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Instrument MI-04-078 · Health

BMI Calculator for Kids

Enter a young child's sex, age, height, and weight to compute BMI and see where it falls on the CDC BMI-for-age curve — scoped to the ages where a child's healthy BMI is naturally at its lowest.

Instrument MI-04-078
Sheet 1 OF 1
Rev A
Verified
Type 04 — Pediatrics SER. 2026-04078

BMI percentile

65.9

L (male reference table, nearest age)

16.46 Body mass index (kg/m2)
-3.183100 LMS L (skewness), reference table
15.7820 Reference median BMI at this age & sex (kg/m2)
0.102100 LMS S (coefficient of variation), reference table
0.386 Z-score vs. the reference population
The working Every figure verified twice
  1. lm = if(96 < 36.25, −2.0112, if(96 < 60.5, −1.7149, if(96 < 84.5, −3.2117, if(96 < 108.5, −3.1831, if(96 < 132.5, −2.7656, if(96 < 156.5, −2.4474, if(96 < 180.5, −2.2274, if(96 < 204.5, −2.039, if(96 < 228.25, −1.8747, −1.8423))))))))) = -3.1831
  2. lf = if(96 < 36.25, −0.9866, if(96 < 60.5, −3.0185, if(96 < 84.5, −3.2256, if(96 < 108.5, −2.6172, if(96 < 132.5, −2.1713, if(96 < 156.5, −1.9755, if(96 < 180.5, −1.9771, if(96 < 204.5, −2.1192, if(96 < 228.25, −2.3037, −2.345))))))))) = -2.6172
  3. mm = if(96 < 36.25, 16.575, if(96 < 60.5, 15.628, if(96 < 84.5, 15.384, if(96 < 108.5, 15.782, if(96 < 132.5, 16.646, if(96 < 156.5, 17.815, if(96 < 180.5, 19.158, if(96 < 204.5, 20.558, if(96 < 228.25, 21.896, 23.02))))))))) = 15.782
  4. mf = if(96 < 36.25, 16.423, if(96 < 60.5, 15.299, if(96 < 84.5, 15.217, if(96 < 108.5, 15.827, if(96 < 132.5, 16.862, if(96 < 156.5, 18.101, if(96 < 180.5, 19.353, if(96 < 204.5, 20.453, if(96 < 228.25, 21.275, 21.717))))))))) = 15.827
  5. sm = if(96 < 36.25, 0.0806, if(96 < 60.5, 0.0719, if(96 < 84.5, 0.083, if(96 < 108.5, 0.1021, if(96 < 132.5, 0.1201, if(96 < 156.5, 0.1314, if(96 < 180.5, 0.1353, if(96 < 204.5, 0.1342, if(96 < 228.25, 0.1323, 0.1345))))))))) = 0.1021
  6. sf = if(96 < 36.25, 0.0855, if(96 < 60.5, 0.0787, if(96 < 84.5, 0.0938, if(96 < 108.5, 0.1172, if(96 < 132.5, 0.1371, if(96 < 156.5, 0.1484, if(96 < 180.5, 0.1513, if(96 < 204.5, 0.1491, if(96 < 228.25, 0.1473, 0.153))))))))) = 0.1172
  7. bmi = 30 ⁄ pow(135 ⁄ 100, 2) = 16.46
  8. Lp = if(1 = 1, -3.1831, -2.6172) = -3.183100
  9. Mp = if(1 = 1, 15.782, 15.827) = 15.7820
  10. Sp = if(1 = 1, 0.1021, 0.1172) = 0.102100
  11. z = if(-3.1831 = 0, ln(16.460905 ⁄ 15.782) ⁄ 0.1021, (pow(16.460905 ⁄ 15.782, -3.1831) − 1) ⁄ (-3.1831·0.1021)) = 0.386
  12. pctile = 100 ⁄ (1 + exp(0 − 1.702·0.386062)) = 65.9
Worksheet log
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How this instrument works

Body mass index (BMI) alone doesn't mean much for a growing child — it has to be read against other children of the same sex and age, because typical BMI actually dips through early-to-mid childhood before rising again toward adolescence (a pattern called adiposity rebound). That's why pediatric BMI is reported as a percentile, and why this calculator is scoped to ages 2 through roughly 12, the range where that early dip and gradual climb happen.

This calculator first computes BMI from the entered height and weight, then uses the CDC 2000 BMI-for-age growth chart, built with the LMS method (Cole 1990): at each reference age, three parameters — L (skewness), M (median), S (spread) — describe the BMI distribution for that sex and age. The result is converted to a z-score against those parameters, then to a percentile using a logistic approximation to the normal curve, the same approximation already used by this site's IQ percentile calculator.

