Superhydrogenated polycyclic aromatic hydrocarbons (PAHs) may be present in H-rich and ultraviolet-poor benign regions. The addition of excess H atoms to PAHs converts the aromatic bonds into aliphatic bonds, the strongest of which falls near 3.4 μm. Therefore, superhydrogenated PAHs are often hypothesized to be a carrier of the 3.4 μm emission feature that typically accompanies the stronger 3.3 μm aromatic C-H stretching feature. To assess this hypothesis, we use density function theory to compute the infrared (IR) vibrational spectra of superhydrogenated PAHs and their ions of various sizes (ranging from benzene and naphthalene to perylene and coronene) and of various degrees of hydrogenation. For each molecule, we derive the intrinsic oscillator strengths of the 3.3 μm aromatic C-H stretch (A3.3) and the 3.4 μm aliphatic C-H stretch (A3.4). By comparing the computationally derived mean ratio of ⟨A3.4/A3.3 ⟩ ≈ 1.98 with the mean ratio of the observed intensities ⟨I3.4/I3.3 ⟩ ≈ 0.12, we find that the degree of superhydrogenation -- the fraction of carbon atoms attached with extra hydrogen atoms -- is only ∼2.2% for neutral PAHs, which predominantly emit the 3.3 and 3.4 μm features. We also determine for each molecule the intrinsic band strengths of the 6.2 μm aromatic C-C stretch (A6.2) and the 6.85 μm aliphatic C-H deformation (A6.85). We derive the degree of superhydrogenation from the mean ratio of the observed intensities ⟨I6.85/I6.2 ⟩ ≲ 0.10 and ⟨A6.85/A6.2 ⟩ ≈ 1.53 for neutrals and ⟨A6.85/A6.2⟩ ≈ 0.56 for cations to be ≲ 3.1% for neutrals and ≲ 8.6% for cations. We conclude that astrophysical PAHs are primarily aromatic and are only marginally superhydrogenated.