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Updated: Jul 19, 2026

Measuring Maxillary Posterior Tooth Movement: A Model Assessment using Palatal and Dental Superimposition
Published on: February 23, 2024
The third-order angle and the maxillary incisor's inclination to the NA line
Michael Knösel1, Dietmar Kubein-Meesenburg, Reza Sadat-Khonsari
1Georg-August-University, Center of Dentistry, Department of Orthodontics and Dentofacial Orthopedics, Goettingen, Germany. mknoesel@yahoo.de
Objective:
To evaluate the relationship between the angular measurement data (incisor's long axis to NA line) and the third-order angle (TA) according to Andrews' description.
Materials And Methods:
The materials in the study included the lateral radiographs and corresponding dental casts of 32 males and 35 females between 10 and 25 years of age, regardless of their skeletal and dental relationships. All subjects were white and none had undergone orthodontic therapy. Using lateral radiographs, upper and lower incisor angulations were assessed in reference to the NA line. These data were compared with third-order angles derived from direct dental cast measurements, which were performed using an incisor inclination recording appliance.
Results:
The third-order angle measurements recorded from the dental casts were a mean of 16.2 degrees (SD = 5.3 degrees) smaller than the axial inclination according to the NA line. In this sample, there was a range of 42.7 degrees for the TA variable (mean = 5.6 degrees, SD = 9.73 degrees) and 47 degrees for the 1NA/deg variable (mean = 21.7 degrees, SD = 8.67 degrees). A highly significant correlation existed (r = 0.84) between Andrews' angle and the inclination estimated in reference to the NA line.
Conclusion:
Incisor inclination can be better estimated by recognizing the relationship between the torque angle and the axial inclination referred to the NA line. Third-order measurements using dental casts can offer a simple way to get an objective and rapid vision of the incisor's inclination.
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