An all-sky comprehensive catalogue of calculated radio and X-ray associations to optical objects is presented. Included are X-ray sources from XMM-Newton, Chandra and ROSAT catalogues, radio sources from NVSS, FIRST and SUMSS catalogues, and optical data, identifications and redshifts from the APM, USNO-A, SDSS-DR7 and the extant literature. This ‘Atlas of Radio/X-ray Associations’ inherits many techniques from the predecessor Quasars.org (2004) catalogue, but object selection is changed and processing tweaked. Optical objects presented are those which are calculated with ≥40% confidence to be associated with radio/X-ray detections, totalling 602 570 objects in all, including 23 681 double radio lobe detections. For each of these optical objects I display the calculated percentage probabilities of its being a QSO, galaxy, star, or erroneous radio/X-ray association, plus any identification from the literature. The catalogue includes 105 568 uninvestigated objects listed as 40% to >99% likely to be a QSO. The catalogue is available at http://quasars.org/arxa.htm.