  We prove upper bounds for the Hilbert-Samuel multiplicity of standard graded
Gorenstein algebras. The main tool that we use is Boij-S\"oderberg theory to
obtain a decomposition of the Betti table of a Gorenstein algebra as the sum of
rational multiples of symmetrized pure tables. Our bound agrees with the one in
the quasi-pure case obtained by Srinivasan [J. Algebra, vol.~208, no.~2,
(1998)].
