Summary Postoperative nausea and vomiting is the most common side‐effect of opioid‐based intravenous patient‐controlled analgesia. Apfel's simplified risk score is popular but it has some limitations. We developed and validated a dynamic predictive model for nausea or vomiting up to 48 postoperative hours, available as an online web application. Fentanyl was used by 22,144 adult patients for analgesia after non‐cardiac surgery under general anaesthesia: we randomly divided them into development (80%) and validation (20%) cohorts, repeated 100 times. We used linear discriminant analysis to select variables for multivariate logistic regression. The incidences of postoperative nausea or vomiting were: 0–48 h, 5691/22,144 (26%); 0–6 h, 2749/22,144 (12%); 6–12 h, 2687/22,144 (12%); 12–18 h, 2624/22,144 (12%); 18–24 h, 1884/22,144 (9%); and 24–48 h, 1082/22,144 (5%). The median (95%CI) area under the receiver operating characteristic curve was 0.72 (0.71–0.73) up to 48 postoperative hours compared with 0.65 (0.64–0.66) for the Apfel model, p < 0.001. The equivalent areas for 0–6 h, 6–12 h, 12–18 h, 18–24 h and 24–48 h were: 0.70 (0.69–0.72); 0.71 (0.69–0.73); 0.69 (0.68–0.71); 0.70 (0.67–0.72); and 0.69 (0.66–0.71), respectively. Our web application allows clinicians to calculate incidences of nausea and vomiting in patients receiving intravenous fentanyl for patient‐controlled analgesia.