Scaling of quantum capacitances is explored for lanthanide and actinide atoms. For lighter atoms, quantum capacitances have been seen to scale linearly with mean radii of the atoms' outermost occupied orbitals. This scaling law is used to analyze two recent, differing sets of theoretical calculations for lanthanide electron affinities A. Consistent with the scaling law, A values predicted by O'Malley and Beck for lanthanides [Phys. Rev. A 78, 012510 (2008)], using a relativistic configuration interaction (RCI) method, produce capacitances that scale with the atoms' mean radii along a single line to a high degree of confidence. Similar linear scaling behavior also results for the actinides from O'Malley and Beck's RCI calculations of their A values. However, lanthanide A values predicted by Felfli et al. [Phys. Rev. A 81, 042707 (2010)], using a Regge-pole approach, unexpectedly produce capacitance scaling along two different lines for atoms with similar neutral electron configurations. Both types of linear capacitance scaling are internally consistent, though, and do not serve to determine definitively which set of electron affinity predictions for the lanthanides is likely to be more accurate. Still, evidence from this and prior capacitance scaling investigations tends to favor the O'Malley and Beck results. In addition, linear capacitance scaling for the actinides is applied to estimate the previously unknown A values for Fm and Md as 0.007 eV and −0.006 eV, respectively.