In order to conveniently analyze the laser-spot-position detection performance of quadrant detectors (QDs), a new mathematical model of the Gauss spot''s position resolution is established in this paper. First, the principles and approximate mathematical model for QD-based position detection in the Gauss spot model are analyzed. Then, a mathematical model of the relationships among the position resolution, total signal-to-noise ratio, position of spot center, and spot radius are deduced by deriving certain error function and theory properties. Finally, the proposed model''s correctness is verified via numerical simulations and an experimental system. The results show that, over a ±0.45-mm range of spot center position, the proposed model''s estimated error is approximately 36% for a spot radius of 0.74 mm and total signal-to-noise ratio of 66.96 dB. Compared with the original approximate model, the proposed model offers approximately twice the accuracy. It can effectively estimate the resolution of laser-spot-position detection systems, which is of great assistance in engineering applications.