Population Growth Rate Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The continuous growth rate is calculated with r = ln(final population ÷ initial population) ÷ time, expressed as a percentage. A population going from 1,000 to 1,500 individuals over 10 periods grows at a rate of about 4.055% per period.
Explanation
This calculator finds a population's continuous growth rate from two observations (a starting count and an ending count) separated by a known time span, assuming a continuous exponential growth model — the same model used by our doubling time calculator, which works the other way around (finding the doubling time from the rate). A positive result indicates a growing population, a negative result a declining one. The result is expressed in the unit of the period entered for the duration (years, hours for a bacterial culture, generations): a growth rate per hour doesn't mean the same thing as a rate per year. As with doubling time, this model assumes a constant growth rate over the entire observed period, a simplification that departs from reality once limiting factors (resources, predation, competition) come into play.
Example: a population going from 1,000 to 1,500 individuals over 10 periods
Inputs
Initial population: 1,000. Final population: 1,500. Duration: 10 periods.
Calculation
Growth rate = ln(1,500 ÷ 1,000) ÷ 10 × 100 = ln(1.5) ÷ 10 × 100 ≈ 0.405465 × 10 ≈ 4.055%.
Result
This population grows at a continuous rate of about 4.055% per period.
Frequently asked questions
What does a negative growth rate mean?
A negative result indicates the population is shrinking rather than growing: the final population entered is lower than the initial one. The formula stays the same, but the logarithm of a ratio below 1 is negative.
What's the difference from a simple annual growth rate?
A simple growth rate (final population ÷ initial population − 1, divided by the number of periods) assumes linear growth. The continuous rate calculated here instead assumes exponential growth, where each period grows on top of the already-increased previous period — a more realistic model for biological populations over the short and medium term.
Can this calculator be used for a human population, or only in biology?
The mathematical model is generic and applies to any quantity undergoing continuous exponential growth: an animal population, a cell culture, but also a human population at the scale of a city or country over a given period, as long as the assumption of a constant rate remains a reasonable approximation.