Advanced computerized systems, digital models, and mobile applications offer promising clinical solutions for orthodontists. However, before deciding to introduce a new method into daily practice, it is necessary to ensure that this new measurement method is easily accessible, accurate, repeatable, and reproducible, just like methods currently considered more traditional. Therefore, the purpose of this study has been to compare the reliability and validity of orthodontic measurements using “Nemocast” software, the “Ruler” mobile app, and the conventional method using a digital caliper.

Although manual measurements of the study model are often considered the standard, the accuracy of tooth width values measured with different methods depends both on the accuracy of the dentition replication process and on the consistency and accuracy of the measurement process. In theory, when using orthodontic plaster models, the expansion caused by the setting of dental plaster is compensated by the contraction that occurs in the impression material [29]. Consequently, the three most important factors that could significantly alter the accuracy of measurements made using calipers on physical study models are: the challenging access in dentitions with crowding, difficulties in locating distal and mesial reference points due to aberrant interproximal dental anatomy, and inconsistencies in carrying out established measurement protocols [26, 29].

Regarding the standard deviations of the total space measured for each method and time point, the values obtained by the mobile app “Ruler” (-1.52 mm at T1 and − 0.33 mm at T2) were the closest to the manual method (-1.20 mm at T1 and − 0.49 mm at T2). The values obtained by the software were the lowest at both time points; a finding consistent with the studies by Grünheid T et al. [7] and Nalcaci et al. [17], where similar results were obtained, showing that the values obtained by software, in digital models, were always lower. However, in the study conducted by Koretsi V et al. [19], greater mesiodistal sizes were obtained in digital measurements compared to manual ones.

Regarding the measurements of each quadrant, no statistically significant differences were found. No statistically significant differences were obtained in individual measurements at the level of each dental piece except for piece 11 with the “Ruler” app method. Therefore, it could be concluded that the three methods measured each of the quadrants similarly. Other authors have reached similar conclusions in their studies where no statistically significant differences were found in the values obtained in both digital and physical models [20, 26,27,28,29,30,31,32].

Moreover, measurements in each arch were also analyzed, where software measurements were more reliable in the upper arch with no significant differences in the comparison of mean differences at T1 and T2 (p = 0.065). In the lower arch, it seems that the measurements were reliable with all three methods.

Regarding the upper arch, significant differences were found in the measurements of the left and right sectors (p = 0.004 and p = 0.001 respectively) in the manual method, obtaining greater validity in the measurements by software and mobile app. And regarding the lower arch, significant differences were found in all sectors in the manual method (AAL: p = 0.022, IAL: p = 0.010, DAL: p = 0.013), with no significant differences found in any of the sectors by the software method.

Therefore, it could be deduced that the software has been the method with the greatest reproducibility and temporal reliability and could be considered as an acceptable alternative in clinical practice. This result is consistent with various studies where the digital workflow using software demonstrated greater reproducibility and reliability, also showing that measurements were significantly faster to obtain compared to those made by the traditional manual method in plaster models [7, 13, 22]. According to different authors consulted, both measurements made by Orthocad [28, 33, 34], Emodels [7, 28], SureSmile [7, 34], AnatoModels [7], Mirror [7], Bibliocast Cécile 3 [33], and Maestro 3D [35] seem to be a good alternative in terms of accuracy and reliability compared to direct measurements on plaster models. This type of software can also be useful for performing other measurements in our field, such as analyzing and quantifying dental movement produced during treatment [36].

Furthermore, Pearson correlations were calculated between the measurements of each model (total and quadrant scores) at each time point. Although the correlations were significant, the measurements obtained from the mobile app “Ruler”; presented lower values than the other two models (0.414 for the quadrant correlation and 0.747 for the total correlation). According to the results obtained, the method with the least reliability and reproducibility would be the measurement by the mobile app “Ruler”. This result is consistent with the study by RS Alwakeel et al. [5], where although the precision in the measurements of conventional models compared to those made using iPhone or Android software was similar, the measurements of available and required space using digitized photographs showed significant differences compared to the manual method. Other authors obtained different results. In the study by Prabhu K et al. [35] with the Scann 3D software for smartphones, although they observed, in the statistical analysis, that the standard deviation was greater in the premolar region, they were able to conclude that this mobile app was adequate and reliable compared to the traditional method; findings similar to the study by Morris RS et al. [37] where digital models created by the smartphone app DM were considered accurate enough for clinical use.

However, the results conducted so far on their reliability show contradictory results regarding the results obtained [5, 37]. Therefore, the use of mobile applications, in spatial analysis, still requires further scrutiny to demonstrate that they are useful and reliable for use as scientific and medical techniques.

One of the largest sources of random error according to different authors is the difficulty in identifying reference points [7, 19, 28, 30, 35]. In the present study, common definitions of anatomical points are adopted, considering that there will always be some imprecision in the identification of points, inherent to the analysis of models itself, regardless of the system used, i.e., a contact point could be a contact area, which would cause certain inaccuracies [19]. This task may be more difficult in digital measurements because examiners rely solely on subjective visual interpretations for the identification of reference points (since a three-dimensional structure appears as a two-dimensional image). Additionally, despite the high resolution of the software, the additional tactile sensation provided by physical models is absent with this new method. It should be noted that, in digital measurements, a specific limitation known as the “shape assumption” phenomenon occurs. The software inherently fills interproximal areas, when these are not entirely clear, are absent, or not captured, using patented mathematical algorithms, which is a potential source of inaccuracies. It may also be important to note that the operator’s experience in making measurements may alter the results [15, 29].

These inaccuracies in measurements could also be due to another factor that alters the reliability or reproducibility of the values obtained, such as the training and experience of the examiner with the systems used in digital measurements [5, 19, 28, 30]. Reuschl RP et al. [28]. also suggest that there is a learning curve, more specifically in digital measurements, which will lead to smaller deviations as the observer becomes familiar with the technique. Therefore, errors are inevitable, as the measurements were carried out by human operators and these can improve with experience [30].

Tomasseti et al., analyzed the accuracy and efficiency of the total analysis using manual techniques and computerized methods and although they considered that all techniques are similar in terms of accuracy, the use of computerized methods could be more efficient in terms of the time used for measurements [14]. Other authors reached the same results [7, 28]. The comparative results improved in terms of reliability, validity, and time in the models analyzed digitally and obtained directly in the mouth by scanning instead of on the conventional plaster model [29, 38]. In the study carried out by Okamoto et al. [39], it was observed that the measurements made digitally by different operators were more consistent and reproducible than those made on a manual model.

No studies with similar objectives using artificial intelligence have been found in the literature. We consider that this aspect may be interesting for future studies.

One of the limitations when conducting our study was the difficulty in obtaining a larger homogeneous sample size in the study sample. Although the size used is similar to that of other studies analyzed [4, 7, 17, 28], we consider that an increase in the number of participants could help us improve our results. In the literature, we find that different authors analyze in their studies only one or two types of software in comparison with manual measurements, so we consider that, apart from increasing the sample size, adding more types of measurement software to the analysis would give us a more global view on the subject. Likewise, most of these studies, like ours, analyze permanent teeth and patients without growth, not finding any study that analyzes whether these results are comparable to those we would obtain if we studied deciduous dentition. We believe this could be a good future line of research.