An x-ray computer tomograph, having an x-ray source that generates a fan beam of x radiation and having a two-dimensional energy-resolving detector array, both of which are situated on opposite sides of a gantry so that the x-ray radiation passes completely through a test region. A row of detector elements is situated in the plane of the fan beam and is adjoined in at least one direction perpendicular to the fan beam by several additional rows of detector elements. During the measurement, no secondary collimator is positioned between the test region and the detector array. The following equation applies for the width (B) of the detector elements: B=ZP*arc sin(qmax*λ), where qmax is a pulse transmission, λ is a wavelength of the x radiation, and ZP is the distance of the measurement point from the detector.