The electrostatic properties of a molecule are often essential in determining its behavior; as such, the ability to approximate these electrostatic potentials computationally is often essential to obtaining a full understanding of how these molecules function. An approximate, analytical solution to the (linearized) Poisson-Boltzmann equation is proposed that is suitable for realistic biomolecules of virtually any size. A comparison with accepted numerical approaches on a large test set of biomolecular structures shows that the proposed method is considerably less expensive computationally, yet accurate enough to be considered as a possible alternative. The utility of the approach is demonstrated by computing and analyzing the electrostatic potential generated by full capsid of the tobacco ringspot virus (half a million atoms) at atomic resolution. The details of the potential distribution on the molecular surface sheds light on the mechanism behind the high selectivity of the capsid to the viral RNA. These results are generated with the modest computational power of a desktop PC. The applicability of the analytical approximation as an initial guess for traditional numerical methods as a means of improving the convergence of iterative solutions is investigated and found to be quite promising.