  We introduce the concept of quantifying the extent to which a finitely
generated group is residually finite. The quantification is carried out for
some examples including free groups, the first Grigorchuk group, finitely
generated nilpotent groups, and certain arithmetic groups such as
$SL_n(\mathbb{Z})$. In the context of finite nilpotent quotients, we find a new
characterization of nilpotent groups.
