Electroencephalography (EEG) is a diagnostic test that involves placing electrodes at specific locations on the human head to detect and study electrical signals of brain activity. Current practitioners use a measuring tape and wax pencil to determine electrode positions and mark them using the internationally recognized 10–20 system. This meticulous procedure is time-consuming and laborious as it is manual. Hence, in this paper, we propose a rapid and robust method to determine the optimal electrode positions using an optical motion capture system (Optitrack) and a customized stylus. The stylus affixed with reflective markers is tracked by the motion capture system as it is used to trace different regions of the head in order to estimate the head geometry utilizing the 3D coordinate data of the trace throughout time. The 21 EEG electrode positions are then algorithmically predicted using the acquired spatial coordinate data. With testing under various experimental settings, the accuracy value in terms of Root Mean Square Error (RMSE) of the predicted EEG electrode positions is less than 1 cm with half the amount of time needed. Thus, the proposed method is assured to be faster and decreases errors due to imprecise electrode placement and determination.