Algebra
The growth rate at any point
The differential equation behind the curve, and the fastest way to read the current momentum.
The Formula
dP/dt = r x P x (1 - P/K)
The differential equation behind the curve, and the fastest way to read the current momentum.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| dP/dt | Growth rate | units per unit time | How fast the population is rising right now. |
| r | Intrinsic rate | per unit time | The unconstrained rate when the population is tiny. |
| 1 - P/K | Room left | unitless | The fraction of capacity still unused. |
What Each Symbol Means
dP/dtunits per unit time
Growth rate
How fast the population is rising right now.
rper unit time
Intrinsic rate
The unconstrained rate when the population is tiny.
1 - P/Kunitless
Room left
The fraction of capacity still unused.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate logistic growth page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Logistic Growth, filed under Math. Every number the guide produces comes from substituting into this one line.