Potassium-ion batteries (KIBs) are emerging as a promising alternative technology to lithium-ion batteries (LIBs) due to their significantly reduced dependency on critical minerals. KIBs may also present an opportunity for superior fast-charging compared to LIBs, with significantly faster K-ion electrolyte transport properties already demonstrated. In the absence of a viable K-ion electrolyte, a full-cell KIB rate model in commercial cell formats is required to determine the fast-charging potential for KIBs. However, a thorough and accurate characterisation of the critical electrode material properties determining rate performance---the solid state diffusivity and exchange current density---has not yet been conducted for the leading KIB electrode materials. Here, for the first time, we accurately characterise the effective solid state diffusivities and exchange current densities of the graphite anode and potassium manganese hexacyanoferrate KMn[Fe(CN)6] (KMF) cathode, through a combination of optimised material design and state-of-the-art analysis. Finally, we present the first Doyle-Fuller-Newman model of a KIB full cell in a hypothetical commercial cylindrical cell format, identifying the critical materials properties that limit their rate capability.