# How to Calculate Inflation in Three Different Ways

Here's how to calculate the annual rate of inflation both by comparing prices several years apart, and also by several months apart.

8953 Today, in the third quarter of 2021, the business press is churning out an avalanche of articles about the return of inflation. Although some of these concerns are well-founded, some are not.

For example, suppose that the average price of a commodity was \$100 before Covid. And suppose that the price fell to \$80 one year ago, because of the Covid recession. And now suppose that its price has returned to \$100.

By the standard way of calculating inflation, that commodity’s inflation rate is:
\$100/\$80 – 1 = 25% That’s a significant rate of inflation. But because the price has merely returned to its pre-Covid level, that 25% inflation rate seems overstated somehow.

But that’s not the end of the story, as this figure illustrates.

As Excel users in business, we can’t dismiss a cost increase so quickly. But we can look at it in different ways to try to get a better idea about the patterns of inflation that we’re facing.

### Extend the Time Horizon

One way to look at inflation in a different way is to extend the time period for which we calculate inflation from one year to two or three years. So, for example, we could calculate the Compound Average Growth Rate (CAGR) of prices over a period that begins before the Covid recession began.

Suppose, for example, that the cost of a commodity was \$75 three years ago, and that it’s now \$100. As I explain in How to Calculate BOTH Types of Compound Growth Rates in Excel, the three-year CAGR of the price is equal to the formula shown here. That is, the three-year rate of inflation in this example is:
(\$100/\$75)^(1/3)-1 = 10% per year.

### Shorten the Time Horizon

Another way to look at price increases is to compare prices that are only a few months apart. For example, it might be that until four months ago, prices hadn’t increased much at all. But now, in just a few months, prices have started to skyrocket—as the Dirty Dozen table above suggests.

That equation would look like this… …where the value for Number Months is the number of months between the Current Price and the Old Price.

So, in Excel, the formula would look like this:

=( ( CurPrice/OldPrice )^(1/NumMos) )^12-1

This is the formula I used to calculate the Dirty Dozen values above.