# Dimensional Formula of Planck’s Constant

The dimensional formula of Planck’s Constant is

[ M1  L2  T-1 ]

where [M], [L], and [T] are the fundamental quantities: Mass, Length, and Time.

From the above formula, the dimensions of Planck’s constant are (1, 2, -1).

## How to calculate the dimensional formula of Planck’s constant?

We can define this formula using the mathematical formula of Plack’s constant. Mathematically,

``````
Planck's constant (h) = Energy / Frequency
``````

We know that,

``````
Energy = Work Done

= Force * displacement

= mass * acceleration * displacement
``````

Also,

• acceleration = speed / time
• speed = distance / time
• acceleration = distance / time2
• acceleration = distance * time-2

So, Energy = (mass * distance * displacement * time-2)

And the formula of frequency is 1 / time = time-1. Hence, the formula of Planck’s constant becomes

``````
Planck's constant = (mass * distance * displacement * time-2) / time-1

= ( mass * distance * displacement * time-1 )
``````

Dimensionally, we use

Dimensionally, we use

• [M] for mass
• [L] to represent both distance and displacement
• and, [T] for time

Now, the formula becomes

``````
Planck's constant = [M1] * [L2] * [T-1]
``````

Hence, the dimensional equation of Planck’s constant is h = [ M1 L2 T-1 ].

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