How to use the logistic population growth calculator
Model population growth limited by carrying capacity. Enter initial population, carrying capacity, intrinsic growth rate, time in the fields above; the population at t, percent of carrying capacity, maximum growth rate are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- N0 — Initial population
- K — Carrying capacity
- r — Intrinsic growth rate
- t — Time
Worked example
With initial population = 50, carrying capacity = 1000, intrinsic growth rate = 0.3, time = 20, the calculator gives population at t ≈ 955.022; percent of carrying capacity ≈ 95.5022 %; maximum growth rate ≈ 75.
Frequently asked questions
What is the formula for the logistic population growth calculation?
Population at t = K / (1+((K-N0) / N0) × exp(-r × t)). Percent of carrying capacity (%) = 100 × [Population at t] / K. Maximum growth rate = r × K / 4. Here N0 is initial population, K is carrying capacity, r is intrinsic growth rate, t is time.
What inputs do I need for the logistic population growth calculator?
You need initial population, carrying capacity, intrinsic growth rate, time. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.