The pyranose ring of L-iduronic acid (IdoA), a major constituent of the anticoagulant heparin, is an equilibrium of multiple ring puckers that have evaded quantification by experiment or computation. In order to resolve this enigma, we have calculated the free energy landscape of IdoA and two related monosaccharides from extensive microsecond simulations. After establishing that the simulated puckers had reached equilibrium, hypotheses were confirmed that (a) IdoA C-1(4)- and C-4(1)-chair conformations exchange on the microsecond time scale, (b) C5 epimerization leads to a C-4(1)-chair, and (c) IdoA 2-O-sulfation (IdoA2S) stabilizes the C-1(4) conformer. The IdoA and IdoA2S C-1(4) conformers were isoenergetic and computed to be 0.9 and 2.6 kcal mol(-1) lower in free energy than their respective C-4(1)-chair conformations. The simulations also predicted that the IdoA S-2(o)-skew-boat was less populated than previously thought. Novel chemical synthesis and ultra-high-field NMR supported these observations, but slight discrepancies in observed and predicted NMR vicinal couplings implied that the simulation overestimated the population of the IdoA C-4(1)-chair with respect to (1)C(4-)chair due to small force field inaccuracies that only manifest in long simulations. These free-energy calculations drive improvements in computational methods and provide a novel route to carbohydrate mimetic biomaterials and pharmaceuticals.