Why must observed change be less than rN?

In the logistic model, density limits reduce growth below the unrestricted rN value.

Can K change over time?

Yes. This calculator estimates one fixed K for the entered observation.

Estimate carrying capacity from current population and observed logistic growth.

Answer

3,600

Estimated carrying capacity

Share of capacity: 33.33%

Remaining capacity: 2,400

Unrestricted growth rN: 180

Density limit factor: 0.33

Current population (N)Growth rate (r)Observed change (dN/dt)Projection step

Examples

Projected logistic growth

Time	Projected population	Projected change	Share of capacity
0	1,200	0	33.33%
5	1,851	651	51.42%
10	2,489	638	69.14%
15	2,973	484	82.59%
20	3,274	301	90.94%
25	3,438	164	95.51%
30	3,522	83	97.83%

dN/dt = rN(1 - N/K); K = N / (1 - (dN/dt)/(rN))

The calculator rearranges the logistic growth equation to estimate K from observed population change.

Symbol	Variable	Description
N	Current population	Population at the observation point.
r	Growth rate	Intrinsic growth rate per time unit.
dN/dt	Observed change	Population increase per matching time unit.

1
Enter observed values
Use the same time unit for r and observed change.
2
Read K
The top answer is the estimated carrying capacity.
3
Check projections
The table shows how the estimated K shapes future logistic growth.

These checks help decide whether the inferred K is usable.

Check	Meaning
rN	Growth expected without density limits
Density limit factor	1 - N/K
Share of capacity	N divided by estimated K

Logistic Growth Model Calculator

Model logistic population growth with carrying capacity, K percentage, inflection point, and a time-series growth table.

Population Growth Calculator

Model exponential population growth over time in ecology.

Shannon Diversity Index Calculator

Calculate Shannon H', evenness, richness, effective species, and per-species contribution from abundance counts.