This work presents the mathematical modelling of an integrated gradient field based Hall- angle sensor excited by a diametrically polarized disc magnet. It starts with the computation of the magnetic field of such a magnet based on the results presented in relevant publications. Coordinate transformations are then performed to simulate the assembly tolerances of the sensor and magnet. An abstraction of the real sensor has been designed and coded to simulate the data path of the sensor product. It has been shown that this simplified model delivers results consistent with more detailed and complex models. An increasing complexity of the model has little effects on further accuracy. The results of the data path are then processed using a Kalman Filter algorithm to compensate errors arising from noise as well as signal processing and transmission delays. All models are implemented in m-code (MATLAB). These models enable the simulation of uncertainty propagation using a toolbox. This toolbox uses the approach presented in "Guide to the expression of Uncertainty in Measurement" (GUM). The results deployed by this toolbox have been validated against Monte Carlo simulations. The possibilities and limitations of this toolbox are shown for the magnetic field calculation, data path calculation and filtering using Kalman's algorithm. The results of the simulation are consistent with experimental results conducted on uncalibrated test chips. Time series analysis has been performed on this results to remove systematical error contribution. After such thorough calibration, the angle error results reduce to values of as low as 0.05° (1σ value), which is simply the remaining noise level. This work enables concept engineers for such sensor products to perform fast and yet accurate uncertainty analysis. It allows statistical optimization at an early stage and therefore significantly reduces the time required for product development.