  In a previous paper, the second author used embedded contact homology (ECH)
of contact three-manifolds to define "ECH capacities" of four-dimensional
symplectic manifolds. In the present paper we prove that for a four-dimensional
Liouville domain with all ECH capacities finite, the asymptotics of the ECH
capacities recover the symplectic volume. This follows from a more general
theorem relating the volume of a contact three-manifold to the asymptotics of
the amount of symplectic action needed to represent certain classes in ECH. The
latter theorem was used by the first and second authors to show that every
contact form on a closed three-manifold has at least two embedded Reeb orbits.
