Logistic Population Growth Calculator

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Logistic Population Growth Calculator: Growth With a Carrying Capacity

Real populations don't grow forever — as they approach the environment's carrying capacity, growth slows and eventually levels off, producing the characteristic S-shaped logistic curve rather than an ever-accelerating exponential one. This calculator projects population size under that more realistic model.

The Formula

N(t) = K / (1 + ((K − N0)/N0) × e(−r × t))

Worked Example

A population of 100 individuals with a carrying capacity of 1,000, growing at 10% per year, projected 20 years out.

N(20) = 1,000 / (1 + 9 × e−2) = 450.85 individuals

How to Use This Calculator

  1. Enter the initial population size.
  2. Enter the environment's carrying capacity.
  3. Enter the intrinsic growth rate as a percentage.
  4. Enter the number of years to project forward.
  5. Click Calculate to get the projected population under logistic growth.

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Compare against the Population Growth Rate Calculator for the unconstrained exponential case.