  We calculate the $m_d-m_u$ contribution to the mass splittings in baryonic
isospin multiplets using SU(3) chiral perturbation theory and lattice QCD.
Fitting isospin-averaged perturbation theory functions to PACS-CS and
QCDSF-UKQCD Collaboration lattice simulations of octet baryon masses, and using
the physical light quark mass ratio $m_u/m_d$ as input, allows $M_n-M_p$,
$M_{\Sigma^-}-M_{\Sigma^+}$ and $M_{\Xi^-}-M_{\Xi^0}$ to be evaluated from the
full SU(3) theory. The resulting values for each mass splitting are consistent
with the experimental values after allowing for electromagnetic corrections. In
the case of the nucleon, we find $M_n-M_p= 2.9 \pm 0.4 \textrm{MeV}$, with the
dominant uncertainty arising from the error in $m_u/m_d$.
