Dimension Formula Of Energy

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Energy is the rate at which work is done. In other words, it is the capacity of doing work. In Physics, energy is a quantitative property that is transferred to the object by the object in order to perform work in the form of heat or any other form as per desired results. Various common forms of energy are kinetic energy, potential energy, thermal energy, elastic energy, gravitational energy, magnetic energy, radiant energy, etc. All these forms of energy are interconvertible from one form to another depending on the parameters available for these conversions.

The SI unit of energy is joule and can be defined as the amount of the work done to move an object by applying the force 1N to the distance of 1 metre.

Dimensional Formula of Energy

The energy possessed by the body or transferred to or by the body is expressed in terms of joule. The unit of energy is named after James Prescott Joule because he independently discovered the mechanical equivalent in a series of experiments using his famous Joule apparatus which comprises a descending weight attached to a string, caused rotation of a paddle immersed in water and was insulated from heat transfer. 

The apparatus showed that the gravitational potential energy lost by the weight while descending was equal to the internal energy gained by the water through friction with the paddle. Thus it states that energy change or work is done in applying a force of one newton through a distance of one metre and establishing energy equivalence with the work.

Numerically, Energy is equivalent to work done. Thus mathematically 

Energy =Work Done=Force*displacement

SI unit of force  = Newton

1 Newton=1kgms-2

SI unit of displacement = metre

Thus, 1 Joule=1kgm2s-2  

Dimension of mass =M

Dimension of length=L

Dimension of time =Seconds

Using the above derivation 1 Joule=1kgm2s-2  

We can derive the dimension of energy =ML2T-2

An Alternate Method to Derive the Unit of Energy

Using Einstein’s famous equation of mass energy equivalence, that gives the relation between mass and energy conversion and states that 


Where m= mass and c=velocity

Since mass is measured is kg 

Thus the dimension of mass is M

And velocity is the rate of change of position and has unit ms-1  

Therefore the dimension of velocity  = LT-1

Thus dimension formula of energy =ML2T-2

From both the derivation using E=work done and E=mc2

We can say that the dimension formula of energy is ML2T-2

Dimensional Formula of Energy Density

Energy density is defined as the energy stored per unit volume.

Thus mathematically,

Energy Density = Energy/Volume 

And, Energy=Force×displacement


Where m=mass,a=acceleration and d=displacement

Thus,dimensions formula of energy = [M1 L2 T-2]

Dimension formula of Volume = [M0 L3 T0]

Using,Energy Density = Energy × [Volume]-1

= [M1 L2 T-2] × [M0 L3 T0]-1 = [M1 L-1 T-2]

Therefore, the dimension formula of energy density is represented as [M1 L-1 T-2]

FAQ (Frequently Asked Questions)

Q1. What is the dimension of Surface Energy?

Ans: Surface energy can be defined as the energy required to increase the surface area of the liquid by one unit. Thus, the dimension of surface energy is Jm-1.

Q2. What is energy and what is the dimension for Potential Energy?

Ans: In physics, energy is defined as the capacity of doing work. Now the expression for the potential energy is. P.E. = mgh and its dimension is the same as that of energy.

Q3. How can we calculate Power from work done?

Ans: Power is the measure of the amount of total work done or energy transfer that is done in a given amount of time. Power equals work (J) divided by time (s). Thus the standard unit of the power is the watt (W), which equals 1 joule of work per second (J/s).

Q4. What are the different forms of Energy?

Ans: The different forms of energy are thermal energy, radiant energy, chemical energy, nuclear energy, electrical energy, sound energy, elastic energy, gravitational energy, etc.