Experimentally motivated parameters from a base-pair-level discrete DNA model are averaged to yield parameters for a continuum elastic rod with a curved unstressed shape reflecting the local DNA geometry. The continuum model permits computations with discretization lengths longer than the intrinsic discretization of the base-pair model, and, for this and other reasons, yields an efficient computational formulation. Obtaining continuum stiffnesses is straightforward, but obtaining a continuum unstressed shape is hindered by the "noisy" small-scale structure and rapid helix twist of the discrete unstressed shape. Filtering of the discrete data and an analytic transformation from the true normal-vector field to a natural (untwisted) frame allows a stable continuum fit. Equilibrium energies of closed rings predicted by the continuum model are found to match the energies of the underlying discrete model to within 0.5%. The model is applied to a set of 11 short DNA molecules (approximate to 150 bp) and properly distinguishes their cyclization probabilities (J factors) when compared both to experimental cyclization rates and to Monte Carlo simulations. The continuum model does not include entropic contributions to the free energy. However, because of its rapid and accurate computation of internal energy, the continuum model should, when combined with further work on entropic effects, be a useful method for computing experimental DNA free energies.