  In this paper we study the Weil-Petersson geometry of
$\overline{\mathcal{M}_{g,n}}$, the compactified moduli space of Riemann
surfaces with genus g and n marked points. The main goal of this paper is to
understand the growth of the diameter of $\overline{\mathcal{M}_{g,n}}$ as a
function of $g$ and $n$. We show that this diameter grows as $\sqrt{n}$ in $n$,
and is bounded above by $C \sqrt{g}\log g$ in $g$ for some constant $C$. We
also give a lower bound on the growth in $g$ of the diameter of
$\overline{\mathcal{M}_{g,n}}$ in terms of an auxiliary function that measures
the extent to which the thick part of moduli space admits radial coordinates.
