A thermodynamic assessment of the KF-ThF4 binary system using the CALPHAD method is presented, where the liquid solution is described by the modified quasichemical formalism in the quadruplet approximation. The optimization of the phase diagram is based on experimental data reported in the literature and newly measured X-ray diffraction and differential scanning calorimetry data, which have allowed to solve discrepancies between past assessments. The low temperature heat capacity of α-K2ThF6 has also been measured using thermal relaxation calorimetry; from these data the heat capacity and standard entropy values have been derived at 298.15 K: Cp,mo(K2ThF6,cr,298.15K)=(193.2±3.9) J·K-1·mol-1 and Smo(K2ThF6,cr,298.15K)=(256.9±4.8) J·K-1·mol-1. Taking existing assessments of the relevant binaries, the new optimization is extrapolated to the ternary systems LiF-KF-ThF4 and NaF-KF-ThF4 using an asymmetric Kohler/Toop formalism. The standard enthalpy of formation and standard entropy of KNaThF6 are re-calculated from published e.m.f data, and included in the assessment of the ternary system. A calculated projection of the NaF-KF-ThF4 system at 300 K and the optimized liquidus projections of both systems are compared to published phase equilibrium data at room temperature and along the LiF-LiThF5 and NaF-KThF5 pseudobinaries, with good agreement.@en