📈 Population Growth Calculator
Project a population under exponential growth, or logistic growth with a carrying capacity — from the initial size, growth rate and time.
Population (exponential)
N(t) = N₀·e^(rt)
739
Doubling time
ln(2) / r
1.386 time units
How the population growth calculator works
Exponential growth is N(t) = N₀·e^(r·t). With a carrying capacity K, logistic growth is N(t) = K / (1 + ((K − N₀)/N₀)·e^(−r·t)), which levels off as the population approaches K. Enter a carrying capacity of 0 for pure exponential growth. The doubling time under exponential growth is ln(2)/r.
Pure ecological formulas with no reference data, so nothing to maintain. Useful for AP-Biology and ecology problems on exponential versus logistic growth.
Frequently asked questions
What is the exponential growth formula?
N(t) = N₀·e^(r·t), where N₀ is the starting population, r the per-capita growth rate and t the time. Growth is unbounded — the population keeps accelerating.
What is the logistic growth formula?
N(t) = K / (1 + ((K − N₀)/N₀)·e^(−r·t)), where K is the carrying capacity. Growth is fast at first, then slows and levels off as the population approaches K.
What is the difference between exponential and logistic growth?
Exponential growth assumes unlimited resources and never levels off. Logistic growth includes a carrying capacity K, so the curve is S-shaped and plateaus. Enter K = 0 here for exponential, or a positive K for logistic.
What is carrying capacity (K)?
The maximum population an environment can sustain given its resources. In the logistic model the population grows toward K and stabilises there.
How is the growth rate r related to doubling time?
Under exponential growth the doubling time is ln(2)/r. A growth rate of 0.5 per unit time gives a doubling time of about 1.39 time units.
What does r mean?
r is the intrinsic per-capita rate of increase — births minus deaths per individual per unit time. Positive r means growth, negative r decline.