Kaup Index & Rohrer Index Calculator (Child Growth Check)
Enter your child's age, height, and weight to calculate the Kaup Index (infants) or Rohrer Index (school-age children) automatically, matched against age-specific standards from underweight to overweight.
Kaup Index Standards by Age
Kaup Index (3 months to 5 years) = weight (g) ÷ height (cm)² × 10. Because infants' typical proportions change quickly as they grow, the standard range shifts by age band.
| Age | Underweight | Slightly Underweight | Normal | Slightly Overweight | Overweight |
|---|---|---|---|---|---|
| 3 – 11 months | Below 14.5 | 14.5 – 16 | 16 – 18 | 18 – 20 | 20 and above |
| 1 yr 0 mo – 1 yr 5 mo | Below 14.5 | 14.5 – 15.5 | 15.5 – 17.5 | 17.5 – 19.5 | 19.5 and above |
| 1 yr 6 mo – 1 yr 11 mo | Below 14 | 14 – 15 | 15 – 17 | 17 – 19 | 19 and above |
| 2 yr 0 mo – 2 yr 11 mo | Below 13.5 | 13.5 – 15 | 15 – 17 | 17 – 18.5 | 18.5 and above |
| 3 yr 0 mo – 5 yr 11 mo | Below 13 | 13 – 14.5 | 14.5 – 16.5 | 16.5 – 18 | 18 and above |
Rohrer Index Standards
Rohrer Index (roughly ages 6–11) = weight (kg) ÷ height (cm)³ × 10,000,000. Unlike the Kaup Index, a single standard applies regardless of exact age.
| Category | Index Range |
|---|---|
| Underweight | Below 100 |
| Slightly Underweight | 100 – 115 |
| Normal | 115 – 145 |
| Slightly Overweight | 145 – 160 |
| Overweight | 160 and above |
What Are the Kaup Index and Rohrer Index?
The Kaup Index and Rohrer Index are child growth indices calculated from height and weight, similar in spirit to the adult BMI. Unlike BMI, though, infants and school-age children change body proportions dramatically as they grow, so what counts as "normal" shifts across age bands rather than staying fixed.
The Kaup Index is used for infants from about 3 months to 5 years old, while the Rohrer Index is mainly used for school-age children around 6 to 11 years old. This tool automatically picks the right index based on the age you enter and compares the result against the matching age band's standards.
Reference figures used in this calculation
The figures below are not set by law. They are reference values used as a guide, and the actual amounts differ from provider to provider.
- Health and body-composition estimation formulas (BMR, body fat, one-rep max, growth indices and so on) — Estimation formulas from published research (not an official standard) （No unified official dataset exists） Last checked 2026-09-21
How to Use
- Enter the age Enter years and months. The tool covers ages from 3 months to 11 years 11 months.
- Enter the height Enter the height in centimeters (cm), as recorded at a checkup.
- Enter the weight Enter the weight in kilograms (kg).
- Check the result The Kaup Index or Rohrer Index is calculated automatically based on age, along with a category from underweight to overweight.
Tips for getting more out of it
- If you have a checkup record with height, weight, and the exact age at measurement, entering those same figures makes it easy to compare against your checkup results.
- The Kaup Index and Rohrer Index are only statistical guides — body types vary between individuals. Rather than reacting to a single result, it's better to track the trend over time, similar to how a growth chart in a health record book is used.
- The tool automatically switches from the Kaup Index to the Rohrer Index right at the boundary between 5 years 11 months and 6 years 0 months.
- If the result comes back "slightly underweight" or "slightly overweight," remember that individual growth timing varies. Rather than judging on your own, bring it up at the next infant or school health checkup if you're concerned.
When this is useful
Going back over a check-up result at home
**The thresholds themselves shift with age band**, so this guards against reading this year's figure by last year's standard.
Looking at weight after a growth spurt
The index tends to dip just after a child grows taller; reading it as a trend rather than a single point avoids alarm.
Reinterpreting around the start of school
**The index in use changes entirely — Kaup in infancy, Rohrer in the school years.**
Comparing siblings
At different ages the same number means different things; checking which index applies comes before any comparison.
Glossary
- Kaup Index
- A growth index used for infants from about 3 months to 5 years old. It is calculated as weight (g) divided by height (cm) squared, multiplied by 10. The formula resembles adult BMI, but the "normal" range shifts depending on the child's age in months.
- Rohrer Index
- A growth index mainly used for school-age children around 6 to 11 years old. It is calculated as weight (kg) divided by height (cm) cubed, multiplied by 10,000,000. A single standard (115–145 as normal) is generally applied regardless of exact age.
- School Age (Gakudo-ki)
- A Japanese term referring to elementary school age, roughly 6 to 11 or 12 years old. The Rohrer Index is commonly used as a growth guide during this period.
- BMI
- Body Mass Index, a body composition index for adults calculated as weight (kg) divided by height (m) squared. It is typically used from age 18 onward; the Kaup Index and Rohrer Index are used for infants and school-age children instead.
- Standard Weight
- A statistically derived reference weight for a given height, age, and sex. The Kaup Index and Rohrer Index indirectly express how a child's actual weight compares to this reference.
FAQ
Side Note — The History of Measuring Growth With a Single Number
The Kaup Index is generally credited to the German pediatrician Carl Kaup in the early 20th century. Its formula — weight divided by height squared — is the same shape as today's Body Mass Index (BMI), but the Kaup Index accounts for the rapid changes in infant body proportions by setting different standard values for each age band. A newborn typically has a rounder body shape relative to its weight, and as the child begins to walk, muscle develops and the balance of the body gradually shifts.
The Rohrer Index is named after the Swiss anatomist Eugen Rohrer, and is calculated by dividing weight by height cubed rather than squared. Using the cube of height — which scales roughly with volume — reflects an attempt to capture a more "three-dimensional" sense of body fullness relative to size. In Japan, it has long been used in school health programs to assess the physiques of schoolchildren.
Internationally, organizations such as the World Health Organization (WHO) and the U.S. Centers for Disease Control and Prevention (CDC) tend to favor growth charts that show a child's percentile position within a reference population, rather than a single fixed index. The growth curves found in Japan's maternal and child health handbooks reflect this same percentile-based thinking. Single-number indices like the Kaup and Rohrer Indices offer quick, simple guidance, while percentile charts show where a child stands relative to peers of the same age — each has its place in tracking how children grow.