A uniform, comprehensive theoretical interpretation of spectroscopic data is presented for 51 radical ion species of polycyclic aromatic hydrocarbons (PAHs) with the aid of (Tamm-Dancoff) time-dependent density functional theory (TDDFT). TDDFT is capable of predicting the transition energies to the low-lying excited states of PAH ions with quantitative accuracy (the standard deviation from experimental results being less than 0.3 eV) and their intensity patterns qualitatively correctly. The accuracy is hardly affected by the sizes of PAH ions (azulene through dinaphthocoronene), the types of transitions (Koopmans or satellite transitions), the types of orbitals involved (pi* <-- pi, pi* <-- sigma, or sigma* <-- pi transitions), the types of ions (cations or anions), or other geometrical or electronic perturbations (nonplanarity, sp(3) carbons, or heterocyclic or nonbenzenoid rings).