In this study we report on the accurate computation of the biomolecular partial specific volume (PSV) from explicit-solvent molecular dynamics (MD) simulations. The case of DNA is considered, and the predictions from two state-of-the-art biomolecular force fields, the CHARMM36 additive (C36) and Drude polarizable models, are presented. Unlike most of the existing approaches to assess the biomolecular PSV, our proposed method bypasses the need for the arbitrarily defined volume partitioning scheme into the intrinsic solute and solvent contributions. At the same time, to assess the density of the hydration layer water, we combine our simulation analysis approach with some of the existing fixed-size methods to determine the solute's intrinsic volume, and also propose our own approach to compute all required quantities exclusively from MD simulations. Our findings provide useful insights into the properties of the hydration layer, specifically its size and density, parameters of great importance to the variety of techniques used to model hydrodynamic and structural properties of biological molecules. The computed PSV values are found to be in close agreement with the values obtained from analytical ultracentrifugation (AUC) experiments performed on canonical B-form duplex DNAs and single-stranded DNAs forming G-quadruplex structures. Since the biomolecular PSV represents an important quantitative measure of solute-solvent interactions, near quantitative agreement with AUC measurements is indicative of the quality of the all-atom models used in the MD simulations, particularly the reliability of the CHARMM force-field parameters for nucleic acids, water, mobile ions, and interactions among these entities.