# How does dimensional analysis work?

##### 1 Answer

Dimensional analysis is simply a way of testing whether the base units of a given equation work out. It operates on a simple principle: the units you have on one side of an equation must match those that you have on the other.

It's analogous to baking a cake. Your cake can only have what ingredients you put in to it.

Consider the following equation:

Force in base units is

Mass is just

Acceleration is

So now let's evaluate this by plugging in these units into the equation:

This equation works, therefore it can be classified as dimensionally correct.

Let's look at another equation:

Now let's just plug everything in:

Notice that I have not included the

Now we simplify:

Since this equation does not work out, this equation is not dimensionally correct.

Hope that helped :)