The Clar aromatic sextet theory can provide a qualitative description of the dominant modes of cyclic pi-electron:, conjugation in benzenoid molecules and of the relative stability among a series of isomeric benzenoid systems. In a series of nonplanar fully benzenoid hydrocarbons, the predictions of the Clar theory were tested by means of several different theoretical approaches: topological resonance energy (TRE), energy effect (ef), harmonic oscillator model of aromaticity (HOMA) index, six center delocalization index (SCI), and nucleus-independent chemical shifts (NICS). To assess deviations from planarity in the examined molecules, four different planarity descriptors were employed. It was shown how the planarity indices can be used to quantify the effect of nonplanarity on the local and global aromaticity of the studied systems.