A population's growth potential is significantly underestimated by con
ventional calculations of population momentum which assume an immediat
e drop to replacement level fertility. Here we assume that the growth
rate of births linearly declines to zero over a specified time interva
l, and find simple and intuitively meaningful expressions for the size
of the ultimate birth cohort and the resultant population momentum. I
n particular, we find that the increase in the number of births over t
he transition is equal to growth at the initial rate for half the time
needed to attain a constant birth level. Thus our formula readily cal
culates the growth potential of a population under a gradual approach
to stationarity without the need for a numerical projection. Calculati
ons for actual and hypothetical populations are presented to show the
demographic impact of such gradual approaches to zero growth.