Arch Form and Mathematical Ratio in Orthodontics Patients: A Cross–sectional Study


  • Surendra Maharjan Department of Orthodontics and Dentofacial Orthopedics, People’s Dental College and Hospital, Sorhakhutte, Kathmandu
  • Anjana Rajbhandari
  • Resina Pradhan
  • Manju Bajracharya
  • Pushkar Manandhar
  • Bashu D Pant


Orthodontic treatment aims to achieve a pleasing and stable occlusion. To attain these, the patient's arch shape should be determined before treatment and maintained during treatment. Many attempts have been made to find out the original arch form, but those procedures have had some difficulties. The aim of this study was to determine the arch form using a comparatively simpler mathematical ratio.

This was an observational, descriptive cross-sectional study conducted in the Department of Orthodontics, People’s Dental College and Hospital, Kathmandu, Nepal, from November 2022 to March 2023. The ethical approval was obtained from the Institutional Review Committee (Reference Number: 1/41, 2079/2080) of the same institute. A total of 300 maxillary pretreatment casts from various malocclusion cases were collected. To determine the arch form, the mathematical ratio (CD/CW)/ (MD/MW) was used. Data were collected in Microsoft Excel and analyzed in Statistical Package for Social Sciences version 20 (IBM SPSS) for descriptive statistics and one way ANOVA.

Among 300 individuals, 108 (36%) were males and 192 (64%) were females. In 29 (9.67%) males had square, 48 (16%) had oval, and 31 (10.33%) had tapered shaped arch forms, while 54 (18%) females had square, 77 (25.67%) had oval, and 61 (20.33%) had tapered shaped arch forms. The mean values of arch form were significant in both gender and age groups.

In general, the majority of participants had an oval arch form, followed by a tapered and square-shaped arch form.

Key words
Arch form, mathematical ratio, orthodontic treatment




How to Cite

Maharjan, S., Rajbhandari, A. ., Pradhan, R. ., Bajracharya, M. ., Manandhar, P. ., & Pant, B. D. (2023). Arch Form and Mathematical Ratio in Orthodontics Patients: A Cross–sectional Study. Journal of Institute of Medicine Nepal, 45(2), 49–53. Retrieved from