The number of $\psi(3686)$ events collected by the BESIII detector during the 2021 run period is determined to be $(2259.3\pm 11.1)\times 10^6$ by counting inclusive $\psi(3686)$ hadronic events. The uncertainty is systematic and the statistical uncertainty is negligible. Meanwhile, the numbers of $\psi(3686)$ events collected during the 2009 and 2012 run periods are updated to be $(107.7\pm0.6)\times 10^6$ and $(345.4\pm 2.6)\times 10^6$, respectively. Both numbers are consistent with the previous measurements within one standard deviation. The total number of $\psi(3686)$ events in the three data samples is $(2712.4\pm14.3)\times10^6$. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.