Logistic Growth Calculator
Calculate a bounded logistic population trajectory with entered initial population, capacity and intrinsic growth rate.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the closed-form logistic differential-equation solution with fixed rate and carrying capacity.
dN/dt=rN(1−N/K); N(t)=Kp/[p+(1−p)e^(−rt)], p=N₀/K
Worked example
Initial 10, capacity100 and intrinsic rate10% per day give approximately23.1969317 after10days. Initial zero remains zero, and an initial population at capacity stays there.
Assumptions and input details
Use 0≤initial≤capacity≤1e12 and positive capacity, nonnegative intrinsic rate and elapsed time. Rate is the continuous intrinsic parameter, not an observed compounded percent increase each day. Model time units are converted consistently. Capacity and rate are entered assumptions; no fitting, births/deaths census, migration, delay, seasonality or forecast accuracy is inferred.
References: OpenStax: logistic equation
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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