Two different methods are proposed to estimate the persistence length (P) of DNA from the measured torsion elastic constant (alpha) and the twist energy parameter (E-T) that governs the supercoiling free energy. The first method involves Monte Carlo simulations and reversible-work calculations of E-T for model DNAs that possess the measured a. and selected trial values of P. Comparison of the computed E-T values with the experimental value allows estimation of P (or equivalently the bending elastic constant (K-beta)) by interpolation. A far simpler, though less accurate, alternative is to solve a previously conjectured analytical relation connecting E-T, alpha, kappa(beta) (or P), and an unknown "constant" (B). The present simulations are used to ascertain the optimum value of B and to assess the validity and accuracy of that relation. Within the simulation errors, P values obtained from the measured alpha and E-T via this analytical expression agree with those determined from the simulations and E-T. values reckoned from the input alpha and kappa(beta) by this analytical expression agree with the corresponding simulated values. Although B is found to be insensitive to variation in alpha, it appears to decline slightly with increasing K. The original analytical expression is modified to take this apparent variation of B with kappa(beta) into account. By using this modified analytical relation to estimate P (from the measured cc and E-T) or E-T (from the input alpha and kappa(beta)), much closer agreement is obtained respectively with the values of P or E-T obtained from the simulations. As specific examples, these methods are applied to determine P in 0 and 20 w/v % ethylene glycol, which has been shown to induce a structural transition in duplex DNA.