What this calculator does
For teeth to fit together properly, the upper and lower arches need to be proportionate. Wayne Bolton measured that proportion in 1958 and found consistent means: 77.2 per cent for the front six teeth and 91.3 per cent across twelve.
A meaningful departure from those means cannot be fixed by moving teeth alone. If the lower front teeth are collectively too wide for the uppers, closing the bite properly requires reducing or building up tooth width somewhere.
The formula
The mandibular tooth width sum is divided by the maxillary sum and expressed as a percentage, separately for the anterior six and the full twelve. Each is compared against its published mean.
| Term | Meaning |
|---|---|
| Anterior ratio | Lower six front teeth over upper six, with a mean of 77.2 per cent. |
| Overall ratio | Lower twelve over upper twelve, with a mean of 91.3 per cent. |
| Tooth-size discrepancy | A departure from the mean large enough to affect how the bite can close. |
The inputs explained
| Field | What to enter |
|---|---|
| Mandibular anterior width sum (6 teeth) (mm) | Sum of the mesiodistal widths of the six lower anterior teeth, in millimetres. |
| Maxillary anterior width sum (6 teeth) (mm) | Sum of the six upper anterior teeth. |
| Mandibular total width sum (12 teeth) (mm) | Sum of all twelve lower teeth from first molar to first molar. |
| Maxillary total width sum (12 teeth) (mm) | Sum of all twelve upper teeth. |
When to use it
Planning orthodontic treatment
A discrepancy found before treatment changes the plan; found afterwards it is a problem.
Diagnosing a bite that will not close
A tooth-size mismatch prevents ideal occlusion however well the teeth are aligned.
Deciding on interproximal reduction
The size of the discrepancy indicates how much width needs removing and from where.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does upper tooth width shift the ratio?
The same lower teeth against three upper anterior sums.
| Upper anterior sum | Anterior ratio | Difference from anterior mean |
|---|---|---|
| 44.0 mm | 83.6% | +6.4 points |
| 47.7 mm | 77.1% | -0.1 points |
| 52.0 mm | 70.8% | -6.4 points |
Questions
What size of discrepancy matters?
Bolton reported a standard deviation of roughly 1.65 points on the anterior ratio, and departures beyond about two standard deviations are generally treated as clinically significant. Smaller variations are common and usually absorbed in treatment.
What is done about a discrepancy?
Depending on direction and size: interproximal enamel reduction to narrow teeth, composite or veneers to widen them, or in some cases extraction. Which is appropriate is an orthodontic judgement.
Why measure both anterior and overall?
Because a discrepancy can sit in the front teeth alone or be distributed across the arch, and the two call for different responses. Comparing both localises where the mismatch is.
How are the measurements taken?
Mesiodistal widths at the widest point of each tooth, traditionally with calipers on plaster models and now usually from digital scans. Measurement error accumulates across twelve teeth, so technique matters.
For eye focusing range, see the amplitude of accommodation calculator. For a general size baseline, see the BMI calculator.