Journal of Dental Research and Review

: 2021  |  Volume : 8  |  Issue : 3  |  Page : 143--148

Evaluation of maxillary anterior tooth proportion using the novel TR proportion

Tarulatha R Shyagali1, Ruchi Jha1, Deepak Bhayya2, Abhishek Gupta1, Anil Tiwari1, Rahul Patidar1,  
1 Department of Orthodontics and Dentofacial Orthopedics, Hitkarini Dental College and Hospital, Jabalpur, Madhya Pradesh, India
2 Department of Pediatric and Preventive Dentistry, Hitkarini Dental College and Hospital, Jabalpur, Madhya Pradesh, India

Correspondence Address:
Tarulatha R Shyagali
Department of Orthodontics and Dentofacial Orthopedics, Hitkarini Dental College and Hospital, Jabalpur, Madhya Pradesh


Aim: The aim is to evaluate the maxillary anterior tooth proportion relationship using different calculations. Materials and Methods: Forty pleasing smile photographs were evaluated for the different calculations. Mesiodistal width of all the maxillary anterior teeth were measured and were subjected to different calculations like individual tooth width divided by the combined width of all the anterior teeth of one side and individual tooth width divided by the combined width of the remaining two teeth of one side. Calculated results were tabulated and were subjected to descriptive statistics. Results: Among the various formulas, the mesiodistal width of canine divided by the sum of mesiodistal width of central, lateral incisors, and canine showed the consistent quotient of 0.3 for all the subjects. Mesiodistal width individual teeth like central incisors when divided by the combined width of central incisor, lateral incisor and canine, also showed the constant quotient of 0.3 for all the patients. The sum of Mesiodistal width of central and lateral incisor when divided by combined width of central, lateral incisor and canine gave the constant value of 0.6. Conclusion: The consistent quotients obtained by the formulas like width of central incisors and the canine divided by the combined width of central-lateral incisors-canine and the other formulas can be used for building up of the missing teeth and the smile designing.

How to cite this article:
Shyagali TR, Jha R, Bhayya D, Gupta A, Tiwari A, Patidar R. Evaluation of maxillary anterior tooth proportion using the novel TR proportion.J Dent Res Rev 2021;8:143-148

How to cite this URL:
Shyagali TR, Jha R, Bhayya D, Gupta A, Tiwari A, Patidar R. Evaluation of maxillary anterior tooth proportion using the novel TR proportion. J Dent Res Rev [serial online] 2021 [cited 2021 Nov 27 ];8:143-148
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Smile is rightly said to be the first step toward communication and an attractive smile adds all the more value to the prospective of communication. Its age old sciences to correlate the beauty with the mathematical formula. Golden proportion is not only a mathematical formula, but also a valid tool to judge the attractiveness of the smile. Modern day smile designing tools also include golden proportion for construction of esthetic smile.[1]

Leonardo da Vinci said “No human inquiry can be called science unless it pursues its path through mathematical exposition and demonstration.”[2] Golden proportion has been studied since antiquity and since ages scientists have tried to rule out natures secret of beauty, many gave various proportions to justify the same. Some said it is genetically determined. Lombardi was the first to suggest the application of the golden proportion in dentistry.[3]

Golden proportion is a constant ratio of 1.618:1. Literature on the golden proportion is explicit, giving it rather an oversimplified outlook. But in reality, the theoretical concepts which look simple to follow are practically very complex to apply. Apart from symmetry, deviations, the color-hue of teeth and the overall face also plays a major role in making smile attractive.[4],[5]

Golden percentage even though widely used is inconsistent to judge the teeth width.[6],[7],[8],[9],[10] However, few studies also have emphasized the its utility in difficult clinical conditions.[11] Controversy still persists regarding the validity of golden proportion as a tool to evaluate the smile, thus the current study was undertaken with the aim to evaluate whether any other proportion is followed for tooth width in attractive smiles.

 Materials and Methods

A cross-sectional study was done on a sample of 40 smile photographs. Ethical clearance was obtained from the institutional ethical committee. Dental under graduate students and interns were asked to rate the most pleasing smile in the order of 1–10 of their classmates, where rating 1 represented most attractive smile. All the students who were having an attractive smile were enlisted and were asked to report to the department of orthodontics and dentofacial orthopedics. Assembled students were explained about the purpose of the study and an informed consent was obtained for their willing participation in the current research. Each student was scanned for the following selection criteria such as presence of all maxillary and mandibular teeth, healthy gingival and periodontal condition, absence of spacing and crowding, and no previous history of orthodontics and anterior restoration. After the selection scanning, 30 students met the said criteria and data related to golden proportion was collected from this final sample.

