  The solution of the Poisson--Boltzmann equation for counterions confined
between two charged plates is known analytically up to a constant, namely, the
ion density in the middle of the channel. This quantity is relevant also
because it gives access, through the contact theorem, to the osmotic pressure
of the system. Here we compare the values of the ion density obtained by
numerical and simulation approaches, and report a useful analytic approximation
for the weak coupling regime in the absence of added salt, which predicts the
value of the ion density in the worst case within 5%. The inclusion of higher
order terms in a Laurent expansion can further improve the accuracy, at the
expense of simplicity.
