We hypothesised that a large acromial cover with an upwardly tilted glenoid fossa would be associated with degenerative rotator cuff tears (RCTs), and conversely, that a short acromion with an inferiorly inclined glenoid would be associated with glenohumeral osteoarthritis (OA). This hypothesis was tested using a new radiological parameter, the critical shoulder angle (CSA), which combines the measurements of inclination of the glenoid and the lateral extension of the acromion (the acromion index). The CSA was measured on standardised radiographs of three groups: 1) a control group of 94 asymptomatic shoulders with normal rotator cuffs and no OA; 2) a group of 102 shoulders with MRI-documented full-thickness RCTs without OA; and 3) a group of 102 shoulders with primary OA and no RCTs noted during total shoulder replacement. The mean CSA was 33.1° (26.8° to 38.6°) in the control group, 38.0° (29.5° to 43.5°) in the RCT group and 28.1° (18.6° to 35.8°) in the OA group. Of patients with a CSA > 35°, 84% were in the RCT group and of those with a CSA < 30°, 93% were in the OA group. We therefore concluded that primary glenohumeral OA is associated with significantly smaller degenerative RCTs with significantly larger CSAs than asymptomatic shoulders without these pathologies. These findings suggest that individual quantitative anatomy may imply biomechanics that are likely to induce specific types of degenerative joint disorders.