Aims. To assess how the cost-effectiveness of total hip arthroplasty (THA) and total knee arthroplasty (TKA) varies with age, sex, and preoperative Oxford Hip or Knee Score (OHS/OKS); and to identify the patient groups for whom THA/TKA is cost-effective. Methods. We conducted a cost-effectiveness analysis using a Markov model from a United Kingdom NHS perspective, informed by published analyses of patient-level data. We assessed the cost-effectiveness of THA and TKA in adults with hip or knee osteoarthritis compared with having no arthroplasty surgery during the ten-year time horizon. Results. THA and TKA cost < £7,000 per quality-adjusted life-year (QALY) gained at all preoperative scores below the absolute referral thresholds calculated previously (40 for OHS and 41 for OKS). Furthermore, THA cost < £20,000/QALY for patients with OHS of ≤ 45, while TKA was cost-effective for patients with OKS of ≤ 43, since the small improvements in quality of life outweighed the cost of surgery and any subsequent revisions. Probabilistic and one-way sensitivity analyses demonstrated that there is little uncertainty around the conclusions. Conclusion. If society is willing to pay £20,000 per QALY gained, THA and TKA are cost-effective for nearly all patients who currently undergo surgery, including all patients at and above our calculated absolute referral thresholds. Cite this article: Bone Joint J 2020;102-B(7):950–958