A matrix-independent fundamental parameter-based calibration model for an energy-dispersive X-ray fluorescence spectrometer has been developed. This model, which is part of a fundamental parameter approach quantification method, accounts for both the excitation and detection probability. For each secondary target a number of relative calibration constants are calculated on the basis of knowledge of the irradiation geometry, the detector specifications, and tabulated fundamental physical parameters. The absolute calibration of the spectrometer is performed by measuring one pure element standard per secondary target. For sample systems where all elements can by analyzed by means of the same secondary target the absolute calibration constant can be determined during the iterative solution of the basic equation. Calculated and experimentally determined relative calibration constants agree to within 5–10% of each other and so do the results obtained from the analysis of an NBS certified alloy using the two sets of constants.