Bolton Analysis: Overall and Anterior Ratios, Step by Step

The Bolton analysis answers a simple question: are the teeth of the two arches the right size for each other? When they are not, you can align both arches perfectly and still fail to obtain a Class I canine relationship with normal overjet and overbite. This guide covers how to measure, the overall and anterior ratios with their norms, how to turn a percentage into millimeters on the right arch, and the criteria that guide what to do next. Every value matches our free Bolton analysis calculator, so you can follow the worked example in it.

What is a tooth-size discrepancy?

For the teeth to intercuspate with normal overjet and overbite, the mesiodistal widths of the mandibular teeth must be in proportion to those of the maxillary teeth. When this proportion is broken, there is a tooth-size discrepancy (often abbreviated TSD, and called Bolton discrepancy): one or more teeth are too small (microdontia) or too large (macrodontia) for the opposing arch.

The typical examples are small maxillary lateral incisors, large mandibular incisors, or small maxillary incisors. The maxillary lateral incisor, reduced or peg-shaped, is the most common culprit. According to the textbooks used in French university courses (Boileau), the discrepancy is frequent, but it is often compensated by wear or occlusal adaptation.

Do not confuse it with the tooth size–arch length discrepancy, which compares the teeth with the space available in the bone. Crowding is measured with a space analysis (try our free space analysis tool); the Bolton analysis only compares one arch with the other.

Measuring the teeth

Which teeth, and when

• The permanent dentition only. In the mixed dentition, the size of the primary teeth does not predict that of the permanent teeth, and a transient discrepancy is possible. The analysis is postponed until the permanent teeth are in place (see our article on mixed dentition analysis, in French).
• From first molar to first molar, in both arches: 12 maxillary teeth (16 to 26) and 12 mandibular teeth (36 to 46), in FDI notation.
• The six anterior teeth, canine to canine (13 to 23 and 33 to 43), are used on their own for the anterior ratio.

How to measure

Measure the greatest mesiodistal width of each tooth on a cast or a digital model, with a caliper or the measuring tool of your software. Bolton measured his sample to the nearest quarter of a millimeter. Precision matters more than it seems: a small error repeated over twelve teeth adds up and shifts the ratio.

The two Bolton ratios and their norms

Bolton (1958, 1962) studied 55 excellent occlusions and derived two ratios from them.

• Overall ratio = sum of the 12 mandibular teeth / sum of the 12 maxillary teeth × 100.
• Anterior ratio = sum of the 6 mandibular anterior teeth (33 to 43) / sum of the 6 maxillary anterior teeth (13 to 23) × 100.

These are the values used by our calculator, taken from the knowledge base of a university orthodontic program (Boileau’s textbook and course handouts):

A note on the standard deviation of the overall ratio. Sources do not all agree. Our reference gives 1.81, and the calculator uses that value. Other publications quote Bolton’s overall ratio as 91.3 ± 1.91%, for example Ajami and colleagues in a 2018 study of an Iranian population (PubMed). In practice the difference is small: one standard deviation around the mean covers about 89.5 to 93.1% with 1.81, and about 89.4 to 93.2% with 1.91. Check which value your own program or textbook uses before comparing results.

How to read the ratio

• Ratio above the mean: the mandibular teeth are too large for the maxillary teeth (mandibular excess).
• Ratio below the mean: the maxillary teeth are too large for the mandibular teeth (maxillary excess).

The range matters as much as the mean: excellent occlusions went from 87.5 to 94.8% for the overall ratio, so a ratio slightly off the mean is common.

From a percentage to millimeters

A percentage means little at the chair. As with Bolton’s original chart, you convert it into millimeters by computing the "correct" sum of one arch from the other.

• Ratio too high (mandibular excess): expected mandibular sum = maxillary sum × 0.772 (anterior) or × 0.913 (overall). Mandibular excess = actual mandibular sum − expected mandibular sum.
• Ratio too low (maxillary excess): expected maxillary sum = mandibular sum / 0.772 (anterior) or / 0.913 (overall). Maxillary excess = actual maxillary sum − expected maxillary sum.

Worked example

This is the fictitious patient behind the "Fill in an example" button of our Bolton calculator.

Anterior ratio. 36.6 / 45.5 × 100 = 80.4%. The deviation from the mean is 80.4 − 77.2 = +3.2 points, i.e. 3.2 / 1.65 = 1.94 standard deviations. The ratio is too high: the analysis points to a mandibular excess.

