Population Growth (Exponential) Calculator

Work out population growth (exponential) instantly with clear inputs, formula shown and shareable results.

About Population Growth (Exponential) Calculator

Applies the continuous exponential growth model, in which the intrinsic rate of increase acts on the whole population at every instant.

Formula

Exponential growth

N(t) = N0 x e^(rt); doubling time = ln 2 / r

Worked example

With the default values below, Population Growth (Exponential) Calculator returns Population after the period of 1,648.7. Change any input above and every figure here is recalculated in your browser.

Inputs used

Initial populationaccepts 1–1,000,000,000,000: 1,000
Intrinsic growth rateaccepts -20–100: 5
Timeaccepts 0.1–500 years: 10 years

Results

Population after the period: 1,648.7
Net increase: 648.7
Doubling time: 13.863 years
Fold change: 1.6487

Step by step

1Values used
2Exponential growth
3Population after the period= 1,648.7
4Net increase= 648.7
5Doubling time= 13.863 years
6Fold change= 1.6487

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

When is exponential growth realistic?

Only when resources are effectively unlimited, such as early colonisation or a bacterial culture in fresh medium.

How does it differ from geometric growth?

Geometric growth uses discrete breeding seasons with a finite rate lambda; exponential growth is continuous.