Surface free energy remains a fundamental material property to characterize the interfacial interactions between liquid and solid. Here, we developed a precise approach to determine surface energy by using contact angles of binary mixtures of water-dimethyl sulfoxide (DMSO), water-formamide, water-ethylene glycol, and water-glycerol and analyzed using the Owens-Wendt method. A mixing equation was developed to estimate liquid-dispersive surface tension (gamma(d)(L,mix)) and polar surface tension (gamma(p)(L,mix)) parameters for binary mixtures. To test the approach, two hydrophobic surfaces, flat polydimethylsiloxane (PDMS), and silane-derivatized glass were prepared and the contact angle of mixtures on the surfaces were obtained. Surface energy of PDMS determined by three binary mixtures agrees with that from pure solvents, but the uncertainty decreases to less than 13%; remarkably, the uncertainty drops to around 5% once we combined measured contact angles from all the mixtures, namely, water-DMSO, water-formamide, and water-ethylene glycol. Surface energies of silane-derivatized glass bearing ethyl (C-2), hexyl (C-6), and octadecyl (C-18) alkyl chains were determined with water-formamide and water-glycerol mixtures. Measured contact angles fit the Owens-Wendt model, and surface energy value determined from different binary mixtures agree with each other within error. Contact angle measurement of liquid mixtures is a simple method for determination of surface energy that improves the precision of surface energy determined by measurements of multiple pure solvents.