Ponderal Index Calculator (Corpulence Index)

Background.

The ponderal index — also called the corpulence index or Rohrer's index — is weight divided by height cubed, in kilograms per cubic metre. BMI divides by height squared; this divides by height three times. Enter a weight and a height and the calculator returns the ponderal index, BMI beside it for comparison, the reciprocal convention that confusingly shares the same name, and the g/cm³ form used for newborns. Read the result as a weight-for-height index, not a body-fat measurement and not a diagnosis.

The reason to cube rather than square is geometric, and it is genuinely compelling at first glance. If you take a person and scale them up uniformly — every dimension multiplied by the same factor — their mass grows with the cube of the scaling factor while their height grows with the first power. So mass divided by height cubed should be exactly unchanged, while mass divided by height squared should grow. The calculator's own numbers show this precisely: scale an 82 kg, 175 cm person by 0.9 and by 1.1, and their ponderal index stays at exactly 15.3003 in both cases, while their BMI moves from 24.10 to 29.45. On the geometry, the ponderal index wins outright.

On the data it loses, and this page is not going to pretend otherwise. In 1972 Ancel Keys and colleagues compared weight-for-height indices in twelve groups of men — 7,425 in total, aged 18 to 60, across five countries — against skinfold measures of fatness. It was that paper that coined the name 'body mass index' for weight over height squared and concluded it 'seems preferable' to the alternatives, and Livi's cube-root ponderal index had the lowest correlations with the sum of skinfolds of any index tested. A 2025 mathematical review of the whole family of indices in Obesity Reviews puts the reason plainly: when you fit weight ÷ height^β and look for the exponent that makes the index independent of height in adult populations, the answer approaches zero correlation when β is 'slightly larger than 2.0'. Cubing overcorrects. Real adults are not scaled copies of one another — taller people are proportionally leaner and less dense than isometric scaling predicts — so an index built on perfect geometric similarity fights the data.

There is a real counter-argument and it deserves to be here too. Robert Burton, writing in the Annals of Human Biology in 2007 under the title 'Why is the body mass index calculated as mass/height², not as mass/height³?', argued that 'in adult populations mass must vary more nearly with height(3) than with height(2)' — while immediately noting that 'conventional statistical techniques suggest otherwise' for reasons he explains, and concluding that 'nevertheless the BMI is a valid predictor of fatness from mass and height in adults'. Both statements are true and the tension between them is the interesting part. BMI's exponent of 2 is not a claim about geometry; it is the value that empirically decorrelates the index from height, which is what Benn's criteria for a good adiposity index require. The ponderal index is what geometry alone would suggest, and geometry alone turns out not to be enough.

One warning matters more than any of this. There are two different indices called the ponderal index and they run in opposite directions. The one this page leads with is Rohrer's corpulence index, weight ÷ height³, where a higher number means stockier. The other is Livi's, height ÷ the cube root of weight, where a higher number means more linear and slimmer. Our worked example returns 15.30 on the first and 40.28 on the second — for the same person. Both are printed here, both are labelled, and you should never compare one with the other. If you have a number from another source and you do not know which convention it uses, check whether it is near 15 or near 40 before you interpret it.

Where the index is still genuinely used is neonatology. Rohrer's index computed as birth weight in grams times 100 divided by length in centimetres cubed distinguishes newborns whose growth restriction is symmetric — small all over — from those who are asymmetrically thin for their length, which points at different underlying causes. That neonatal figure is exactly one tenth of the adult kilograms-per-cubic-metre value, and the calculator prints it. It does not interpret it: doing so needs birthweight-percentile reference tables we could not source, and newborn assessment is not something to do from a web page. For the same reason no 'normal range' is shown for adults either. The band of 11 to 15 that circulates widely could not be traced to any primary publication, so it is not displayed here.

What is ponderal index calculator?

