As modern engines are being downsized, turbochargers are becoming increasingly common. The operation of turbochargers is usually captured by a map provided by the manufacturer. However, the complexity of these maps makes them difficult to use for turbocharger estimation and control strategies. This work focuses on a method that is able to reduce the compressor and turbine maps from a cloud of points into a set of equations with some associated coefficients. To do this a series of non-dimensional and normalized variables is computed to define a plane transformation. In this new plane, all the points of the map converge approximately into a line and the equation for this line can be later found using a least square regression. This method included an optimization in the process, which proved to be better at replicating the original maps than existing methods. The new technique is shown to accurately replicate the data contained in the maps and variables such as compressor mass flow were able to be predicted with less 10% error for 97% of the points considered. The turbine and compressor models were also coupled to a simple combustion model to evaluate the performance of the equation-based model versus the map-based model. The execution time of the equation-based model was about 400 times less than the map based one. This last aspect makes this kind of model ideal for control strategies which use model based prediction. This innovative characterization of the compressor and turbine has several advantages. First, capturing the compressor and turbine efficiency and mass flow with a set of equations allows for direct, faster computation of the operating parameters of the turbomachine. Second, this model requires much less memory to store the model, since a map could contain thousands of points while the equation based model only contains ten to twenty coefficients.