The interconversion between the well-characterized A- and B-forms of DNA is a structural transition for which the intermediate states and the free energy difference between the two endpoints are not known precisely. In the present study, the difference between the Root Mean Square Distance (RMSD) from canonical A-form and B-form DNA is used as an order parameter to characterize this free energy difference using umbrella sampling molecular dynamics (MD) simulations with explicit solvent. The constraint imposed along this order parameter allows relatively unrestricted evolution of the intermediate structures away from both canonical A- and B-forms. The free energy difference between the A- and B-forms for the hexamer DNA sequence CTCGAG in aqueous solution is conservatively estimated to be at least 2.8 kcal/mol. A continuum of intermediate structures with no well-defined local minima links the two forms. The absence of any major barriers in the free energy surface is consistent with spontaneous conversion of the A-form DNA to B-form DNA in unconstrained simulations. The extensive sampling in the MD simulations (>0.1 mus) also allowed quantitative energetic characterization of local backbone conformational variables such as sugar pseudorotation angles and BI/BII state equilibria and their dependence on base identity. The absolute minimum in the calculated free energy profile corresponds closely to the crystal structure of the hexamer sequence, indicating that the present method has the potential to identify the most stable state for an arbitrary DNA sequence in water.