Smiling (social smile) front photographs of each patient [Figure 1] was taken with a digital single-lens reflex camera (Canon, Tokiyo, Japan) with 1/125 shutter speed, F1/5.6 aperture, and ISO 200 sensitivity.{Figure 1}

All the subjects were made to stand in natural head position with 11 inch of gap from the background screen and the distance between the triploid and the patient was fixed to 5 feet. Mesiodistal width of the maxillary central incisors and lateral incisors and canine were measured bilaterally on the smiling photographs [Figure 2] indirectly using adobe photo shop application 7 (Adobe Inc., for Windows and macOS).{Figure 2}

To check whether the tooth follow any pattern of association various equations were tried. Following which the frequency calculation was done. Equation tried for the current study is represented in the [Table 1].{Table 1}

All the measurements were done by a single examiner and to know the intraexaminer variability the 10 consecutive photographs were measured twice within the gap of a week and the obtained data were subjected to kappa statistics (95%).

Obtained data were tabulated and descriptive statistics was performed to know the frequency of distribution of the different calculations using Microsoft excel office (Microsoft office 2010).


[Table 2] shows the various calculations for all the subjects. The formula which showed consistency was seen in relation to the mesiodistal width of lateral incisor was divided by the sum of mesiodistal width of central and lateral incisors and we obtained a proportionality constant (coefficient of proportionality) of 0.4. Moreover, if we assign the parameter to this constant with central as X, Y, and Z as lateral incisor and canine measurement, respectively, then we have the formula;{Table 2}

Y = 0.4 (X + Y)

Similarly, formulas like mesiodistal width of central incisor divided by the combined width of central incisor, lateral incisor and canine, showed the constant quotient of 0.3 as a proportionality constant. Again if we assign the parameters, then we have the formula.

X = 0.3(X + Y + Z)

Mesiodistal width of canine divided by the combined mesiodistal width of the central, lateral incisor and canine fetched the proportionality constant of 0.3 for all the patients.

Z = 0.3(X + Y + Z)

The sum of mesiodistal width of central and lateral incisor when divided by combined width of central, lateral incisor, and canine gave the constant proportionality value of 0.6.

(X + Y) = 0.6 (X + Y + Z)


The golden proportion (phi) (1.618:1.0) describes the ratio between the dimensions of a larger and a smaller length. Nowadays, for all patient dental esthetics have become a major consideration and to achieve an excellent esthetics various authors have provided valuable guidelines.[5]

The golden proportion is said to be a reliable predictor for determining the width of the maxillary central incisors.[6] on the other hand Gillen et al., 1994, Rosenstiel et al., 2000 and Ward, 2001 found that anterior teeth widths did not follow golden proportion.[12],[13],[14]

The result of the current study for tooth proportion showed that many of the measurements were not consistent for various calculations except for the four formulas which showed constant value for all the subjects. Lateral incisor width showed a proportionality constant of 0.4 for the formula width of lateral incisor divided by the combined width of central and lateral incisor. The most common congenital missing teeth are maxillary laterals incisors[15] and this formula can be used for building up or for the replacement of lateral incisors in such cases. We are proposing these particular proportions as, TR proportion as an acronym on the name of authors (Tarulatha-Ruchi Proportion). The same proportion formulas were used to build up the missing lateral incisors with satisfactory results [Figure 3] and [Figure 4].{Figure 3}{Figure 4}

Combined width of the maxillary central, lateral incisors and canines when used as a divisor to the individual teeth such as central incisors, lateral incisor, and canines, there was a consistent value obtained for central incisor and canine. These relationships can be used to design the esthetic smile for the required patients.

Most of the literature so far gave lots of importance to the golden proportion, however, there are very few studies which give consistent results.[16] There are other proportion measuring tools such as recurring esthetic dental, the Chu's gauge and preston propotion.[2],[17] Among these, golden percentage and Chu's gauges are considered good for clinical practice.[2],[18]

The current study is one of its kinds as none of the previous studies have explored the different proportions proposed here. Similar study of same nature was proposed by German et al. (2015), where they advised various measurements like maxillary lateral incisor is 2 mm less than the central incisors and maxillary canine was 1 mm less than the maxillary central incisor.[19]

The proportion relationship was consistent for all the subjects studied the measured width of maxillary lateral was more than the ideal value. Similar results were also found in the earlier study on South Indian population by Subhashini et a.[20]

However, we did notice the repetition of a particular pattern for the different proportion involving the combined width of central incisor, lateral incisor and canine to the individual width of either canine, lateral, or central. One important point to be noted is that most of the dentist preferred building their patients smile based on the overall smile balance than based on any of these proportion.[21] However, considering the ease of the formulas used here, most of the dentist can take advantage of the simplicity of these calculations.

The study carries the scope to explore the results further on the larger population.


The divine proportion of the tooth cannot be emphasized as a sole criterion to judge an attractive smile. Within the limitation of this study, it can be concluded that the consistent quotients obtained by the formulas like width of central incisors and the canine divided by the combined width of central-lateral incisors-canine and the other formula like width of lateral incisors divided by the combined width of central-lateral incisors can be used successfully to design the smile esthetics. These values can be applied for building up of the missing teeth and the smile designing.

Ethical clearance

HDCH/IEC/2019/521. (HDCH: Hitkarini Dental College and Hospital).

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.


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