How to Find Per Capita Growth Rate of Populations

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  • 0:04 Growth Rate in Perspective
  • 0:46 Determining the Rate
  • 1:59 Example One
  • 3:16 Example Two
  • 4:48 Lesson Summary
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Lesson Transcript
Instructor: Lauren Posey

Lauren has taught intermediate reading in an English Language Institute, and she has her Master's degree in Linguistics.

When looking at growth rate of populations, calculating it in proportion to the actual population is very useful. This is what the per capita growth rate does. Learn more about it in this lesson.

Growth Rate in Perspective

Let's say you are looking at your hometown, and you notice that the population has increased by 2,000 people in the last ten years. What does this mean? Is it a lot? If the population started at 4,000, then this would be a huge increase. However, if it started at two million, then an increase of 2,000 really isn't all that much.

Having population growth stated as a number of individuals does not put it into perspective. To do this, it has to be related to the population at the starting point, so you can see how much it has grown expressed as a percentage of the population. This is what the per capita growth rate does: It gives a rate that is proportional to the number of individuals in a population.

Determining the Rate

To determine the total per capita growth rate of a population for a certain time period, you use the following formula:

CGR = G / N

Here, CGR is per capita growth rate. G is the change in size of the population, expressed as a number of individuals. You find this by taking the initial population and subtracting it from the current population. Finally, N is the initial population.

This formula will give you CGR as a decimal. To set it as a percentage, all you have to do is multiply it by 100. This gives you the percent the population has grown over the entire time period you're looking at. From there, you can also calculate it as an annual percentage, or monthly, or whatever time period you want. All you have to do is take the CGR percentage you just found and divide it by the number of years, months, etc.

The complete formula for annual per capita growth rate is:

((G / N) * 100) / t, where t is the number of years.

Finding the annual per capita growth rate, as opposed to only the rate for the entire time period, makes it easier to predict future population changes because it relates to both time and overall population.

Example One

Now, let's look at some examples.

Let's say you want to find the per capita growth rate of a town between 1990 and 2000. To start, you need to know the population in 1990 and the population in 2000. You check the records, and find that the population in 1990 was 480,000 people, and the population in 2000 was 550,000 people.

Now you have the information to find G, or the change in the population. G = 550,000-480,000. So, G = 70,000. This means that the total population increased by 70,000 people over the ten year period.

Next, plug in this information to the per capita growth rate formula:

CGR= 70,000 / 480,000 = 0.15. Multiply by 100 to get a percentage, and you see that the population grew by 15% over the entire ten year period.

At this point, finding the annual per capita growth rate is simple. Divide the per capita growth rate percent (or 15) by the number of years (or 10).

15 / 10 = 1.5. This means that the population of the town grew by 1.5% annually during the 1990-2000 time period.

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