Space Analysis Calculator
Perform Bolton ratio analysis and arch length discrepancy measurement for orthodontic treatment planning.
About this calculator
Bolton Overall Ratio is a straightforward ratio -- Mandibular 12 Tooth Sum divided by Maxillary 12 Tooth Sum, times 100 -- so only those two measurements affect it; the four anterior and arch-length inputs (Mandibular Anterior 6, Maxillary Anterior 6, Arch Perimeter Available, Total Tooth Width Sum) play no role in the overall ratio at all, since Bolton analysis and arch-length discrepancy are two independent measurements that happen to share this calculator rather than two parts of the same formula. Maxillary 12 Tooth Sum sits in the denominator, and because a rise in a denominator moves a ratio less than the same-sized rise in the numerator while a matching drop moves it more, swinging Maxillary 12 Tooth Sum up and down by an equal percentage edges out doing the same to Mandibular 12 Tooth Sum for the larger measured two-sided spread -- a mechanical property of division rather than a clinical judgment about which arch matters more.
The 91.3% ideal ratio (SD 1.91) this calculator compares against comes from orthodontist Wayne Bolton's original 1958 Angle Orthodontist study correlating maxillary and mandibular tooth widths across orthodontically normal occlusions, and the Overall Significant flag fires only when the measured ratio deviates from that ideal by more than two standard deviations -- a statistical threshold for clinically meaningful tooth-size discrepancy, not an automatic extraction or interproximal-reduction recommendation, which still requires the clinician's judgment alongside cephalometric and facial evaluation.
Medical Disclaimer
This calculator is for informational and educational purposes only. It is not a substitute for professional medical advice, diagnosis, or treatment. Always consult a qualified healthcare provider before making decisions about your health. Never disregard professional medical advice or delay seeking it because of results from this tool.
Inputs
Results
Bolton Overall Ratio (%)
91.21%
Figures current as of 1958. Source: Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. Angle Orthod. 1958;28(3):113-130.
How to Use This Calculator
- Measure and enter tooth widths (mm) for each tooth in the arch using a Boley gauge or digital calipers.
- Enter arch length (mm) measured along the dental arch from first molar to first molar.
- Read arch length discrepancy (mm): negative = crowding, positive = spacing.
- Use Bolton analysis outputs to identify tooth size discrepancies between maxillary and mandibular arches.
- Incorporate space analysis into extraction decision-making alongside cephalometric and facial evaluation.
How the result changes with Maxillary 12 Tooth Sum (mm)
| Maxillary 12 Tooth Sum (mm) | Bolton Overall Ratio (%) |
|---|---|
| 46 | 180.43% |
| 68 | 122.06% |
| 130 | 63.85% |
What each input means
- Mandibular 12 Tooth Sum (mm)
- Sum of mesiodistal widths of all 12 mandibular teeth (1st molar to 1st molar).
- Maxillary 12 Tooth Sum (mm)
- Sum of mesiodistal widths of all 12 maxillary teeth (1st molar to 1st molar).
- Mandibular Anterior 6 Sum (mm)
- Sum of mesiodistal widths of 6 mandibular anterior teeth (canine to canine).
- Maxillary Anterior 6 Sum (mm)
- Sum of mesiodistal widths of 6 maxillary anterior teeth (canine to canine).
- Arch Perimeter Available (mm)
- Available arch length measured along the arch form.
- Total Tooth Width Sum (mm)
- Sum of mesiodistal widths of all teeth in the arch being analyzed.
What each result means
- Bolton Overall Ratio (%)
- Mandibular 12 / Maxillary 12 * 100. Ideal = 91.3% (+/- 1.91).
- Bolton Anterior Ratio (%)
- Mandibular anterior 6 / Maxillary anterior 6 * 100. Ideal = 77.2% (+/- 1.65).
- Overall Deviation from Ideal (%)
- Difference from ideal 91.3%. Positive = relative mandibular excess.
- Anterior Deviation from Ideal (%)
- Difference from ideal 77.2%. Positive = relative mandibular excess.
- Overall Tooth Size Excess (mm)
- Positive = mandibular tooth material excess; Negative = maxillary excess.
- Anterior Tooth Size Excess (mm)
- Anterior Bolton discrepancy in mm.
- Arch Length Discrepancy (mm)
- Arch perimeter minus tooth width sum. Negative = crowding, Positive = spacing.
How this is calculated
Worked example, using the default values
- Identify Input Parameters6 parametersMandibular 12 Tooth Sum (mm) = 83, Maxillary 12 Tooth Sum (mm) = 91, Mandibular Anterior 6 Sum (mm) = 37, Maxillary Anterior 6 Sum (mm) = 48, Arch Perimeter Available (mm) = 75, Total Tooth Width Sum (mm) = 80 = 6 input(s) provided
- Calculate Bolton Overall RatioBolton Overall Ratio91.21 = 91.21%
- Calculate Bolton Anterior RatioBolton Anterior Ratio77.08 = 77.08%
- Calculate Overall Deviation from IdealOverall Deviation from Ideal-0.09 = -0.09
Figures and sources
- Bolton tooth-size ratio analysis (91.3% overall / 77.2% anterior ideal ratios) (1958) — Bolton WA. Disharmony in tooth size and its relation to the analysis and treatment of malocclusion. Angle Orthod. 1958;28(3):113-130.
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Does Arch Perimeter Available affect the Bolton Overall Ratio?
No -- Bolton Overall Ratio is calculated purely from Mandibular 12 Tooth Sum divided by Maxillary 12 Tooth Sum, and Arch Perimeter Available has no role in it. Arch Perimeter Available instead feeds the separate Arch Length Discrepancy calculation, which measures available space against total tooth width and is an independent analysis from Bolton tooth-size ratios.
Why does Maxillary 12 Tooth Sum have a slightly larger effect on the ratio than Mandibular 12 Tooth Sum?
Maxillary 12 Tooth Sum sits in the denominator of the Bolton Overall Ratio calculation (Mandibular 12 Tooth Sum divided by Maxillary 12 Tooth Sum). A rise in the denominator alone actually moves the ratio less than the same-sized rise in the numerator; it's an equal-sized drop in the denominator that moves the ratio more. Because a two-sided percentage swing combines both directions, Maxillary 12 Tooth Sum ends up with a marginally larger measured spread -- a mechanical property of division, not a clinical statement that the maxillary arch matters more in tooth-size discrepancy analysis.
What does it mean when Overall Significant is flagged as true?
Overall Significant fires when the measured Bolton Overall Ratio deviates from the 91.3% ideal value by more than two standard deviations (2 x 1.91), a statistical threshold from Bolton's original research indicating the discrepancy is unlikely to be normal variation. It flags a tooth-size mismatch worth clinical attention -- interproximal reduction, restorative buildup, or extraction planning -- but does not by itself dictate which treatment approach to use; that decision requires the clinician's judgment alongside cephalometric and facial evaluation.
Are Bolton analysis and Arch Length Discrepancy the same measurement?
No -- they are independent analyses that this calculator reports side by side. Bolton analysis (Overall Ratio and Anterior Ratio) compares mandibular and maxillary tooth widths to each other to detect tooth-size mismatches between arches, while Arch Length Discrepancy compares total tooth width against available arch perimeter within a single arch to detect crowding or spacing, and neither set of inputs affects the other's calculation.
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