Tight-binding model (TBM) and density functional theory (DFT) calculations were employed. Both simulations have demonstrated that the electrical conductance for eight polycyclic aromatic hydrocarbons (PAHs) can be modulated by varying the number of aromatic rings (NAR) within the aromatic derivatives. TBM simulations reveal three distinct conductance states: low, medium and high for the studied PAH derivatives. The three distinct conductance states suggested by TBM are supported by DFT transmission curves, where the low conductance evidenced by
T
(
E
) = 0, for benzene, naphthalene, pyrene and anthracene. While azulene and anthanthrene exhibit a medium conductance as
T
(
E
) = 1, and tetracene and dibenzocoronene possess a high conductance with
T
(
E
) = 2. Low, medium and high values were elucidated according to the energy gap
E
g
and
E
g
gaps are strongly dependent on the NAR in the PAH derivatives. This study also suggests that any PAH molecules are a conductor if
E
g
< 0.20 eV. A linear relationship between the conductance and NAR (
G
∝ NAR) was found and conductance follows the order
G
(benzene, 1 NAR) <
G
(anthanthrene, 4 NAR) <
G
(dibenzocoronene, 9 NAR). The proposed study suggests a relevant step towards the practical application of molecular electronics and future device application.