Two limits worth stating plainly. First, this calculator's reference table holds 10 representative ages spanning the full CDC 2-20 year range (this page defaults and scopes input to roughly 2-12 years) rather than the CDC file's full month-by-month resolution — it matches the entered age to the nearest table point rather than interpolating. Second, this is a screening tool, not a diagnostic one: CDC itself describes BMI-for-age as a screening measure, not something that diagnoses disease on its own — a result far from the 50th percentile is a prompt to discuss weight and growth with a pediatrician, not a diagnosis by itself.

BMI = weight (kg) / height (m)²
z = ((BMI / M)^L − 1) / (L × S) [or ln(BMI / M) / S if L = 0]
Percentile = 100 / (1 + e^(−1.702 × z))
L, M, S are the CDC 2000 BMI-for-age LMS parameters at the nearest of 10 representative reference ages for the child's sex. The percentile step is the logistic approximation to the normal CDF (same 1.702 constant used by this site's iq-percentile.json), accurate to roughly half a percentile point versus the exact CDC table.
  • Choose Boy or Girl — the reference curves are sex-specific.
  • Enter the child's age in months (roughly 24 to 145, i.e. 2 to 12 years).
  • Enter height in centimeters and weight in kilograms.
  • Read the computed BMI, the BMI percentile, the z-score, and the reference median BMI matched for that age and sex.
  • Discuss a percentile far from 50, or a fast change over time, with a pediatrician rather than acting on it alone.

Worked example — an 8-year-old boy below the reference median

An 8-year-old boy (96.5 months) at 128 cm and 24 kg: BMI = 24 / 1.28² ≈ 14.65. The CDC 2000 reference median BMI for a boy that age is 15.782, so his BMI sits a bit below median — z ≈ −0.82, landing around the 20th percentile, on the leaner side but within a typical range for the reference population at that age.

Compare a 4-year-old girl (48.5 months) at 102 cm and 17 kg: BMI = 17 / 1.02² ≈ 16.34, above the reference median BMI of 15.299 for that age. That gap gives z ≈ 0.76, landing around the 78th percentile — on the higher side for a 4-year-old, a data point worth tracking over subsequent visits rather than judging from a single reading.

Now a 12-year-old boy (144.5 months) at 145 cm and 33 kg: BMI = 33 / 1.45² ≈ 15.70, notably below the reference median BMI of 17.815 for that age. z ≈ −1.13, landing around the 13th percentile — low enough that it's a fair thing to discuss with his pediatrician alongside his height and weight history.

Questions

Why is there a separate BMI calculator just for younger kids?

Typical BMI actually falls through early-to-mid childhood before rising again toward puberty, so a BMI that would be low for a teenager can be perfectly normal for a 5-year-old. This version of the calculator scopes its default age range to roughly 2-12 years, matching this site's general BMI-percentile-child and bmi-teens calculators, which use the identical CDC reference table but default to a wider or older age range.

Is a high or low BMI percentile a diagnosis of overweight or underweight?

No. CDC explicitly describes BMI-for-age as a screening measure, not a diagnostic one — a high or low percentile flags a child whose weight relative to height is unusual for their age and sex, which is a reason for closer clinical evaluation, not a standalone conclusion. A pediatrician weighs the percentile alongside growth trend, family history, diet, activity, and physical exam before drawing any conclusion.

Why does the calculator only use 10 reference ages instead of every month?

The official CDC 2000 BMI-for-age file publishes LMS parameters at fine age resolution, but this calculator hard-codes a representative 10-point subset of those official values and matches the entered age to the nearest one — it does not interpolate between ages or invent any in-between value. Results for an age between two table points reflect the closer reference age, so treat them as approximate.

What do the percentile bands (85th, 95th) actually mean?

In CDC's convention, a BMI-for-age at or above the 85th percentile is classified as overweight and at or above the 95th percentile as obese for that age and sex, while below the 5th percentile is classified as underweight; the range in between is typical. This calculator reports the raw percentile and leaves that classification and its clinical implications to a pediatrician, since the same percentile can mean different things for different children.

How accurate is the percentile number itself?

The percentile is computed with a logistic function as a stand-in for the exact normal cumulative distribution function, which is the same well-documented approximation this site's IQ percentile calculator uses. It differs from the exact table lookup by roughly half a percentile point in most cases — close enough for a screening read, but not a substitute for a clinician's exact chart plot.

Can I use this calculator for a child older than 12?

The underlying reference table and formula cover the full CDC 2-to-20-year range, so entering an older age still computes a valid result, but this page's default and step size are tuned for younger children. For teenagers, this site's bmi-teens calculator offers the same math with inputs and defaults scoped to that age range instead.

References

Read this first: This instrument computes a screening figure from population formulas — it is not a diagnosis, and it cannot see the whole picture a clinician can. Use it to inform a conversation, not to replace one.