Calculate the Corpulence Index (CI) — a height-cubed body-mass index related to the Ponderal Index. Compare CI with BMI for an alternative body-build assessment.
The Corpulence Index (CI) is a body proportionality metric closely related to the Ponderal Index. While the Ponderal Index is defined as mass / height³, some references define the Corpulence Index as height³ / mass (the reciprocal), and others treat it as an identical measure under an alternative name. This calculator computes both interpretations so you can use whichever convention your reference material follows.
Like the Ponderal Index, the Corpulence Index uses the cube of height rather than the square, providing a more height-independent assessment of body build than BMI. This is especially useful when comparing individuals of vastly different statures, from children to very tall adults, and across populations with different average heights.
The term "corpulence" itself dates to Adolphe Quetelet's 19th-century anthropometric work, where he used it to describe body build relative to stature. Today the Corpulence Index appears most frequently in European epidemiological literature and in studies comparing multiple body-mass indices for predictive accuracy in cardiovascular and metabolic disease.
The Corpulence Index offers an alternative perspective on the same data that BMI uses, with a height-cubed denominator instead of height squared. That can be useful when you want to compare how different body-mass formulas behave across shorter and taller people. By computing CI alongside BMI and the Ponderal Index, you can see how different mathematical treatments of the same height and weight data emphasize body build differently.
Corpulence Index (as mass/height³): CI = Mass (kg) / Height (m)³ This is identical to the Ponderal Index in kg/m³. Reciprocal form: CI′ = Height (m)³ / Mass (kg) BMI for comparison: BMI = Mass (kg) / Height (m)² Normal adult CI (mass/height³): approximately 11–15 kg/m³ Normal adult CI′ (height³/mass): approximately 0.067–0.091 m³/kg
Result: CI = 14.2 kg/m³ (Normal)
A person 170 cm (1.70 m) tall weighing 70 kg has CI = 70 / 1.70³ = 70 / 4.913 = 14.2 kg/m³. The reciprocal form is 4.913 / 70 = 0.0702 m³/kg. Their BMI is 70 / 1.70² = 24.2. All three metrics classify this person as normal weight, though the CI value is less familiar to most people than BMI.
The word "corpulence" entered anthropometric literature through 19th-century body-measurement research associated with Adolphe Quetelet and later height-cubed alternatives to the Quetelet index. Depending on the paper or textbook, Corpulence Index may refer either to the same mass/height³ quantity as the Ponderal Index or to its reciprocal. That naming inconsistency is why this page shows both forms explicitly.
The relationship to BMI is direct: because BMI = mass / height² and CI = mass / height³, the height-cubed version is simply BMI divided by height. That changes how the index behaves across shorter and taller statures and is the main reason researchers compare CI-style measures with BMI when studying height-related bias.
Height-cubed indices appear mainly in anthropometry, pediatric growth work, and comparative epidemiology. They are useful when you want to contrast body-build metrics rather than rely on a single screening number. They are not a replacement for body-composition assessment and do not have the same breadth of guideline thresholds that BMI has.
For everyday screening, BMI remains the more familiar reference standard. CI is best used as a secondary comparison tool, especially when looking at proportionality, cross-height comparisons, or historical literature that reports height-cubed indices.
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This calculator converts the entered height and weight to metric units, then computes the mass-over-height-cubed form of the Corpulence Index together with its reciprocal representation. It also shows BMI alongside those values so you can compare how a height-squared and height-cubed index behave for the same person.
Because published definitions are inconsistent, this page deliberately reports both common conventions instead of assuming one naming scheme is universal. The output is a proportionality worksheet, not a stand-alone clinical diagnosis.
The Corpulence Index is a body-mass metric that uses height cubed in its calculation. Depending on the source, it may be defined as mass/height³ (identical to the Ponderal Index) or as height³/mass (the reciprocal). Both forms aim to provide a more height-independent measure of body build than BMI.
When defined as mass/height³, yes — it is numerically identical. Some authors use "Corpulence Index" and "Ponderal Index" interchangeably, while others define the Corpulence Index as the reciprocal (height³/mass). This calculator shows both forms to eliminate ambiguity.
For adults, the normal range in the mass/height³ form is approximately 11–15 kg/m³. In the reciprocal form (height³/mass), normal is approximately 0.067–0.091 m³/kg. These ranges correspond roughly to a BMI of 18.5–24.9.
CI uses height cubed, which more closely follows how body volume scales with height. BMI's height-squared denominator can introduce height-related bias in some populations, especially at the extremes of stature. CI may reduce some of that bias, although outcome thresholds for BMI remain much better established.
The Corpulence Index appears primarily in European epidemiological research and comparative anthropometric studies. It is less commonly used in routine clinical practice than BMI, but it shows up in academic papers evaluating which body-mass metric best predicts cardiovascular or metabolic outcomes.
Some studies have found that height-cubed indices correlate similarly to BMI with cardiovascular risk factors, and may be slightly better predictors in height-diverse populations. However, BMI has far more outcome data supporting its clinical thresholds, which is why it remains the default screening tool in most guidelines.
Yes — height-cubed indices are sometimes considered more theoretically appropriate for children, whose body proportions change rapidly during growth. The Rohrer Index (a scaled version of CI) has been used in some pediatric screening programs. Age- and sex-specific reference values should still be used for children.
CI (kg/m³) = BMI / Height(m). So for a person 1.75 m tall with a BMI of 24, CI = 24 / 1.75 = 13.7 kg/m³. Conversely, BMI = CI × Height(m). This simple relationship shows that BMI and CI differ only by a factor of height.