Magnetically induced current densities have been calculated for porphycenes at the density functional theory level using gauge-including atomic orbitals to ensure gauge-origin independence and a fast basis-set convergence of the current densities. The current densities have been analyzed by using the gauge-including magnetically induced current (GIMIC) method. The porphycenes are aromatic, sustaining strong diatropic ring currents. The ring-current pathways have been determined by integrating the strength of the current density passing selected bonds. The calculations show that the ring current of the porphycenes splits into an outer and inner branch at the pyrrolic rings implying that the ring current involves all 26 pi electrons of the porphycenes, which is similar to the ring current of porphyrins. The pyrrolic rings of the aromatic porphycenes do not sustain any significant local ring currents. Dihydroporphycene with four inner hydrogens is antiaromatic with weakly aromatic pyrrolic rings. The annelated benzoic rings in benzoporphycene sustain local paratropic ring currents, whereas the global ring current of dibenzoporphycene splits into an outer and inner branch at the benzoic rings. Comparison of calculated H-1 NMR shieldings with ring-current strengths shows that interactions between the inner hydrogen and the neighbor nitrogen is more significant for differences in the H-1 NMR shieldings than variations in global ring-current strengths. Calculated excitation energies show that the antiaromatic dihydroporphycene has a smaller optical gap than the aromatic porphycene, even though its HOMO-LUMO gap is larger.