How do you calculate annual growth rates?

One of the most basic analyses we perform in environmental science is estimating growth rates, whether it’s the growth rate of Koala populations in a forest reserve, the growth rate of fossil fuel use, or the growth rate of human populations over time.

Calculating a growth rate is not much more difficult than calculating a percentage. We know that 5 people out of 20 is 25% of the population. That calculation looks like this

But what if we want to know how fast we’re adding people? Again, calculating this isn’t much more difficult than figuring out how fast you’re going on a road. Let’s say we’ve traveled 30 km in 10 hours. We can easily work out we’ve been walking at 3km/hr by dividing 30 km by 10 hours.

So let’s keep percentages and rates in the back of our mind and start with an example for calculating human population growth:

In 1990, the population of Tasmania, Australia was 250,000 people. In 2000, it was 280,000 people.

In this case, t₀ is population the first time it was measured, or 250,000 people (the 0 subscript in t₀ indicates the initial, or starting, time). The population at Time 1, or t₁, is 280,000 people.

Population Growth Calculation

To calculate the Population Growth (PG) we find the difference (subtract) between the initial population and the population at Time 1, then divide by the initial population and multiply by 100.

The Population Growth Rate (PGR) for that period of time (10 years) was 12%. Compare this equation to the one we used above to calculate percent and you will see that they are very similar.

Now, that’s the total Population Growth (PG) over 10 years – it’s not a rate yet. A rate is simply, change per unit of time. We know that the growth took place over 10 years, so if we divide the total PG by 10 years, we’ll be left with a percentage change per year, or the Population Growth Rate (PGR).

What if we want to know how long it will take for a population to double, or the Doubling Time (DT)? Once we know the Population Growth Rate (PGR) we can use the Rule of 70 (a neat little trick from the field of economics) to help us figure out how many years it will take for a population to double.

Let’s use our Tasmanian example. We know that every year the population of Tasmania increases 1.2%. To calculate the estimated DT (in years) of the population in Tasmania, simply divide 70 by 1.2% per year.

So, if the PGR of Tasmania doesn’t change, then it will take just over 58 years to double the population. In the next step, you’ll get to use your calculator to calculate the PG, PGR and DT of a nation.

Give it a try, and feel free to apply this great method to lots of other things in your life, environmental or otherwise.