The quadrant detector (QD) is widely utilized in guidance and tracking applications. We explore the impact of the QD’s dead zone width on tracking precision. We establish a spot centroid calculation model that accounts for the QD’s dead zone based on a Gaussian spot distribution. Introducing Gaussian-distributed noise, we construct a QD measurement error model under conditions of noise interference. To validate the model’s accuracy, we perform numerical simulations and experimental analyses focused on the standard deviation of the measurement error. This error model quantitatively demonstrates how the spot centroid coordinates, spot radius, system signal-to-noise ratio, and dead zone width influence the QD’s measurement error standard deviation under noisy conditions, offering theoretical insights for enhancing tracking accuracy.