An extremely fast model to estimate the degree of stratospheric ozone depletion during polar winters is described. It is based on a set of coupled differential equations that simulate the seasonal evolution of vortex-averaged hydrogen chloride (HCl), nitric acid (HNO3), chlorine nitrate (ClONO2), active forms of chlorine (ClOx = Cl + ClO + 2 ClOOCl) and ozone (O3) on isentropic levels within the polar vortices. Terms in these equations account for the chemical and physical processes driving the time rate of change of these species. Eight empirical fit coefficients associated with these terms are derived by iteratively fitting the equations to vortex-averaged satellite-based measurements of HCl, HNO3 and ClONO2 and observationally derived ozone loss rates. The system of differential equations is not stiff and can be solved with a time step of one day, allowing many years to be processed per second on a standard PC. The inputs required are the daily fractions of the vortex area covered by polar stratospheric clouds and the fractions of the vortex area exposed to sunlight. The resultant model, SWIFT (Semi-empirical Weighted Iterative Fit Technique), provides a fast yet accurate method to simulate ozone loss rates in polar regions. SWIFT's capabilities are demonstrated by comparing measured and modeled total ozone loss outside of the training period.