Abstract Full geometrical alignment of CT instruments remains a complicated endeavor. This paper therefore presents a fast and comprehensive method for determination and compensation of geometrical misalignments. First, a reference object, consisting of spheres mounted on a carbon fiber tube, is X-ray imaged at different angular positions. Subsequently, the misalignment parameters of the CT instrument are determined by minimizing the residual errors between observed and modelled sphere center coordinates. Finally, the FDK-based tomographic reconstruction algorithm is adapted to account for the determined misalignment parameters. The paper discusses the fundamentals of the approach and provides an experimental validation of its performance.