The ponderal index is a weight-for-height index defined as body mass divided by the cube of height, conventionally expressed in kilograms per cubic metre. It is also known as the corpulence index and as Rohrer's index, after Fritz Rohrer, who proposed it in the early twentieth century; a 2025 review in Obesity Reviews lists it as 'Rohrer (1908, 100×W/H³, Corpulence or Rohrer Index)', while it is more commonly cited to his 1921 paper in the Münchner Medizinische Wochenschrift. Confusingly, the name 'ponderal index' is also attached to a different quantity — Rodolfo Livi's L'indice ponderale of 1897, given as 100 × W^(1/3)/H, which is usually inverted in practice to height divided by the cube root of weight. The two run in opposite directions and must never be compared. Both belong to the family Reginald Benn formalised as W/H^β, of which BMI is the special case β = 2 and the ponderal index the case β = 3. Benn's argument was that a good adiposity index must be independent of height and well correlated with actual fatness, and in adult populations the exponent that achieves the first of those is close to 2, not 3. That is why BMI displaced the ponderal index in the epidemiological literature after Keys and colleagues' 1972 comparison. The ponderal index retains one property BMI lacks — exact invariance under isometric scaling — and one enduring practical use, in assessing whether a newborn is proportionately or disproportionately small for its length.

How to use this calculator.

1. 01Enter a weight and pick kilograms or pounds.
2. 02Enter a height and pick centimetres or inches. Height is cubed in this index, so measure it carefully: a 1 % error in height moves the result by about 3 %.
3. 03Read the ponderal index in kg/m³. There is no published normal band on this page, deliberately — the 11-to-15 range you may have seen elsewhere has no primary source we could find.
4. 04Compare it with the BMI tile. The ponderal index is exactly BMI divided by your height in metres, so if the two disagree about you it is telling you something about your height, not about your fat.
5. 05Check which convention any number from elsewhere uses before comparing. Roughly 15 means the Rohrer form on this page; roughly 40 means the reciprocal Livi form, which is also printed here.
6. 06For a newborn, use the neonatal Rohrer tile, which is the same value expressed as grams per cubic centimetre times 100. This calculator will not interpret it for you — take it to a clinician.

The formula.

The ponderal index is PI = weight in kilograms ÷ (height in metres)³, giving kg/m³. The reciprocal or Livi convention is RPI = height in centimetres ÷ the cube root of weight in kilograms, giving cm·kg^(−1/3); it is a different quantity on a different scale running in the opposite direction, and the two must never be compared. The neonatal convention, birth weight in grams × 100 ÷ (length in centimetres)³, is exactly one tenth of the kg/m³ value — that is an identity, not an approximation, since (1000·W)·100 ÷ (100·H)³ = 0.1 · W/H³. There is also an exact relationship to BMI: because BMI = W/H² and PI = W/H³, we have PI ≡ BMI ÷ H, with H in metres. Working the shipped example: 82 kg at 175 cm gives H = 1.75 m and H³ = 5.359375 m³ exactly, so PI = 82 ÷ 5.359375 = 15.3002915452 kg/m³. BMI is 82 ÷ 3.0625 = 26.7755102041 kg/m², and 26.7755102041 ÷ 1.75 = 15.3002915452, confirming the identity. The cube root of 82 is 4.3444814858, so RPI = 175 ÷ 4.3444814858 = 40.2809864821 cm·kg^(−1/3), and the neonatal form is 1.5300291545. TWO DIRECTIONAL FACTS, checked against the equation rather than assumed: heavier at a fixed height RAISES the ponderal index linearly, and taller at a fixed weight LOWERS it with the cube — going from 160 cm to 200 cm at the same weight divides the index by 1.25³ = 1.953125, almost in half. The reciprocal index moves the other way in both cases. SCALING PROPERTY, which is the index's whole point: scale a body isometrically, so weight multiplies by k³ while height multiplies by k, and the ponderal index is exactly unchanged while BMI multiplies by k. At k = 0.9 and k = 1.1 our example returns a ponderal index of 15.3002915452 in all three cases while BMI runs 24.0979591837, 26.7755102041 and 29.4530612245. ROUNDING STAGE: everything, including the cube root, is carried at full decimal precision and rounded once at the end. DOMAIN: weight and height must be positive; there are no other guards, and the index has no singularity anywhere in that domain.

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 for this build. 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 ONLY — 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.