Background: The COVID-19 pandemic has disrupted routine hospital services globally. This study estimated the total number of adult elective operations that would be cancelled worldwide during the 12 weeks of peak disruption due to COVID-19. Methods: A global expert response study was conducted to elicit projections for the proportion of elective surgery that would be cancelled or postponed during the 12 weeks of peak disruption. A Bayesian β-regression model was used to estimate 12-week cancellation rates for 190 countries. Elective surgical case-mix data, stratified by specialty and indication (surgery for cancer versus benign disease), were determined. This case mix was applied to country-level surgical volumes. The 12-week cancellation rates were then applied to these figures to calculate the total number of cancelled operations. Results: The best estimate was that 28 404 603 operations would be cancelled or postponed during the peak 12 weeks of disruption due to COVID-19 (2 367 050 operations per week). Most would be operations for benign disease (90·2 per cent, 25 638 922 of 28 404 603). The overall 12-week cancellation rate would be 72·3 per cent. Globally, 81·7 per cent of operations for benign conditions (25 638 922 of 31 378 062), 37·7 per cent of cancer operations (2 324 070 of 6 162 311) and 25·4 per cent of elective caesarean sections (441 611 of 1 735 483) would be cancelled or postponed. If countries increased their normal surgical volume by 20 per cent after the pandemic, it would take a median of 45 weeks to clear the backlog of operations resulting from COVID-19 disruption. Conclusion: A very large number of operations will be cancelled or postponed owing to disruption caused by COVID-19. Governments should mitigate against this major burden on patients by developing recovery plans and implementing strategies to restore surgical activity safely.