The Extrapolar SWIFT model is a fast ozone chemistry scheme for interactive calculation of the extrapolar stratospheric ozone layer in coupled general circulation models (GCMs). In contrast to the widely used prescribed ozone, the SWIFT ozone layer interacts with the model dynamics and can respond to atmospheric variability or climatological trends. The Extrapolar SWIFT model employs a repro-modelling approach, where algebraic functions are used to approximate the numerical output of a full stratospheric chemistry and transport model (ATLAS). The full model solves a coupled chemical differential equations system with 55 initial and boundary conditions (mixing ratio of various chemical species and atmospheric parameters). Hence the rate of change of ozone over 24  h is a function of 55 variables. Using covariances between these variables, we can find linear combinations in order to reduce the parameter space to the following nine basic variables: latitude, pressure altitude, temperature, local ozone column, mixing ratio of ozone and of the ozone depleting families (Cly, Bry, NOy and HOy). We will show that these 9 variables are sufficient to characterize the rate of change of ozone. An automated procedure fits a polynomial function of fourth degree to the rate of change of ozone obtained from several simulations with the ATLAS model. One polynomial function is determined per month which yields the rate of change of ozone over 24 h. A key aspect for the robustness of the Extrapolar SWIFT model is to include a wide range of stratospheric variability in the numerical output of the ATLAS model, also covering atmospheric states that will occur in a future climate (e.g. temperature and meridional circulation changes or reduction of stratospheric chlorine loading). For validation purposes, the Extrapolar SWIFT model has been integrated into the ATLAS model replacing the full stratospheric chemistry scheme. Simulations with SWIFT in ATLAS have proven that the systematic error is small and does not accumulate during the course of a simulation. In the context of a 10 year simulation, the ozone layer, simulated by SWIFT, shows a stable annual cycle, with inter-annual variations comparable to the ATLAS model. The application of Extrapolar SWIFT requires the evaluation of polynomial functions with 30–100 terms. Nowadays, computers can calculate such polynomial functions at thousands of model grid points in seconds. SWIFT provides the desired numerical efficiency and computes the ozone layer 104 times faster than the chemistry scheme in the ATLAS CTM.