Attenuation measurements for primary x-ray spectra from 25 kVp to 18 MV were made using aluminum filters for all energies except for orthovoltage where copper filters were used. An iterative perturbation method, which utilized these measurements, was employed to derive the apparent x-ray spectrum. An initial spectrum or pre-spectrum was used to start the process. Each energy value of the pre-spectrum was perturbed positively and negatively, and an attenuation curve was calculated using the perturbed values. The value of x-rays in the given energy bin was chosen to minimize the difference between the measured and calculated transmission curves. The goal was to derive the minimum difference between the measured transmission curve and the calculated transmission curve using the derived x-ray spectrum. The method was found to yield useful information concerning the lower photon energy and the actual operating potential versus the nominal potential. Mammographic, diagnostic, orthovoltage, and megavoltage x-ray spectra up to 18 MV nominal were derived using this method. The method was validated using attenuation curves from published literature. The method was also validated using attenuation curves calculated from published spectra. The attenuation curves were then used to derive the x-ray spectra.