How to Calculate Population Growth Rate
Understanding population dynamics is crucial for demographers, city planners, and government policymakers. The population growth rate measures how the size of a population changes over a specific period. It is usually expressed as a percentage, indicating the rate of natural increase (births minus deaths) combined with the effects of net migration.
This calculator determines three key metrics: the absolute change in population, the total percentage growth over the entire period, and the Compound Annual Growth Rate (CAGR), which represents the smoothed annualized growth rate.
The Population Growth Formulas
Depending on whether you need the total growth or the annual rate, different formulas are used. Our calculator uses the exponential growth model to determine the annual rate, which assumes growth compounds over time.
Change = Final Population ($P_t$) – Initial Population ($P_0$)
Growth % = $\left( \frac{P_t – P_0}{P_0} \right) \times 100$
$r = \left( \left( \frac{P_t}{P_0} \right)^{\frac{1}{t}} – 1 \right) \times 100$
Where $t$ is the number of years.
Example Calculation
Let's say you want to calculate the growth rate of a city:
- Initial Population (Year 0): 500,000
- Final Population (Year 10): 650,000
- Time Period: 10 Years
Step 1: Absolute Change
$650,000 – 500,000 = 150,000$ new residents.
Step 2: Total Percentage
$(150,000 / 500,000) \times 100 = 30\%$ total growth.
Step 3: Annual Rate
To find the annual rate, we calculate: $(650,000 / 500,000)^{(1/10)} – 1$.
$1.3^{0.1} – 1 \approx 1.0266 – 1 = 0.0266$.
Expressed as a percentage: 2.66% per year.
Key Factors Influencing Population Growth
When analyzing the data derived from this calculator, consider the components of population change:
- Natural Increase: The difference between the number of live births and the number of deaths during the year.
- Net Migration: The difference between the number of immigrants (people moving into an area) and emigrants (people moving out).
A positive rate indicates a growing population, while a negative rate (depopulation) indicates a shrinking population.