Biology & Life Sciences
Basic

Per Capita Growth Rate

Net growth rate from birth and death rates.

Formula

r=b−dr = b - d

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Variables

bBirth rate
dDeath rate

Example

b=0.05,d=0.02 ⇒ r=0.03

How it works

Per capita growth rate tells you how quickly a population changes per individual, which makes it easier to compare populations of different sizes. It is found by subtracting the death rate from the birth rate because each birth adds one individual and each death removes one, so the net change is births minus deaths. If births outnumber deaths, the population grows; if deaths outnumber births, it shrinks.

When to use it

Use this formula in ecology, population biology, or demographic studies when you want a simple measure of whether a population is increasing or decreasing. It is especially useful for modeling bacteria, animal populations, or human populations when birth and death rates are given separately.

Worked example, step by step

Suppose a fish population has a birth rate of b = 0.08 and a death rate of d = 0.03. Use the formula: r = b - d Substitute the values: r = 0.08 - 0.03 Calculate: r = 0.05 So, the per capita growth rate is 0.05, meaning the population is growing by 5% per unit time.

Common mistakes to avoid

  • Adding birth and death rates instead of subtracting death rate from birth rate
  • Forgetting that r can be negative when death rate is larger than birth rate
  • Confusing per capita growth rate with total population change, which depends on population size too

Did You Know?

The per-capita growth rate captures how fast a population expands relative to its own size.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026