Excess in millimeters. For 45.5 mm of maxillary anterior teeth, the expected mandibular sum is 45.5 × 0.772 = 35.13 mm. Mandibular excess = 36.6 − 35.13 ≈ 1.5 mm.

Overall ratio. Adding the premolars and first molars, the maxillary sum is 93.2 mm and the mandibular sum 86.2 mm: 86.2 / 93.2 × 100 = 92.5%, i.e. +1.2 points or 0.66 standard deviation. The overall ratio stays within the norm; the discrepancy is anterior.

Which arch is at fault? The ratio cannot tell. The same 80.4% can be read the other way: the expected maxillary sum is 36.6 / 0.772 = 47.41 mm, so the maxillary anterior teeth are about 1.9 mm short. Here the maxillary lateral incisors measure 6.3 and 6.4 mm against central incisors of 8.6 and 8.5 mm. Small lateral incisors point to a maxillary deficiency rather than to oversized mandibular incisors, and that reading changes the options: adding volume to the lateral incisors rather than reducing the mandibular incisors. Examining the teeth, not the ratio, settles the question.

Interpretation: when is a discrepancy significant?

The threshold used by the tool

The calculator suspects a discrepancy when the ratio deviates from the mean by at least one standard deviation, then asks for confirmation with a diagnostic set-up. This follows Boileau, who rejects the use of the Bolton ratio as a strict cut-off and requires a diagnostic (Kesling) set-up reproducing the planned tooth axes before any decision.

Other thresholds in use

Sources differ here too, and the choice is yours:

• the university course handouts give the means without dispersion, any deviation counting as a discrepancy;
• many studies count as significant only a ratio beyond two standard deviations from Bolton’s mean (this is the criterion used by Ajami and colleagues, cited above);
• others reason in millimeters: Ajami and colleagues report that Proffit considers a discrepancy above 1.5 mm clinically significant, and that a threshold of 2 mm has also been proposed.

A literature review by Othman and Harradine (Journal of Orthodontics, 2006, PubMed) adds a nuance: Bolton’s sample was appropriate for indicating which ratio goes with an excellent occlusion, but not for defining the size or the prevalence of a clinically significant discrepancy. The studies reviewed reported 20 to 30% of significant anterior discrepancies and 5 to 14% of overall ones, and most reported their measurement error poorly.

Neff and overbite

Tooth widths are not the whole story. Harmony between the arches also depends on incisor inclination, the occlusal plane, the curves of Spee and Monson, cusp height and, above all, overbite. According to Neff, as reported by Boileau, there is no standard anterior ratio: the anterior coefficient varies with overbite, and an excessive overbite may be the adaptation to a tooth-size discrepancy. A ratio is a warning light, not a diagnosis.

The clinical pictures

• Anterior mandibular excess: lower incisor crowding with aligned, or even spaced, upper incisors. At the end of treatment, it becomes difficult to obtain both a Class I canine relationship and normal overjet and overbite.
• Anterior maxillary excess: spacing in the mandibular arch, or increased overjet and overbite with a Class I canine relationship. A maxillary excess is one of the causes of deep bite (see our article on deep bite, in French).
• Overall discrepancy with a normal anterior ratio: the difference lies in the premolars and molars; it affects the intercuspation of the buccal segments more than the incisors.

What to do with a discrepancy

These are criteria to discuss, not decisions. Before any irreversible procedure, the diagnostic set-up checks whether the discrepancy is real and how large it is once the planned tooth axes are reproduced.

Adding volume

With microdontia, for example small maxillary lateral incisors, restorations are usually preferred: the lateral incisors are positioned in a Class I canine relationship with mesial and distal spaces, then built up with composite or a prosthetic restoration. In the worked example above, this is the option to discuss first.

Removing volume

With true or relative macrodontia, the options are interproximal reduction (IPR, stripping) or extractions.

• IPR of the mandibular incisors is the usual answer to a moderate anterior mandibular excess. The amount should be quantified on the set-up. An older reference (Bassigny) limits the gain to about 1.5 to 2 mm for the six anterior teeth.
• Extraction of a mandibular incisor is considered for an anterior mandibular excess of 4 to 6 mm, and only after a set-up: if it is not justified, it increases overjet and overbite. A peg-shaped lateral incisor is another cited indication for an incisor extraction. In adults with reduced papillae, IPR is generally preferred to incisor extraction because of the risk of black triangles (see our article on adult orthodontics and the periodontium, in French).

