Appendicectomy remains the standard treatment for appendicitis. No international consensus exists on the surgical urgency for acute uncomplicated appendicitis, and recommendations vary from surgery without delay to surgery within 24 h. Longer in-hospital delay has been thought to increase the risk of perforation and further morbidity. Therefore, we aimed to compare the rate of appendiceal perforation in patients undergoing appendicectomy scheduled to two different urgencies (<8 h vs <24 h). In this pragmatic, open-label, multicentre, non-inferiority, parallel, randomised controlled trial in two hospitals in Finland and one in Norway, patients (aged ≥18 years) with presumed uncomplicated acute appendicitis were randomly assigned (1:1) to an appendicectomy scheduled within 8 h or within 24 h to determine whether longer in-hospital delay (time between randomisation and surgical incision) is not inferior to shorter delay. Patients were excluded in cases of pregnancy, suspicion of perforated appendicitis (C-reactive protein level of ≥100 mg/L, fever >38·5°C, signs of complicated appendicitis on imaging studies, or clinical generalised peritonitis), or other reasons requiring prompt surgery. The recruiters were on-duty surgeons who decided to proceed with the appendicectomy. The randomisation sequence was generated using block randomisation with randomly varying block sizes and stratified by hospital districts; neither physicians nor patients were masked to group assignment. The primary outcome was perforated appendicitis diagnosed during surgery analysed in all patients who received an appendicectomy by intention to treat. The absolute difference in rates of perforated appendicitis was compared between the groups. Complications and other safety outcomes were analysed in all patients who received an appendicectomy. A margin of 5 percentage points was used to establish non-inferiority. This trial was registered at ClinicalTrials.gov (NCT04378868) and is closed to accrual. Between May 18, 2020, and Dec 31, 2022, 2095 patients were assessed for eligibility, of whom 1822 were randomly assigned to appendicectomy scheduled within 8 h (n=914) or 24 h (n=908). After randomisation, 19 (1%) of 1822 patients were excluded due to protocol violation. 1803 patients were included in the intention-to-treat analyses, 985 (55%) of whom were male and 818 (45%) female. Appendiceal perforation rate was similar between groups (77 [8%] of 907 patients assigned to the <8 h group and 81 [9%] of 896 patients assigned to the <24 h group; absolute risk difference 0·6% [95% CI -2·1 to 3·2], p=0·68; risk ratio 1·065, 95% CI 0·790 to 1·435). No significant difference was found between the complication rates within 30 days (66 [7%] of 907 patients in the <8 h group vs 56 [6%] of 896 patients in the <24 h group; difference -1·0% [-3·3 to 1·3]; p=0·39), and no deaths occurred during this follow-up period. In patients with presumed uncomplicated acute appendicitis, scheduling appendicectomy within 24 h does not increase the risk of appendiceal perforation compared with scheduling appendicectomy within 8 h. The results can be used to allocate operating room resources, for example postponing night-time appendicectomy to daytime. The Finnish Medical Foundation, Mary and Georg Ehrnrooth's Foundation, Biomedicum Helsinki Foundation, and the Finnish Government.