Cognitive effort is reflected in pupil dilation, but the assessment of pupil size is potentially susceptible to changes in gaze position. This study exemplarily used sentence reading as a stand-in for paradigms that assess pupil size in tasks during which changes in gaze position are unavoidable. The influence of gaze position on pupil size was first investigated by an artificial eye model with a fixed pupil size. Despite its fixed pupil size, the systematic measurements of the artificial eye model revealed substantial gaze-position-dependent changes in the measured pupil size. We evaluated two functions and showed that they can accurately capture and correct the gaze-dependent measurement error of pupil size recorded during a sentence-reading and an effortless z-string-scanning task. Implications for previous studies are discussed, and recommendations for future studies are provided.