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Carrying Capacity Calculator

Work out carrying capacity instantly with clear inputs, formula shown and shareable results.

About Carrying Capacity Calculator

Rearranges the logistic growth equation to infer carrying capacity from the current population, its observed growth and the intrinsic rate of increase.

Formula

Capacity from logistic growth

dN/dt = rN(1 - N/K) rearranges to K = rN^2 / (rN - dN/dt); maximum sustainable yield = rK/4

Worked example

With the default values below, Carrying Capacity Calculator returns Implied carrying capacity of 2,133.3. Change any input above and every figure here is recalculated in your browser.

Inputs used

Current populationaccepts 1–1,000,000,000
800
Observed growthaccepts 0.01–100,000,000 per year
200 per year
Intrinsic growth rateaccepts 0.001–5 per year
0.4 per year

Results

Implied carrying capacity
2,133.3
Share of capacity currently occupied
37.50%
Maximum sustainable yield
213.33 per year
Remaining headroom
1,333.3

Step by step

  1. 1Values used
  2. 2Capacity from logistic growth
  3. 3Implied carrying capacity= 2,133.3
  4. 4Share of capacity currently occupied= 37.50
  5. 5Maximum sustainable yield= 213.33 per year
  6. 6Remaining headroom= 1,333.3

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 2 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

Why can the answer be undefined?

If observed growth equals or exceeds rN the population is not following logistic growth, and no finite capacity fits.

Is carrying capacity fixed?

No. It shifts with habitat quality, climate and competition, so an inferred value applies only to current conditions.

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