The quadrupolarity of carbodiimide, HN═C═NH, has been studied in comparison to carbon dioxide. Both heterocumulenes exhibit {- + -} quadrupolarity in all directions. Concepts are formulated to develop an understanding of the origins of quadrupole moments and to trace theoretical level effects to the underlying changes of the electron density. The quadrupole moment tensors have been computed using RHF, MP2 and QCISD theory as well as the B3LYP density functional method. A variety of basis sets have been employed, the two best basis sets are of the types [5s, 4p, 2d, 1f] (23s, 8p, 2d, 1f) and [5s, 4p, 3d, 1f] (12s, 6p, 3d, 1f). The results suggest that the MP2 and B3LYP methods in conjunction with well-polarized triple-ζ basis sets provide a cost-effective and quite accurate method for the estimation of correlation effects on quadrupole moments. The quadrupole moment tensor component Qxx of carbodiimide falls between -16 and -18 DÅ. The components Qyy and Qzz, are similar and they range from -16.5 to -17.5 DÅ and from -17 to -18 DÅ. The correlated methods consistently predict an increase of Qxx, whereas they predict a more modest reduction of Qyy and Qzz. It is for these opposing correlation effects that the average values of the diagonal elements, <Qii>, are essentially independent of the method and exhibit only a minor basis set dependence. The traceless quadrupole moment of carbon dioxide, Θ = Q∥ - Q⊥, is -4.3 DÅ. In stark contrast, all of the Θii values of carbodiimide are close to zero and only the off-diagonal quadrupole moment element Θxy is quite large with Θxy = -6.2 DÅ.