The geometry of high-energy X-ray diffraction setups using an area detector and a rotation axis is analysed. The present paper (part 1) describes the methodology for determining continuously varying spatial distortions and tilt of the area detector based on the reference diffraction rings of a certified powder. Analytical expressions describing the degeneration of Debye rings into ellipses are presented and a robust calibration procedure is introduced. It is emphasized that accurate detector calibration requires the introduction of spatial distortion into the equation describing the tilt. The method is applied to data sets measured at the Advanced Photon Source and at the European Synchrotron Radiation Facility using detectors with different physical characteristics, the GE 41RT flat-panel and the FReLoN4M detector, respectively. The spatial distortion of the detectors is compared with regard to their use in structural and strain tensor analysis, a subject treated in part 2 of the calibration work [Borbely, Renversade & Kenesei (2014). J. Appl. Cryst. Submitted].