The atomic polarizabilities of carbon dioxide and carbodiimide, HN=C=NH, have been studied with ab initio theoretical methods. Structures were optimized and properties were determined using RHF, MP2, and QCISD theories and a variety of basis sets up to quadruple-zeta quality. The static electric dipole polarizability tensor components were determined using the finite field method. The isotropic polarizability [alpha] and the anisotropic polarizabilities Delta alpha and kappa were calculated for both heterocumulenes from the respective tensor components. The experimental tensor components and polarizabilities [alpha], Delta alpha, and kappa are known for carbon dioxide, and these values are used to assess the accuracy of the theoretical me;hods. This knowledge about the achievable accuracy is then employed in the prediction of the polarizability values of carbodiimide. The only measurable polarizability values for carbodiimide are [alpha] and kappa. The best level of theory employed in this study is QCISD(fc)/6-311++G(3df,2pd) and this level gives [alpha] and kappa values of 16.722 and 0.289 au(3) for carbon dioxide. These values deviate somewhat from the experimental values of 17.762 and 0.267 au(3) and we rationalize these differences based on the calculated polarizability tensor components. The calculated [alpha] and kappa values of carbodiimide are 28.963 and 0.310 au(3). Taking into account the deviations from experiment for the carbon dioxide values, we predict [alpha] and kappa values of 30.764 and 0.286 au(3) for carbodiimide. The discussion emphasizes the important role of the inclusion of three sets of d-polarization functions. The third, diffuse set of d-functions is essential to polarize the electron density described by the diffuse functions and also by the outer valence p-functions.