  We combine the known asymptotic behaviour of the QCD perturbation series
expansion, which relates the pole mass of a heavy quark to the MSbar mass, with
the exact series coefficients up to the four-loop order to determine the
ultimate uncertainty of the top-quark pole mass due to the renormalon
divergence. We perform extensive tests of our procedure by varying the number
of colours and flavours, as well as the scale of the strong coupling and the
MSbar mass. Including an estimate of the internal bottom and charm quark mass
effect, we conclude that this uncertainty is around 110 MeV. We further
estimate the additional contribution to the mass relation from the five-loop
correction and beyond to be around 300 MeV.
