||An analytical framework to predict skyglow due to distant sources is presented, which can be applied to model sky brightness from the zenith toward the horizon along a vertical plane crossing the hemisphere in the azimuthal position of a light source. Although various powerful algorithms have been developed over the last few decades, the time needed for calculation grows exponentially with increasing size of the modelling domain. This is one of the key issues in skyglow computations, because the numerical accuracy improves only slowly as the modelling domain extends. We treat the problem theoretically, by introducing an analytical formula that is well-suited for light sources located at intermediate and long distances from an observation point and allows tremendous time savings in numerical analyses, while keeping the error at a low level. Field experiments carried out in Eastern Austria provided a unique opportunity to validate the model using real-sky luminance data. The fact that the theoretical model allows the prediction of sky luminance within an acceptable error tolerance is not only in line with the experimental data, but also provides new means of remote characterization of light emissions from artificial sources. The method is particularly attractive for rapid and simple retrieval of the amount of light escaping upwards from the dominant light sources surrounding the observation point. We expect that the method can advance the numerical modelling of skyglow substantially, because it allows real-time computations for very large territories.