Ponderal Index, Rohrer & Kaup Index Calculator

Understanding the ponderal index calculator — concept and principle

The ponderal index (also called the corpulence index) relates weight to the cube of height instead of the square used by BMI. The same idea appears under two other names: the Rohrer index, used in school health checks in Korea and Japan, and the Kaup index, which is simply BMI applied to infants and toddlers. They help compare build in children and in adults who are much taller or shorter than average.

Same person, three indices: squared height gives 24.49, cubed height 13.99, and Rohrer is simply ten times that.

How it is calculated

With weight W in kg and height H in cm:

Ponderal index = W ÷ (H/100)³, in kg/m³
Rohrer index = W ÷ H³ × 10⁷, with H in cm
Kaup index = W ÷ (H/100)², in kg/m², the same number as BMI

Because 1 m³ = 10⁶ cm³, the Rohrer index is always exactly 10 times the ponderal index. Only the scaling factor differs.

The principle

Weight is roughly proportional to volume, and volume of a similarly shaped body grows with height³. Dividing by height³ therefore removes the effect of size more completely than dividing by height². BMI is known to rate taller people as relatively heavier and shorter people as relatively lighter, even at the same build. The ponderal index corrects that: at the same BMI of 22, a 150 cm person has a ponderal index of about 14.7 and a 190 cm person about 11.6. In infants, however, body proportions change so fast that the squared form (Kaup) is the traditional choice, while the cubed form (Rohrer) is used once children are of school age.

Worked example

Inputs: weight 75 kg, height 175 cm (1.75 m).
Ponderal index: 1.75³ = 5.359; 75 ÷ 5.359 = 13.99 kg/m³.
Rohrer index: 175³ = 5,359,375; 75 ÷ 5,359,375 × 10⁷ = 139.94.
Kaup index: 1.75² = 3.0625; 75 ÷ 3.0625 = 24.49 (equal to BMI).

Each point is the calculator re-run with only “Height (cm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Height (cm)	Ponderal index (kg/m³)
43.8	895.63
87.5	111.95
131	33.17
175	13.99
219	7.17
262	4.15
350	1.75

How to read the result

Higher values mean more weight per unit of body size. For school-age children this page uses a Rohrer range of about 115–145 as a rough normal band; the exact cut-offs vary between countries and textbooks. For infants and young children, Kaup values must be read against age-specific references, and for adults most clinical guidelines still use BMI. A handy link: ponderal index = BMI ÷ height in metres.

Common mistakes

Entering height in metres for the Rohrer formula, which expects centimetres.
Comparing a Rohrer value with a ponderal value without the factor of 10.
Applying adult BMI categories to the Kaup index of a toddler.

Keep in mind: These indices describe build, not health. A child's growth should be judged on growth charts by a paediatrician, and none of these numbers is a diagnosis.

Frequently asked questions

Is the ponderal index better than BMI for tall people?

It reduces the height bias, but there are few agreed adult cut-offs, so it works best for comparisons rather than classification.

What is the ponderal index of a newborn?

Neonatal units often use weight in grams ÷ length in cm³ × 100 to spot growth restriction; check the reference chart your hospital uses.

Why is the Kaup index identical to BMI?

It is the same formula, weight ÷ height²; the name Kaup is simply used in infant health.

Sources: Rohrer F. Der Index der Körperfülle als Maß des Ernährungszustandes. Münchener Medizinische Wochenschrift 1921 · World Health Organization. Physical status: the use and interpretation of anthropometry. Technical Report Series 854, 1995

Checked 8 Nov 2026. Published formulas cited on the page. For information only — not medical advice.

Your numbers