Purpose Semiconductor detectors are widely used in computed tomography (CT). Their high spatial resolution and sensitivity give them an advantage compared to ionization chambers. Unfortunately, their air kerma response is strongly energy-dependent. The aim of this study is the accurate calibration of semiconductor detectors with respect to CT scanner specific spectra at different values of the tube voltage. Methods The air kerma response of several semiconductor detectors of the same type (Doseprofiler, RTI) has been measured free-in-air using ISO-N X-ray qualities. The machine-specific, kerma-averaged calibration factors for different tube potentials are using the known X-ray fluence spectra of a GE Optima CT 660. The results are validated by comparing dose measurements made with the Doseprofiler, which was placed inside the isocenter of the CT, with measurements made using a calibrated ionization chamber with known energy response. In anthropomorphic phantoms, the beam-hardening characteristics of the phantom and the CT source must be considered. The simulation of X-ray fluence spectra inside the inhomogeneous object is very complex, as the angle-dependent material composition of both the phantom and the X-ray source of the CT must be incorporated. Hence, direct calibration with calibrated ionization chambers inside the phantom has been performed, which is the more direct approach. Results It has been shown that the measured response of the semiconductor detectors varies by ∼ 80% for different ISO-N X-ray modalities. Consequently, the calculated CT-specific calibration factors free-in-air in total change by 24% for tube voltages between 80 kV and 140 kV. Dose measurements with the ionization chamber and Doseprofiler showed good agreement, with the results diverging by less than 2% after correction. The in-phantom calibration with an ionization chamber lead to comparable results with differences of 20%-24% in the calibration factors for values of the tube voltage between 80 kV and 140 kV and for different anthropomorphic phantoms. Conclusions Semiconductor detectors have the advantage of high spatial resolution and sensitivity. However, the air kerma response of these detectors is typically very poor. Hence spectral-corrected calibration factors or cross-calibration with ionization chambers is absolutely necessary in order to achieve the highest accuracy in the absolute dose measurement for all tube potentials.