Logistic Population Growth Calculator

Work out logistic population growth instantly with clear inputs, formula shown and shareable results.

About Logistic Population Growth Calculator

Solves the logistic equation, where growth slows as the population approaches carrying capacity and is fastest at half of it.

Formula

Logistic growth

N(t) = K / (1 + ((K - N0)/N0) e^-rt); dN/dt = rN(1 - N/K), maximal at N = K/2

Worked example

With the default values below, Logistic Population Growth Calculator returns Population at that time of 2,635.09. Change any input above and every figure here is recalculated in your browser.

Inputs used

Initial populationaccepts 1–1,000,000,000: 100
Carrying capacityaccepts 2–1,000,000,000: 5,000
Intrinsic growth rateaccepts 0.001–5 per year: 0.4 per year
Timeaccepts 0.1–200 years: 10 years

Results

Population at that time: 2,635.09
Instantaneous growth: 498.540 per year
Share of carrying capacity reached: 52.70%
Time to the inflection point: 9.730 years

Step by step

1Values used
2Logistic growth
3Population at that time= 2,635.09
4Instantaneous growth= 498.540 per year
5Share of carrying capacity reached= 52.70
6Time to the inflection point= 9.730 years

Assumptions and limits

The result is derived only from the 4 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 3 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

Where is growth fastest?

At half the carrying capacity, which is also the maximum sustainable yield point in simple harvest models.

Does the population ever exceed K?

Not in the continuous logistic model, though time-lagged and discrete versions can overshoot and oscillate.