Population growth calculator

This calculator projects how a population grows over time at a constant rate, using either the discrete model (1 + r)ᵗ or the continuous exponential model e^(rt). Enter a starting population, a growth rate per period, and the number of periods to see the projected size, the total increase, the overall percentage growth, and the approximate doubling time. It works for people, animals, bacteria, or any quantity that grows by a fixed percentage.

Discrete vs continuous growth

The discrete model, P = P₀(1 + r)ᵗ, applies when growth happens in steps — for example, a yearly census. The continuous model, P = P₀e^(rt), applies when growth happens constantly, such as bacteria dividing. For small rates the two give very similar answers; they diverge as the rate grows.

Doubling time and the rule of 70

Doubling time is how long it takes a population to double. A handy shortcut is the “rule of 70”: divide 70 by the percentage growth rate to estimate it — so 2% growth doubles in about 35 years. The calculator works out the exact doubling time for your chosen model. For exponential decay, enter a negative rate.

Frequently asked questions

Can I model decline?

Yes. Enter a negative growth rate (for example −1.5%) to model a shrinking population or exponential decay.