Ponderal Index Calculator (Corpulence Index)

Background.

Why does BMI divide weight by height squared when a body has three dimensions? The ponderal index is what you get if you take that objection at face value: weight in kilograms divided by height in metres cubed, in kilograms per cubic metre. It also goes by the corpulence index and Rohrer's index, after Fritz Rohrer, who proposed it early in the twentieth century.

The case for the cube is geometric. Enlarge a body evenly, every length multiplied by the same factor, and its mass grows with the cube of that factor while its height grows in proportion. Weight over height cubed stays exactly the same; BMI rises with the scale. An 82 kg, 175 cm adult and copies of them shrunk to 90% or enlarged to 110% of every dimension share a ponderal index of 15.3003, while their BMIs run from about 24.1 to 29.5.

The case against it is empirical. Adults are not scaled copies of one another, and when researchers look for the power of height that makes a weight-for-height index independent of height in real populations, the answer comes out slightly above 2, not 3. Keys and colleagues' 1972 comparison of 7,425 men in twelve groups, the study that gave the body mass index its name, judged weight over height squared preferable, and Livi's cube-root ponderal index correlated worst of all the indices with skinfold measures of fat. BMI became the standard; the cube-based index survives mainly in the assessment of newborns.

Enter weight and height and you get the index in kg/m³ with BMI next to it, the reciprocal form quoted as height over the cube root of weight, and the grams-per-cubic-centimetre version used for babies. No normal range is shown, because the 11 to 15 band that circulates online could not be traced to any primary publication.

What is ponderal index calculator?

The ponderal index, PI = W ÷ H³, is a weight-for-height ratio in kilograms per cubic metre. It sits in the family of indices W ÷ H^β described by Benn, where β = 2 gives BMI and β = 3 gives this one; Benn's test of a good index was that it should not depend on height and should track body fat. A 2025 review dates Rohrer's index to 1908, though it is usually cited to his 1921 paper. The name is shared with an older quantity: Rodolfo Livi's indice ponderale of 1897 used the cube root of weight over height, and is often quoted upside down as height in centimetres divided by the cube root of weight in kilograms, the reciprocal ponderal index. Both forms are fixed functions of W ÷ H³ and carry the same information, but they sit on different scales and the reciprocal runs the opposite way, with higher values meaning a slimmer build.

How to use this calculator.

1. 01Enter body weight and choose kilograms or pounds; 1 lb is exactly 0.45359237 kg.
2. 02Enter height and choose centimetres or inches. Measure it carefully, without shoes: height is cubed, so a 1% error moves the index by about 3%, and 2 cm on a 175 cm adult shifts it by roughly half a unit.
3. 03Read the ponderal index in kg/m³ against the BMI shown with it. The index always equals BMI divided by height in metres, so where the two disagree between people, height is the reason.
4. 04If you are comparing with a figure from elsewhere, check its size first: adult values of the W ÷ H³ form sit in the teens, while the reciprocal form for the same person is around 40.
5. 05For a newborn, enter the weight in kilograms (3.2 for 3,200 g) and the length in centimetres, then read the neonatal Rohrer value. Interpreting it needs growth charts and a clinician.

The formula.

PI = W ÷ H³, with W in kilograms and H in metres. Because BMI = W ÷ H², the index is exactly BMI ÷ H. The reciprocal form is RPI = H(cm) ÷ ∛W, which works out to 100 ÷ ∛PI, so either can be converted into the other. The newborn convention, birth weight in grams × 100 ÷ (length in centimetres)³, equals PI ÷ 10 exactly, since (1,000 W × 100) ÷ (100 H)³ = 0.1 × W ÷ H³.

Weight enters in proportion and height as a cube. At a fixed weight, growing from 160 cm to 200 cm divides the index by 1.25³ = 1.953125, nearly halving it. Under isometric scaling, with weight multiplied by k³ and height by k, the index does not move at all while BMI is multiplied by k.

The trouble appears in population data. The 2025 review in Obesity Reviews reports that the power of height which leaves a weight-for-height index uncorrelated with height in adults is slightly larger than 2, so dividing by H³ overcorrects and the index tends to read low in tall people for reasons unrelated to fat. Robert Burton argued in 2007 that adult mass should in principle scale more nearly with height³, while noting that conventional statistics point the other way, that the exponent Benn's method gives for adult populations is typically 1.1 to 2.5, and that BMI remains a valid predictor of fatness. No ratio of weight and height alone can tell muscle from fat.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Heymsfield SB, Sorkin JD, Thomas DM, et al. "Weight/height²: Mathematical overview of the world's most widely used adiposity index." Obesity Reviews. 2025;26(1):e13842. PMC11611441. Open access and read directly. Source of the definitions quoted here — "Rohrer (1908, 100×W/H³, Corpulence or Rohrer Index)" and Livi's "L'indice ponderale, 100×W^(1/3)/H, in 1897" — of Benn's criteria and the W/H^β family, of the finding that the height-independent exponent in adults is "slightly larger than 2.0", and of the summary of Keys' 1972 results (12 groups, n = 7,425, ages 18–60; W/H² "seems preferable"; Livi's ponderal index had the lowest correlations with the sum of skinfolds).
2. [2]Burton RF. "Why is the body mass index calculated as mass/height², not as mass/height³?" Ann Hum Biol. 2007 Nov–Dec;34(6):656–663. PMID 18092209. The counter-argument quoted on this page, verbatim from the abstract: BMI "is an approximation to the Benn index, mass/height(p), where p (typically 1.1-2.5 for adult populations)"; "in adult populations mass must vary more nearly with height(3) than with height(2), although, for reasons explained, conventional statistical techniques suggest otherwise"; "nevertheless the BMI is a valid predictor of fatness from mass and height in adults". Abstract open access; full text paywalled.
3. [3]Keys A, Fidanza F, Karvonen MJ, Kimura N, Taylor HL. "Indices of relative weight and obesity." J Chronic Dis. 1972;25(6–7):329–343. PMID 4650929. The study that named the body mass index and rejected the ponderal index. Note on provenance: PubMed carries no abstract for this record and the full text is paywalled, so its findings are quoted on this page via the Heymsfield 2025 review above rather than from the paper itself.
4. [4]Rohrer F. "Der Index der Körperfülle als Maß des Ernährungszustandes." Münchner Medizinische Wochenschrift. 1921;68:580–582. Bibliographic origin of the corpulence index. (PRINT) — this 1921 German weekly is not available online. Date conflict disclosed: the Heymsfield 2025 review dates Rohrer's index to 1908; nothing on this page depends on which is right.
5. [5]National Institute of Standards and Technology — "Guide for the Use of the International System of Units (SI)," NIST Special Publication 811, 2008 edition, Appendix B.9. Source of the exact conversions 1 lb = 0.45359237 kg and 1 in = 2.54 cm.