The Basic Formula for Population Growth Rate

Population growth rate measures how fast a population is increasing or decreasing over a set period. The formula is straightforward: subtract the starting population from the ending population, divide by the starting population, then multiply by 100 to express it as a percentage.

The equation looks like this: ((Ending Population − Starting Population) ÷ Starting Population) × 100 = Growth Rate (%).

For example, if a town had 50,000 people at the start of the year and 52,500 at the end, the calculation would be ((52,500 − 50,000) ÷ 50,000) × 100 = 5%. The population grew by 5% over that year.

Key Takeaways

  • Population growth rate is calculated by dividing the population change by the starting population, then multiplying by 100 to get a percentage.
  • You need two data points: the population at the beginning of your time period and the population at the end.
  • A positive result means the population increased; a negative result means it decreased.
  • The time period can be one year, five years, a decade, or any span you choose — just be clear about what period you are measuring.
  • Growth rate tells you the percentage change, not the actual number of people added or lost.

Gathering Your Population Data

Before you calculate, you need two population figures: one from the start of your time period and one from the end. These numbers come from census data, government statistics, or organizational records depending on what population you are tracking.

For national or regional populations, census bureaus publish official counts. In the United States, the U.S. Census Bureau releases decennial census data every 10 years, plus annual estimates in between. Other countries have their own statistical agencies that publish similar figures.

If you are tracking a smaller population — a school district, a company, a neighborhood — you may pull numbers from internal records, local government databases, or published reports from the organization itself. Make sure both figures come from the same source or use the same counting method, because different sources sometimes use slightly different definitions of who counts as part of the population.

Working Through a Multi-Year Example

Let's walk through a longer time span to show how the formula works over several years. Suppose you want to find the growth rate for a country over a 10-year period: 2010 population was 100 million, and 2020 population was 125 million.

Step 1: Find the change. 125 million − 100 million = 25 million people added.

Step 2: Divide the change by the starting population. 25 million ÷ 100 million = 0.25.

Step 3: Multiply by 100 to convert to a percentage. 0.25 × 100 = 25%.

The population grew by 25% over the 10-year period. This does not tell you the growth was even each year — some years may have had faster growth than others — but it gives you the total change across the entire decade.

Calculating Annual Growth Rate from Total Growth

If you know the total growth over multiple years and want to find the average growth per year, you use a different formula. This is called the compound annual growth rate (CAGR), and it accounts for the fact that growth builds on itself year after year.

The CAGR formula is: (Ending Population ÷ Starting Population) ^ (1 ÷ Number of Years) − 1, then multiply by 100 for a percentage.

Using the same example: (125 million ÷ 100 million) ^ (1 ÷ 10) − 1 = (1.25) ^ (0.1) − 1 ≈ 0.0225, or about 2.25% per year on average. This means the population grew by roughly 2.25% each year for 10 years, compounded.

The compound annual rate is lower than dividing the total rate by the number of years (25% ÷ 10 = 2.5%) because compound growth means each year's growth builds on the previous year's total.

Handling Negative Growth and Population Decline

When a population shrinks, the growth rate becomes negative. The formula works exactly the same way — you will straightforward get a negative number as your result.

For example, if a region had 200,000 people in 2015 and 190,000 in 2020, the calculation is ((190,000 − 200,000) ÷ 200,000) × 100 = (−10,000 ÷ 200,000) × 100 = −5%. The population declined by 5% over that five-year span.

Negative growth rates are common in regions with aging populations, outmigration, or lower birth rates. The calculation method does not change — only the sign of the result tells you whether the population is growing or shrinking.

Common Mistakes to Avoid

The most frequent error is dividing by the ending population instead of the starting population. The starting population is your baseline — it is what you divide by to see how much the population changed relative to where it began.

Another mistake is forgetting to multiply by 100. Without that step, you get a decimal (0.05) instead of a percentage (5%). Both numbers represent the same growth, but percentages are the standard way to report population growth rates so they are straightforward to compare across different populations.

A third pitfall is mixing time periods. If you use a population figure from mid-year for the start and an end-of-year figure for the end, your time span is only six months, not a full year. Be consistent about whether you are using figures from the same date each year, or clearly note the exact dates you are using.

Frequently Asked Questions

What if I only have population data for some years, not every year?

Use the earliest year you have as your starting point and the most recent year as your ending point. The formula still works — you are just measuring growth across a longer span. If you have data for 2010 and 2020 but not the years in between, calculate the growth from 2010 to 2020 as a single 10-year period.

Can I use this formula for any population, like a bacteria culture or a wildlife population?

Yes. The formula works for any population where you have a count at two different points in time. Scientists use it to track bacterial growth in labs, wildlife biologists use it for animal populations, and businesses use it to track customer or employee numbers. The math is identical.

Why do growth rates matter if I already know the actual number of people added?

Growth rate lets you compare populations of different sizes fairly. A city that gained 10,000 people might have grown 2%, while a town that gained 5,000 might have grown 10%. The percentage tells you which population is actually growing faster relative to its starting size.

What is the difference between growth rate and doubling time?

Growth rate is the percentage change over a specific period you choose. Doubling time is how long it would take a population to double in size if growth continued at the same rate. You can calculate doubling time from growth rate using the rule of 70 (divide 70 by the annual growth rate), but they measure different things.

Do I need to account for births, deaths, and migration separately?

The basic growth rate formula does not break those out — it just shows the net result. If you need to know how much growth came from births versus immigration, you would need separate data on those components. The straightforward formula tells you the total change, regardless of what caused it.