  The mass of protoplanetary discs sets the amount of material available for
planet formation, determines the level of coupling between gas and dust, and
possibly sets gravitational instabilities. Measuring mass of discs is
challenging, since it is not possible to directly detect H$_2$, and CO-based
estimates remain poorly constrained. An alternative method that does not rely
on tracers-to-H$_2$ ratios has recently been proposed to dynamically measure
the disc mass altogether with the star mass and the disc critical radius by
looking at deviations from Keplerian rotation induced by the self-gravity of
the disc. So far, this method has been applied to weigh three protoplanetary
discs: Elias 2-27, IM Lup and GM Aurigae. We provide here a numerical benchmark
of the method by simulating isothermal self-gravitating discs with a range of
masses from 0.01 to $0.2 \,M_{\odot}$ with the phantom code and post-process
them with radiative transfer (mcfost) to obtain synthetic observations. We find
that dynamical weighing allows to retrieve the expected value of disc masses as
long as the disc-to-star mass ratio is larger than $M_d/M_\star=0.05$. The
estimated uncertainty for the disc mass measurement is $\sim 25\%$.
