Turbochargers are a vital component for aiding engine manufacturers in meeting the latest emissions standards. However, their range of operation is limited for low mass flows by compressor surge. Operation in surge results in pressure and mass flow oscillations that are often damaging to the compressor and its installation. Since surge is a highly complex flow regime, full unsteady 3D models are generally too computationally expensive to run. The majority of current low-dimensional surge models use a cubic compressor characteristic that needs to be fitted to experimental data. Therefore, each time a compressor is studied using these models, costly experimental testing is required. In this paper, a new technique for obtaining an axisymmetric centrifugal compressor characteristic is presented. This characteristic is built using the equations of mass, momentum and energy from first principles in order to provide a more complete model than those currently obtained via experimental data. This approach enables us to explain the resulting cubic-like shape of the characteristic and hence to identify impeller inlet stall as a route into surge. The characteristic is used within a quasi-steady, map-based surge model in order to demonstrate its ability to predict the onset of surge while only providing geometric data as input. Validation is provided for this model by discussion of the qualitative flow dynamics and a good fit to experimental data, especially for low impeller speeds and pressure ratios.