The dimensional formula of Capacitance is

**[ M**^{-1}** L**^{-2}** T**^{2}** A**^{2}**]**

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

From the above formula, the **dimensions of capacitance are (-1, -2, 2, 2)**.

## How to calculate the dimensional formula of capacitance?

In physics, we can determine the amount of charge by the capacitance and the voltage difference across the capacitors. Mathematically, it means

```
Charge (Q) = Capacitance (C) * Voltage (V)
Capacitance = Charge / Voltage
```

We know that,

- Charge = Current * time
- Voltage = Work / Charge

Now, let’s drive this formula in terms of fundamental quantities:

```
Voltage = Work / Charge
```

**Work = Force * displacement**, so the formula becomes

```
Voltage = (Force * displacement) / Charge
```

Replacing the value of **Force by mass * acceleration**, we get

```
Voltage = (mass * acceleration * displacement) / Charge
```

Also,

- acceleration = speed / time
- speed = distance / time
- acceleration = distance / time
^{2}

```
Voltage = (mass * distance / time
```^{2} * displacement) / Charge
= (mass * distance * displacement) / (Charge * time^{2})
= (mass * distance * displacement) / (Current * time * time^{2})
= (mass * distance * displacement ) / (Current * time^{3})
= (mass * distance * displacement * Current^{-1} * time^{-3})

Now, the formula of capacitance becomes

```
Capacitance = (Current * time) / (mass * distance * displacement * Current
```^{-1} * time^{-3})
= (Current * time * Current * time^{3}) / (mass * distance * displacement)
= ( Current^{2} * time^{4} ) / (mass * distance * displacement)
= (Current^{2} * time^{4} * mass^{-1} * distance^{-1} * displacement^{-1})

Dimensionally, we use

**[M]**for mass**[L]**to represent both distance and displacement**[T]**for time- and
**[A]**for current

Now, the formula becomes

```
Capacitance = [A
```^{2}] * [T^{4}] * [M^{-1}] * [L^{-2}]
= [M^{-1}] * [L^{-2}] * [T^{4}] * [A^{2}]

Hence, the **dimensional equation of Capacitance is C = [ M**^{-1}** L**^{-2}** T**^{4}** A**^{2}**]**.

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