  We examine the ability of experimental measurements of top-quark pair
production to constrain both the top-quark mass and the strong coupling within
the global MSHT parton distribution function (PDF) fit. Specifically, we
consider ATLAS and CMS measurements of differential distributions taken at a
centre-of-mass energy of 8 TeV, as well as $t\bar{t}$ total cross section data
taken at a variety of experiments, and compare to theoretical predictions
including next-to-next-to-leading order corrections. We find that supplementing
the global fit with this additional information results in relatively strong
constraints on the top-quark mass, and is also able to bound the strong
coupling in a limited fashion. Our final result is
$m_t=173.0\pm0.6~\mathrm{GeV}$ and is compatible with the world average pole
mass extracted from cross section measurements of $172.5\pm0.7~\mathrm{GeV}$ by
the Particle Data Group. We also study the effect of different top-quark masses
on the gluon parton distribution function, finding changes at high $x$ which
nonetheless lie within the large PDF uncertainties in this region.
