Growth Rate

How to Annualize the Growth Rate

Often, we’ll want to annualize the rate of growth (i.e. “smooth out” the rate of growth across several periods), which can be done by calculating the compound annual growth rate (CAGR).

The CAGR is the annualized growth rate over a specified period, i.e. a single growth rate that treats all the past changes as if they occurred evenly across the entire duration of time covered.

CAGR is conceptually the annual rate of return needed for the initial value of a metric to grow from its current value to its ending value between the two specified dates.

The three inputs necessary to compute the CAGR are listed below.

1. Beginning Value
2. Ending Value
3. Number of Periods

Calculating the CAGR involves dividing the ending value by the beginning value, raising the resulting figure to the inverse number of periods (1 ÷ the number of periods), and subtracting one.

Note: The number of periods refers to the number of compounding periods.

Growth Rate Calculator

We’ll now move to a modeling exercise, which you can access by filling out the form below.

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1. US Population Statistics Assumptions

Suppose we’re attempting to evaluate the growth of the U.S. population.

The data set we’re working with – pulled from Data Commons – can be found below.

Source: Data Commons

2. Growth Rate Calculation Example

To calculate the year-over-year (YoY) growth rate, we’ll divide each year by the preceding year.

For example, the formula for calculating the YoY growth in 2001 is the current population in 2021 (284,968,955) divided by the population in 2000 (282,162,411), minus one.

• 2001 YoY Growth = (284,968,955 ÷ 282,162,411) – 1 = 0.99%

The growth rates for each year are as follows.

• 2000 → 2001 = 0.99%
• 2001 → 2002 = 0.93%
• 2002 → 2003 = 0.86%
• 2003 → 2004 = 0.93%
• 2004 → 2005 = 0.93%
• 2005 → 2006 = 0.97%
• 2006 → 2007 = 0.96%
• 2007 → 2008 = 0.95%
• 2008 → 2009 = 0.88%
• 2009 → 2010 = 0.83%
• 2010 → 2011 = 0.73%
• 2011 → 2012 = 0.74%
• 2012 → 2013 = 0.70%
• 2013 → 2014 = 0.74%
• 2014 → 2015 = 0.74%
• 2015 → 2016 = 0.73%
• 2016 → 2017 = 0.63%
• 2017 → 2018 = 0.53%
• 2018 → 2019 = 0.46%
• 2019 → 2020 = 0.35%
• 2020 → 2021 = 0.73%

3. Compound Annual Growth Rate Calculation Example (CAGR)

Next, the inputs used to calculate the compound annual growth rate (CAGR) are as follows.

• Number of Periods = 21 Years
• Beginning Value = 282,162,411
• Ending Value = 331,893,745

The CAGR of the U.S. population from 2000 to 2021 comes out to 0.78%.

• CAGR = (331,893,745 ÷ 282,162,411) ^ (1 ÷ 21 Years) – 1 = 0.78%