Carrying Capacity Calculator

Enter the population size, intrinsic growth rate, and the average population change over the same time period to estimate the carrying capacity using the logistic growth model.

Use the logistic growth equation to solve for carrying capacity (K) or forecast population over time.

Solve for Carrying Capacity (K)

Logistic Growth Forecast

Formula used: dN/dt = rN(1 − N/K), rearranged to K = N / (1 − (dN/dt) / (rN)).

Current Population N

Intrinsic Growth Rate r (% per time period)

Example: enter 12 for 12% growth per year.

Population Change dN/dt

Formula used: N(t) = K / (1 + ((K − N₀) / N₀)e^−rt).

Initial Population N₀

Carrying Capacity K

Intrinsic Growth Rate r

Time t

Optional target percent of K

Leave blank to skip target-time output.

Carrying Capacity Formula

The logistic population growth model is:

\frac{dN}{dt} = rN\left(1-\frac{N}{K}\right)

If you know the current population size N, the intrinsic growth rate r (per time), and the average change in population per time period (CP ≈ ΔN/Δt), you can rearrange to estimate carrying capacity K:

K = \frac{N}{1-\frac{CP}{rN}}

Where K is the carrying capacity (individuals)
r is the intrinsic growth rate (as a decimal per unit time; e.g., 50% per year = 0.50/year)
N is the current population size (individuals)
CP is the average change in population per unit time (CP ≈ ΔN/Δt, in individuals per unit time)

To estimate the carrying capacity, convert r from percent to a decimal, compute the fraction CP/(rN), then calculate K = N / (1 − CP/(rN)). The time unit used for r and CP must match (for example, both “per year”).

Carrying Capacity Definition

Carrying capacity (often written as K) is the maximum population size of a species that an environment can sustainably support given available resources and other constraints. In simple models it is treated as constant, but in real ecosystems it can change over time as conditions change.

Carrying Capacity Example

How to calculate a carrying capacity?

First, determine the intrinsic growth rate r over a specific time unit. In this example, r = 50% per year, so r = 0.50/year.

Next, determine the current population size. For this example, N = 5000 individuals.

Next, determine the average change in population over the same time unit. In this case, CP = 100 individuals per year (i.e., ΔN/Δt = 100/year).

Finally, calculate the carrying capacity using the formula above:

K = N / (1 − CP/(rN))

K = 5000 / (1 − 100/(0.50·5000))

K = 5000 / (1 − 0.04) = 5000 / 0.96 = 5208.33

Estimated carrying capacity: K ≈ 5208 individuals

FAQ

What is carrying capacity?

Carrying capacity (K) is the maximum population size an environment can sustainably support. It is a key parameter in the logistic population growth model.