  We prove an inequality, valid on any finitely generated group with a fixed
finite symmetric generating set, involving the growth of successive balls, and
the average length of an element in a ball. It generalizes recent improvements
of the Coulhon Saloff-Coste inequality. We reformulate the inequality in terms
of the F{\o}lner function; in the case the finitely generated group is amenable
with exponential growth, this allows us to express the best possible (outer)
constant in the Coulhon Saloff-Coste isoperimetric inequality with the help of
a formula involving the growth rate and the asymptotic behavior of the
F{\o}lner function.
