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For automotive applications like steering wheel position, sensing the angular position of a mechanical axel is detected in a contactless way: a small permanent magnet at the end of the shaft is magnetized perpendicularly to the axis of rotation, and a magnetic field sensor is placed ahead. Even though the magnetic field sensor may be calibrated to have virtually no errors, assembly tolerances of the magnet and the sensor lead to errors in the estimated angular position of the shaft. A Taylor series expansion of the magnetic field up to second order is used to approximate these angle errors. Results of Monte-Carlo simulations show that worst case angle errors may be up to 10 times the average angle error due to error propagation in the nonlinear goniometric relationships. Various shapes of magnets are discussed and criteria for optimization are given. The strong effects of magnet size and distance between sensor and magnet are explained and the limit of infinite homogeneous magnetic field is derived. The results can be used to anticipate production spread of angle sensor systems.