The DANSS detector is placed under the reactor core of the Kalinin NPP and collects up to 5000 $\bar\nu$ events per day. The experiment is aimed to scrutinize the sterile neutrino hypothesis, and the obtained limits exclude practically all sterile neutrino parameters preferred by the BEST experiment. The main goal of the energy calibration is the determination of the energy scale coefficient $K_E$. However, the Birks and Cherenkov effects are also investigated. The report covers calibration with atmospheric muons ($\mu$) stopped inside the sensitive volume of the detector including their decays. Muons were selected by applying geometrical constraints and searching for subsequent $e^-$ or $e^+$. The spectrum of the Michel $e^-/e^+$ is used for $K_E$ determination. The time stability of the energy scale calibration with the Michel spectra is better than 0.4\% over a period of 4 years. Bragg’s curve built using $\mu$ energy release along its track is sensitive not only to $K_E$ but also to nonlinear effects: the Birks effect, and Cherenkov radiation. This calibration complements the results of the calibration via radioactive sources and $^{12}$B $\beta$-decays and results coincide between each other but differs by $\sim 2-3\sigma$ for the Michel spectra