English: Overall view of logistic curve. The vertical axis is N/K, and the horizontal axis is rt. The curves were calculated from the equation

${\displaystyle {\frac {N}{K}}={\frac {1}{1+(K/N_{0}-1)e^{-rt}}}}$,

where, N is population, t is time, r is intrinsic rate of natural increase, K is carrying capacity. N₀ is the value of N when t = 0. The value of N₀/K for each curve is 10000, 1.5, 1.05, 0.75, 0.5, 0.25, -0.05, -0.5, and -9999 in order from the top.

Putting y = N/K and x = rt, above equation may be written in the form

${\displaystyle y={\frac {1}{1+(1/y_{0}-1)e^{-x}}}}$,

where, y₀ is the value of y when x = 0. If y₀ = 0.5,

${\displaystyle y={\frac {1}{1+e^{-x}}}}$.

This is called also (standard) sigmoidal curve.