Eye tracking has become a powerful tool for analyzing cognitive processes in educational research. Educators and researchers can utilize eye tracking to model learners by determining their gaze patterns. In addition, eye tracking can be used directly for teaching by extracting experts' gaze behavior in certain areas and learning from it.

However, eye tracking data is captured in a variety of coordinate systems, which can differ across individual studies. Consequently, algorithms, such as eye movement classifiers, must frequently convert gaze data between different coordinate systems. In particular, the conversion from screen pixels into visual degrees is typically approximated by a linear conversion in current literature and standard practice. However, this approximation introduces inaccuracies, thus potentially obscuring eye movements relevant to educational research.

This paper provides a detailed geometric and analytical examination of the commonly applied linear approximation, quantifying its error in comparison to the exact coordinate conversion from screen pixels to angular degrees. For this purpose, the exact conversion formulas are mathematically derived from geometric optics, enabling researchers and educators to use them in their work. Utilizing these derived transformations can improve the robustness of analyses, for example, when detecting subtle eye movements.

The present work supports educational research using eye tracking to achieve more insightful findings that may have previously been obscured by measurement inaccuracies. Thereby, we provide an important contribution toward more reliable and valid research and educational practices in eye tracking.

Keywords: Eye tracking, coordinate system, conversion, angular degree, pixel.