What the Bolton ratios measure
A Bolton analysis checks whether the upper and lower teeth are the right size for each other. If the mandibular teeth are too wide for the maxillary teeth, or the other way around, you can't get ideal overjet, overbite and buccal interdigitation at the same time, however well the teeth are aligned.
Wayne Bolton measured 55 casts with excellent occlusion and published two ratios in 1958. Each is the sum of the mandibular widths divided by the sum of the maxillary widths, times 100:
| Ratio | Teeth in each arch | Bolton's mean | SD |
|---|---|---|---|
| Overall | 12: first molar to first molar | 91.3% | 1.91 |
| Anterior | 6: canine to canine | 77.2% | 1.65 |
How this tool works
- You enter the greatest mesiodistal crown width of each tooth, in mm. The grid shows each tooth's FDI number with its Universal number below it.
- The tool adds the 12 maxillary and 12 mandibular widths, and the 6 anterior widths in each arch. Each ratio appears as soon as every width it needs is filled in.
- Ratio = mandibular sum ÷ maxillary sum × 100.
- SD distance = (ratio − Bolton's mean) ÷ Bolton's SD. The marker on the scale runs from −3 to +3 SD.
- Tooth-size excess comes straight from the definition of the ratio:
- Ratio above the mean: mandibular excess = mandibular sum − (maxillary sum × mean ÷ 100).
- Ratio below the mean: maxillary excess = maxillary sum − (mandibular sum × 100 ÷ mean).
- The tool also gives the same discrepancy as a shortfall in the other arch. That's the width you would need to add there, for example with composite build-ups, instead of removing it from the excess arch.
Sums and ratios show 2 decimals in the working table. The headline figures are rounded to 1 decimal, so the result doesn't look more precise than a caliper reading.
Worked example
The example pre-filled above has a maxillary sum of 93.60 mm and a mandibular sum of 87.40 mm. Its overall ratio is 87.40 ÷ 93.60 × 100 = 93.38%. That is 2.08 points, or 1.09 SD, above the mean. The mandibular teeth that would fit this maxilla total 93.60 × 0.913 = 85.46 mm, so the mandibular excess is 87.40 − 85.46 = 1.94 mm. The same discrepancy is a maxillary shortfall of 2.13 mm.
Reading the result
- Within 1 SD: well inside the spread of Bolton's sample. Finishing problems from tooth size are unlikely.
- Between 1 and 2 SD: a mild discrepancy. It may show up as small spaces, a slightly deep or shallow overjet, or a canine relationship that won't quite settle.
- More than 2 SD: studies of Bolton's ratios often call this a significant discrepancy. That's a research convention, not a treatment threshold.
Turn a large excess into a plan only after you've rechecked the measurements. Also think about what else changes how the teeth occlude: incisor torque and angulation, incisor thickness, missing or peg-shaped laterals, and extraction patterns. A diagnostic setup is the usual way to confirm what the arithmetic suggests.
Measuring tips
- Measure the greatest mesiodistal crown width at the contact points, parallel to the occlusal plane. Use fine-tipped calipers on casts, or a calibrated tool on digital models. Repeat any reading that seems off, and use the mean of two.
- Measure all 24 teeth. Don't assume left and right are the same. The "fill from the other side" button is for a tooth that's missing, broken down or restored out of shape. Note the substitution in the record.
- Rotated, crowded or heavily restored teeth are harder to measure accurately. Treat a borderline result in a crowded arch with caution.
Limits of the Bolton analysis
- Bolton's sample was small (55 casts) and selected for excellent occlusion. Later studies in other populations often report different means and wider spreads, so a result just past 1 SD in your patient may still be normal for their group.
- The ratios measure tooth size only. They don't account for tooth shape, crown thickness or inclination, which also change how the teeth fit together.
- The excess in mm tells you how big the discrepancy is. It doesn't tell you which teeth to reduce or build up. That depends on where the problem shows in the occlusion.
The chart note below the result is plain text you can paste into the record. It holds both ratios, the sums, the SD distance and the excess. The page also prints cleanly with your widths in the grid. For tooth numbering, see the Tooth Number Chart.
Frequently asked questions
What are the normal Bolton ratios?
What does a Bolton ratio above the mean mean?
How big a Bolton discrepancy matters?
Which teeth do I measure?
What if a tooth is missing or broken down?
Sources
- Bolton WA. The Angle Orthodontist 28(3):113-130. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. 1958. Original source of the 91.3% and 77.2% norms (55 casts with excellent occlusion). Accessed October 26, 2026.
- Ebadifar A, Taliee R. Journal of Dental Research, Dental Clinics, Dental Prospects 7(1):30-35. Comparison of Bolton's Ratios before and after Treatment in an Iranian Population. 2013. Restates Bolton's means and SDs (77.2% ± 1.65; 91.3% ± 1.91) and Bolton's sample; notes that later researchers treat values beyond 2 SD as a significant discrepancy. Accessed October 26, 2026.
Last reviewed by the Dental Health Time editorial team, against the sources above. How we review.