## What is Growth Rate?

The **Growth Rate** reflects the percentage change in a metric, such as the population or sales, across a specified time frame.

How to Calculate Growth Rate?

The term “growth rate” describes the rate of change in the value of a specific metric across a given time period, expressed as a percentage.

Common examples of scenarios where the growth rate is often used are the following:

- Company Sales
- Population Figures
- Gross Domestic Product (GDP)
- Inflation Rate

Under the specific context of financial modeling, the growth rate is most frequently on a quarterly or annual basis (i.e. year-over-year).

More defensible predictions can be made about the future trajectory of a metric in question by determining its historical growth, which can serve as a practical point of reference for forecasting purposes.

However, the metric’s usefulness is still tied to the extent that the underlying drivers are identified and researched in-depth.

By itself, calculating the historical growth is not enough, because what actually caused the past growth and which qualitative factors are likely to determine a metric’s future growth must also be clearly understood.

## Growth Rate Formula

The following formula can be used to calculate the growth rate across two periods.

**Growth Rate (%) =**(Ending Value

**÷**Beginning Value)

**–**1

For example, if a company’s revenue was $100 million in 2020 and grew to $120 million in 2021, its year-over-year (YoY) growth rate is 20%.

- Growth Rate = ($120 million ÷ $100 million) – 1 = 0.20, or 20%

## CAGR: How to Annualize 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).

CAGR represents 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.

- Beginning Value
- Ending Value
- 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.

**CAGR =**(Ending Value

**÷**Beginning Value)

**^**(1

**÷**Number of Periods)

**–**1

Note that 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.

## Step 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.

Year | U.S. Population |
---|---|

2000 | 282,162,411 |

2001 | 284,968,955 |

2002 | 287,625,193 |

2003 | 290,107,933 |

2004 | 292,805,298 |

2005 | 295,516,599 |

2006 | 298,379,912 |

2007 | 301,231,207 |

2008 | 304,093,966 |

2009 | 306,771,529 |

2010 | 309,327,143 |

2011 | 311,583,481 |

2012 | 313,877,662 |

2013 | 316,059,947 |

2014 | 318,386,329 |

2015 | 320,738,994 |

2016 | 323,071,755 |

2017 | 325,122,128 |

2018 | 326,838,199 |

2019 | 328,329,953 |

2020 | 329,484,123 |

2021 | 331,893,745 |

Source: Data Commons

## Step 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%

## Step 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%