This paper presents an analytical theory approach based on the concept of mutual inductance to describe the double magnetic induction method for measuring eye movements. A polynomial approach to quantify the method's inherent nonlinearity is evaluated. The solutions to the one-dimensional problem are further elaborated, giving a simple approximation of the two-dimensional problem. The two-dimensional approximation provides an easily applicable tool for DMI calibration. According to this theory, calibrations need only be performed parallel to the two main magnetic fields. As a final result, eye rotations are given in any direction as a function of the two measured induction voltages.