Despite the wide-ranging applications of binary Rh and Ir oxides, their stability and trends in Rh and Ir oxidation states are not fully understood. Using first-principles electronic structure calculations, we demonstrate that the origin of the categorical stability of Ir4+ is the relativistic contraction of the 6s orbital and, consequently, an expansion of 5d orbitals. Relativistic effects significantly stabilize Ir4+-containing metallic rutile IrO2 over a wide range of O chemical potentials, despite the choice that Ir has of forming semiconducting corundum Ir2O3. In contrast, Rh is found to display a wider stability range for corundum Rh2O3 with Rh3+ and a greater propensity for multiple oxidation states.