The intrinsic oxygen-vacancies and the extrinsic dopants are two major fundamental free-carrier sources for the extrinsic conducting oxides, such as Sn-doped In(2)O(3). Yet, the individual contributions of the above two free-carrier sources to the total carrier concentrations have never been unraveled. A carrier-concentration separation model is derived in this work, which can define the individual contributions to the total carrier concentration from the intrinsic oxygen-vacancies and the extrinsic dopants, separately. The individual contributions obtained from the present carrier-concentration separation model are verified by the two-state trapping model, photoluminescence, and positron annihilation lifetime (PAL) spectroscopy. In addition, the oxygen-vacancy formation energy of the Sn:In(2)O(3) thin film is determined to be 0.25 eV by PAL spectroscopy.