Model logistic population growth toward a carrying capacity.
Logistic growth starts nearly exponentially and slows as the population approaches carrying capacity, giving an S-shaped curve. The inflection point at half capacity is where absolute growth is fastest. Exponential models overshoot badly beyond the inflection point, which is why resource-limited populations need the logistic form.
Population Growth Biology
N(t) = K ÷ (1 + ((K−N₀)/N₀) e^(−rt))
N(t) = K ÷ (1 + ((K−N₀)/N₀) e^(−rt)) Logistic growth starts nearly exponentially and slows as the population approaches carrying capacity, giving an S-shaped curve. The inflection point at half capacity is where absolute growth is fastest.
Exponential models overshoot badly beyond the inflection point, which is why resource-limited populations need the logistic form.
This calculator takes 4 inputs: Initial population, Intrinsic growth rate, Carrying capacity, Years to project. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.