We present a quantitative analysis of the chemical reactions involved in polar ozone depletion in the stratosphere and of the relevant reaction pathways and cycles. While the reactions involved in polar ozone depletion are well known, quantitative estimates of the importance of individual reactions or reaction cycles are rare. In particular, there is no comprehensive and quantitative study of the reaction rates and cycles averaged over the polar vortex under conditions of heterogeneous chemistry so far. We show time series of reaction rates averaged over the core of the polar vortex in winter and spring for all relevant reactions and indicate which reaction pathways and cycles are responsible for the vortex-averaged net change of the key species involved in ozone depletion, i.e., ozone, chlorine species (ClO_x, HCl, ClONO₂), bromine species, nitrogen species (HNO₃, NO_x) and hydrogen species (HO_x). For clarity, we focus on one Arctic winter (2004–2005) and one Antarctic winter (2006) in a layer in the lower stratosphere around 54 hPa and show results for additional pressure levels and winters in the Supplement. Mixing ratios and reaction rates are obtained from runs of the ATLAS Lagrangian chemistry and transport model (CTM) driven by the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis data. An emphasis is put on the partitioning of the relevant chemical families (nitrogen, hydrogen, chlorine, bromine and odd oxygen) and activation and deactivation of chlorine.