Population Growth Calculator for Ecology and AP Biology
Compare continuous exponential growth, logistic growth with carrying capacity, and microbial doubling. Enter a starting population and time to see a model prediction, worked steps and a table. Choose a consistent time unit before interpreting a growth rate.
Enter your values or load an example to see the answer and worked steps. Calculations run in your browser.
Choose the model your biology problem describes
Exponential mode uses N(t) = N₀e^(rt). Logistic mode uses N(t) = K/[1 + (K/N₀ − 1)e^(−rt)], with zero population handled as an equilibrium. Generation-time mode uses N(t) = N₀ × 2^(t/g), where g is the time per doubling. These are different assumptions, not interchangeable labels.
Percent rate and elapsed time must agree
A rate of 10% per day is entered as 10 with days selected; the calculator converts it to r = 0.1 per day. Continuous growth is not the same as increasing by 10% once each day. If your question specifies discrete compounding, its equation is N₀(1 + r)^t and this continuous-rate mode does not apply.
Try a worked population example
Start with 100 organisms, r = 10% per day and t = 10 days. Exponential mode gives 100e¹ ≈ 271.82818 organisms. With the same inputs and K = 1,000, logistic mode gives approximately 231.96932. The difference comes from the carrying-capacity term, not rounding.
Interpret doubling time carefully
For positive exponential r, the doubling time is ln(2)/r. Negative r instead gives a half-life of ln(2)/|r|. Logistic growth does not have a constant doubling time. The microbial mode assumes a fixed doubling time and does not model a lag phase or nutrient exhaustion.
Where the model stops
Population predictions can be fractional because the equations describe an idealized expectation. Migration, changing resources, age structure and random events are not inputs here. Use the table to inspect the model, not as a measurement of a real population.
References
Related free tools
Frequently Asked Questions
Does this calculate human population forecasts?
It evaluates classroom growth equations for ecology and biology. It does not include the demographic inputs required for a population forecast.
Can the starting population be zero?
Yes. With no migration term, all three models keep a zero starting population at zero.
Can a logistic population start above carrying capacity?
Yes. For positive r it declines toward K. The calculator accepts that case instead of incorrectly forcing the starting population below K.
Can I model decay?
Use exponential mode with a negative continuous growth rate. Logistic mode here accepts nonnegative intrinsic growth rates.
Does this include bacterial generation time?
Yes. Choose microbial doubling, enter time per doubling and use the same time unit for elapsed time.
Continue in the app
Use Biology AI: Bionomy for the full guided result after this quick check.
