  We provide a sharp double-sided estimate for Poincar\'e-Sobolev constants on
a convex set, in terms of its inradius and $N-$dimensional measure. Our results
extend and unify previous works by Hersch and Protter (for the first
eigenvalue) and of Makai, P\'olya and Szeg\H{o} (for the torsional rigidity),
by means of a single proof.
