One of the important parameters in orthodontics is the perimeter of the dental arch. Precise assessment is necessary in cases of maxillary constriction treated with a rapid maxillary expander (RME). The orthodontic software allows customization of the processes from diagnosis to manufacturing of the treatment device. The aim of the present study is to evaluate a relationship between the parameters of the dental arch—perimeter, width, and length—and to follow the changes during treatment. The study is based on the digital measurements of 3D models of 33 patients treated with a digitally planned and printed RME. In the results an increase of 3.99 mm in perimeter was achieved. The rest of the parameters were changed as follows: The width of the dental arch was increased in the premolar area by an average of 3.3 mm; in the area of the first molars, the increase was 4.41 mm; the length of the dental arch in the anterior segment was reduced by an average of 0.54 mm; and the whole length by 0.52 mm. Correlation between the studied variables was described by linear equations. In conclusion, rapid maxillary expansion is a reliable method for gaining predictable space in the dental arch.