How to calculate annual percentage change

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How to calculate annual percentage change
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How to Calculate an Average Percent Change

How to Calculate an Average Percent Change

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How to Calculate Average Increase

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Updated November 17, 2020By Kevin Beck

Calculating a percentile change in a number is straightforward; calculating the average of a set of numbers is also a familiar task for many people. But what about calculating the ​average percent change​ of a number that changes more than once?

For example, what about a value that is initially 1,000 and increases to 1,500 over a five-year period in increments of 100? Intuition might lead you to the following:

The overall percent increase is:\bigg(\frac{\text{Final } - \text{ initial value}}{ \text{ initial value}}\bigg) × 100

Or in this case,\bigg(\frac{1500 - 1000}{ 1000}\bigg) × 100 = 0.50 × 100 = 50\%

So the average percent change must be\frac{50\% }{5 \text{ years}} = +10\% \text{ per year}

...right?

As these steps show, this is not the case.

Step 1: Calculate the Individual Percent Changes

For the above example, we have\bigg(\frac{1100 - 1000}{ 1000}\bigg) × 100 = 10\% \text{ for the first year,} \\ \,\\ \bigg(\frac{1200 - 1100}{ 1100}\bigg) × 100 = 9.09\% \text{ for the second year,} \\ \,\\ \bigg(\frac{1300 - 1200}{ 1200}\bigg) × 100 = 8.33\% \text{ for the third year,} \\ \,\\ \bigg(\frac{1400 - 1300}{ 1300}\bigg) × 100 = 7.69\% \text{ for the fourth year,} \\ \,\\ \bigg(\frac{1500 - 1400}{ 1400}\bigg) × 100 = 7.14\% \text{ for the fifth year,}

The trick here is recognizing that the final value after a given calculation becomes the initial value for the next calculation.

Step 2: Sum the Individual Percentages10 + 9.09 + 8.33 + 7.69 + 7.14 = 42.25

Step 3: Divide by the Number of Years, Trials, Etc.\frac{42.25}{5} = 8.45 \%

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References

  • TAMU: Change, Percentage Change, and Average Rates of Change
  • UMB: Absolute Change and Percentage Change

About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.

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