In radiotherapy treatment planning, the conversion of the computed tomography (CT) number to electron density is one of the main processes that determine the accuracy of patient dose calculations. However, in general, the CT number and electron density of tissues cannot be interrelated using a simple one-to-one correspondence. This study aims to experimentally verify the clinical feasibility of an existing novel conversion method proposed by the author of this note, which converts the energy-subtracted CT number (Delta HU) to the relative electron density (rho(e)) via a single linear relationship by using a dual-energy CT (DECT). The Delta HU-rho(e) conversion was performed using a clinical second-generation dual-source CT scanner operated in the dual-energy mode with tube potentials of 80 kV and 140 kV with and without an additional tin filter. The Delta HU-rho(e) calibration line was obtained from the DECT image acquisition for tissue substitutes in an electron density phantom. In addition, the effect of object size on Delta HU-rho(e) conversion was also experimentally investigated. The plot of the measured Delta HU versus nominal rho(e) values exhibited a single linear relationship over a wide rho(e) range from 0.00 (air) to 2.35 (aluminum). The Delta HU-rho(e) conversion performed with the tin filter yielded a lower dose and more reliable rho(e) values that were less affected by the object-size variation when compared to the corresponding values obtained for the case without the tin filter.