Accepting the discrepancy

A small discrepancy can be absorbed by the finish: for an anterior maxillary excess, a slightly deeper overbite can take up the difference. Many discrepancies are already compensated by wear or occlusal adaptation.

Agenesis and peg-shaped lateral incisors

When a maxillary lateral incisor is missing and space is to be opened, the width to open can be set by the contralateral lateral incisor if it is normal, by proportion (lateral incisor about two thirds of the central, roughly 6 mm for a 9 mm central incisor), or by a Bolton calculation, with the set-up as the reference. A peg-shaped contralateral lateral incisor should be looked for in these cases. Our article on lateral incisor agenesis (in French) covers the open-or-close decision.

Pitfalls

1. Measuring in the mixed dentition. A transient discrepancy is possible; wait for the permanent teeth.
2. Measurement error. Small errors add up over twelve teeth. Measure the greatest mesiodistal width of each tooth, carefully, and check any unusual value: the calculator flags widths below 3 mm or above 14 mm as probable entry errors.
3. Rotated and overlapping teeth. On a crowded cast, the caliper is harder to place. Measure the width of the tooth itself, not the space it occupies in the arch, and repeat doubtful measurements.
4. Missing teeth. The analysis assumes all twelve teeth in each arch. To estimate the space to keep for a missing tooth, the width of its contralateral counterpart is often used if that tooth is normal; the set-up remains the reference.
5. Blaming the wrong arch. A "mandibular excess" can just as well be a maxillary deficiency. Look at the teeth before choosing between IPR and build-ups.
6. Using the ratio as a cut-off. A deviation of one standard deviation raises a suspicion; it does not justify an extraction on its own. And the norms, from Bolton’s original sample, may differ between populations.

In practice: a checklist

1. The patient is in the permanent dentition, with all teeth from first molar to first molar.
2. Each tooth is measured at its greatest mesiodistal width, on a cast or a digital model.
3. The anterior ratio and the overall ratio are both calculated, and compared with 77.2% and 91.3%.
4. The deviation is expressed in standard deviations and in millimeters, stating which norm and which threshold you use.
5. The arch at fault is identified by examining the teeth, especially the maxillary lateral incisors.
6. A diagnostic set-up confirms the discrepancy before any IPR, build-up or extraction.

Our free Bolton analysis calculator does steps 3 and 4 live, with each formula shown and both readings of the excess.

Frequently asked questions

What is the Bolton analysis in orthodontics?

It compares the sum of the mesiodistal widths of the mandibular teeth with that of the maxillary teeth. Two ratios are calculated: the anterior ratio (six teeth, canine to canine) and the overall ratio (twelve teeth, first molar to first molar). A ratio far from the norm indicates a tooth-size discrepancy, which can prevent a Class I canine relationship with normal overjet and overbite at the end of treatment.

What is the normal anterior Bolton ratio?

77.2% on average, with a standard deviation of 1.65 and a range of 74.5 to 80.4% in Bolton’s excellent occlusions. The overall ratio is 91.3%, with a standard deviation of 1.81 in our reference (some sources quote 1.91) and a range of 87.5 to 94.8%.

How do I calculate the Bolton discrepancy in millimeters?

If the ratio is too high, multiply the maxillary sum by 0.772 (anterior) or 0.913 (overall) and subtract the result from the actual mandibular sum: that is the mandibular excess. If the ratio is too low, divide the mandibular sum by 0.772 or 0.913 and subtract the result from the actual maxillary sum: that is the maxillary excess.

What is a clinically significant tooth-size discrepancy?

There is no single answer. Our calculator suspects a discrepancy from one standard deviation and asks for a set-up, following Boileau. Many studies use two standard deviations, and others use a threshold in millimeters, 1.5 or 2 mm. Whatever the threshold, the diagnostic set-up confirms the discrepancy before treatment.

Can I do a Bolton analysis online for free?

Yes. Our free Bolton analysis calculator takes the 24 widths and gives both ratios, the deviation in standard deviations and the excess in millimeters. It runs in your browser: no measurement is sent or stored.

With GS Ortho

In GS Ortho, the diagnostic studio guides you through the case step by step, in 12 panels. If a tooth-size discrepancy complicates the plan, you can request an orthodontist’s opinion in one click, straight from the case. The decision stays yours, and the data stays hosted at your practice. The GS Ortho interface is currently available in French.

Book a demo

bolton analysis bolton ratio tooth size discrepancy anterior ratio interproximal reduction