Biology & Life Sciences
Intermediate

Population Growth Rate

Per-capita growth from births and deaths.

Formula

r=B−DNr = \frac{B - D}{N}

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Variables

BBirths
DDeaths
NPopulation

Example

Positive means growing

How it works

This formula gives the net population change per individual in a population over a given time period. It works by taking the number of births and subtracting the number of deaths to find the net gain or loss, then dividing by the population size so the result is comparable across populations of different sizes. A positive value means the population is increasing, while a negative value means it is shrinking.

When to use it

Use this when you need a per-capita measure of how fast a population is changing, such as in ecology, microbiology, or epidemiology. It is especially useful for comparing growth rates between groups that do not have the same starting population size.

Worked example, step by step

Suppose a rabbit population has 200 individuals. In one month, 18 rabbits are born and 10 die. Use the formula: r = (B - D) / N Substitute the values: r = (18 - 10) / 200 Simplify: r = 8 / 200 Calculate: r = 0.04 Final answer: the population growth rate is 0.04 per rabbit per month, or 4% per month.

Common mistakes to avoid

  • Forgetting to subtract deaths from births before dividing
  • Using the wrong population size, such as the number of births instead of the total population
  • Confusing the per-capita growth rate with the total number of new individuals

Did You Know?

Population growth rate balances births against deaths, the simple arithmetic behind booming or shrinking species.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026