The accuracy of radiotherapy dose calculation relies crucially on patient composition data. The computed tomography (CT) calibration methods based on the stoichiometric calibration of Schneider et al (1996 Phys. Med. Biol. 41 111-24) are the most reliable to determine electron density (ED) with commercial single energy CT scanners. Along with the recent developments in dual energy CT (DECT) commercial scanners, several methods were published to determine ED and the effective atomic number (EAN) for polyenergetic beams without the need for CT calibration curves. This paper intends to show that with a rigorous definition of the EAN, the stoichiometric calibration method can be successfully adapted to DECT with significant accuracy improvements with respect to the literature without the need for spectrum measurements or empirical beam hardening corrections. Using a theoretical framework of ICRP human tissue compositions and the XCOM photon cross sections database, the revised stoichiometric calibration method yields Hounsfield unit (HU) predictions within less than ±1.3 HU of the theoretical HU calculated from XCOM data averaged over the spectra used (e.g., 80 kVp, 100 kVp, 140 kVp and 140/Sn kVp). A fit of mean excitation energy (I-value) data as a function of EAN is provided in order to determine the ion stopping power of human tissues from ED-EAN measurements. Analysis of the calibration phantom measurements with the Siemens SOMATOM Definition Flash dual source CT scanner shows that the present formalism yields mean absolute errors of (0.3 ± 0.4)% and (1.6 ± 2.0)% on ED and EAN, respectively. For ion therapy, the mean absolute errors for calibrated I-values and proton stopping powers (216 MeV) are (4.1 ± 2.7)% and (0.5 ± 0.4)%, respectively. In all clinical situations studied, the uncertainties in ion ranges in water for therapeutic energies are found to be less than 1.3 mm, 0.7 mm and 0.5 mm for protons, helium and carbon ions respectively, using a generic reconstruction algorithm (filtered back projection). With a more advanced method (sinogram affirmed iterative technique), the values become 1.0 mm, 0.5 mm and 0.4 mm for protons, helium and carbon ions, respectively. These results allow one to conclude that the present adaptation of the stoichiometric calibration yields a highly accurate method for characterizing tissue with DECT for ion beam therapy and potentially for photon beam therapy.