A one-relator group is a group $G_r$ that admits a presentation $<S | r >$ with a single relation $r$. One-relator groups form a rich classically studied class of groups in Geometric Group Theory. If $r \in F (S)'$, we introduce a simplicial volume $\|G_r \|$ for one-relator groups. We relate this invariant to the stable commutator length of the element $r \in F (S)$ and ask if there is a linear relation between both quantities. A positive answer to this question would imply rationality and quick computability for simplicial volume of one-relator groups and a possible approach to the second-gap conjecture in stable commutator length. Moreover, we give computational bounds in several instances.