, etc).
23 Angular velocity Angle/time [M0 L0 T–1]
.
24 Angular acceleration Angular velocity/time [M0 L0 T–2]
.
25 Radius of gyration Distance [M0 L T0]
.
26 Moment of inertia Mass × (radius of gyration)2 [M L2 T0]
.
, 27 Angular momentum Moment of inertial × angular [M L2 T–1]
. velocity
28 Moment of force, Force × distance [M L2 T–2]
. moment of couple
29 Torque Angular momentum/time [M L2 T–2]
. Or
Force × distance
30 Angular frequency 2π × Frequency [M0 L0 T–1]
.
31 Wavelength Distance [M0 L T0]
.
32 Hubble constant Recession speed/distance [M0 L0 T–1]
.
33 Intensity of wave (Energy/time)/area [M L0 T–3]
.
34 Radiation pressure Intensity of wave [M L–1 T–2]
. Speed of light
35 Energy density Energy/volume [M L–1 T–2]
.
36 Critical velocity Reynold's number × coefficient of viscocity [M0 L T–1]
Mass density × radius
.
37 Escape velocity (2 × acceleration due to [M0 L T–1]
. gravity × earth’s radius)1/2
38 Heat energy, internal Work (= Force × distance) [M L2 T–2]
. energy
39 Kinetic energy (1/2) mass × (velocity)2 [M L2 T–2]
.
40 Potential energy Mass × acceleration due to
. gravity × height
41 Rotational kinetic ½ × moment of inertia × [M L2 T–2]
. energy (angular velocity)2
42 Efficiency output work or energy [M0 L0 T0]
. Input work or energy
43 Angular impulse Torque × time [M L2 T–1]
.
44 Gravitational constant Force × ( distance ) [M–1 L3 T–2]
2
.
mass × mass
45 Planck constant Energy/frequency [M L2 T–1]
.
46 Heat capacity, entropy Heat energy/temperature [M L2 T–2 K–1]
.
47 Specific heat capacity Heat Energy [M0 L2 T–2 K–1]
. Mass × temperature
48 Latent heat Heat energy/mass [M0 L2 T–2]
.
49 Thermal expansion change in dimension [M0 L0 K–1]
. coefficient or thermal Original dimension × temperature
expansivity
2
S.No Physical Quantity Relationship with other Remark Dimensional
physical quantities Formula
1. Area Length × breadth 0 2 0
[M L T ]
2. Volume Length × breadth × height [M L3 T0]
3. Mass density Mass/volume [M L–3 T0]
4. Frequency 1/time period [M0 L0 T–1]
5. Velocity, speed Displacement/time [M0 L T–1]
6. Acceleration Velocity/time [M0 L T–2]
7. Force Mass × Acceleration [M L T–2]
8. Impulse Force × Time [M L T–1]
9. Work, Energy Force × Distance [M L2 T–2]
10 Power Work/Time [M L2 T–3]
.
11 Momentum Mass × Velocity [M L T–1]
.
12 Pressure, stress Force/Area [M L–1 T2]
.
13 Strain change in dimension [M0 L0 T0]
. Original dimension
14 Modulus of elasticity Stress/Strain [M L–1 T–2]
.
15 Surface tension Force/Length [M L0 T–2]
.
16 Surface energy Energy/Area [M L0 T–2]
.
17 Velocity gradient Velocity/distance [M0 L0 T–1]
.
18 Pressure gradient Pressure/distance [M L–2 T–2]
.
19 Pressure energy Pressure × volume [M L2 T–2]
.
20 Coefficient of Force/area × velocity [M L–1 T–1]
. viscosity gradient
21 Angle, Angular Arc/radius [M0 L0 T0]
. displacement
22 Trigonometric ratio Length/length [M0 L0 T0]
. (sinθ, cosθ, tanθ, etc).
23 Angular velocity Angle/time [M0 L0 T–1]
.
24 Angular acceleration Angular velocity/time [M0 L0 T–2]
.
25 Radius of gyration Distance [M0 L T0]
.
26 Moment of inertia Mass × (radius of gyration)2 [M L2 T0]
.
, 27 Angular momentum Moment of inertial × angular [M L2 T–1]
. velocity
28 Moment of force, Force × distance [M L2 T–2]
. moment of couple
29 Torque Angular momentum/time [M L2 T–2]
. Or
Force × distance
30 Angular frequency 2π × Frequency [M0 L0 T–1]
.
31 Wavelength Distance [M0 L T0]
.
32 Hubble constant Recession speed/distance [M0 L0 T–1]
.
33 Intensity of wave (Energy/time)/area [M L0 T–3]
.
34 Radiation pressure Intensity of wave [M L–1 T–2]
. Speed of light
35 Energy density Energy/volume [M L–1 T–2]
.
36 Critical velocity Reynold's number × coefficient of viscocity [M0 L T–1]
Mass density × radius
.
37 Escape velocity (2 × acceleration due to [M0 L T–1]
. gravity × earth’s radius)1/2
38 Heat energy, internal Work (= Force × distance) [M L2 T–2]
. energy
39 Kinetic energy (1/2) mass × (velocity)2 [M L2 T–2]
.
40 Potential energy Mass × acceleration due to
. gravity × height
41 Rotational kinetic ½ × moment of inertia × [M L2 T–2]
. energy (angular velocity)2
42 Efficiency output work or energy [M0 L0 T0]
. Input work or energy
43 Angular impulse Torque × time [M L2 T–1]
.
44 Gravitational constant Force × ( distance ) [M–1 L3 T–2]
2
.
mass × mass
45 Planck constant Energy/frequency [M L2 T–1]
.
46 Heat capacity, entropy Heat energy/temperature [M L2 T–2 K–1]
.
47 Specific heat capacity Heat Energy [M0 L2 T–2 K–1]
. Mass × temperature
48 Latent heat Heat energy/mass [M0 L2 T–2]
.
49 Thermal expansion change in dimension [M0 L0 K–1]
. coefficient or thermal Original dimension × temperature
expansivity
2
