What is Dimensional Analysis?

Dimensional analysis, also known as Factor-Label Method or the Unit Factor Method, is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. Unit factors may be made from any two terms that describe the same or equivalent "amounts" of what we are interested in.

For example, if we are given the following conversion factor: 1.00 inch = 2.54 cm

There are two ways that we can write this information. We can say 1.00in / 2.54cm or 2.54cm / 1.00in

Now if we want to calculate how many cm there are in 12 inches, which factor do we use?

If we use 1.00in / 2.54cm then it will be:

$$\begin{align*}&(12\;in \times 1.00\;in) / 2.54\;cm \cr &=12\;in^2 / 2.54\;cm \end{align*}$$

This can also be written as:

$$\begin{align*}&\frac{12\;in\times1.00\;in}{2.54\;cm}\cr &=\frac{12\;in^2}{2.54\;cm}\end{align*}$$

However, if we use 2.54cm / 1.00in then it will be:

$$\begin{align*}&\frac{12\;in \times 2.54\;cm}{1.00\;in}\cr &= 12 \times 2.54\;cm\cr &= 30.5\;cm\end{align*}$$

Therefore, 12 inches equals to 30.5 centimetres

In the next part we will be looking at some more examples on how to use dimensional analysis to solve problems.

Previous  | Next