  We investigate the inequality ${\rm Findim}\ \! \Lambda^{op} \leq {\rm dell}\
\! \Lambda$ between the finitistic dimension and the delooping level of an
Artin algebra $\Lambda$, and whether equality holds in general. We prove that
equality ${\rm Findim}\ \! \Lambda^{op} = {\rm dell}\ \! \Lambda$ always holds
for Artin algebras with radical square zero.
