Growth Percentiles: What a Child's Centile Really Means

A centile is a rank, not a score

The sentence a centile makes is narrow and entirely descriptive: among the children in the reference population, of the same age and the same sex, this proportion measured at or below your child. The 90th centile means 90% were at or below. The 30th means 30% were. There is no direction of travel implied, no target, and no better or worse end. Half of all healthy children are below the median by construction, and a chart on which nobody sat below the 50th centile would simply be a broken chart.

Two habits of reading make the number say more than it can. The first is treating it as a grade, where higher is achievement and lower is failure — a reading the charts explicitly do not support, since both tails are equally unusual and neither is a mark of quality. The second is treating one reading as a state of affairs. A centile computed from a single visit combines a real measurement with the error in that measurement, and the error is not small. On our worked example, a quarter of an inch of height either way moves the result by more than a centile point in each direction; half an inch moves it from about the 87th to about the 92nd. Nothing about the child changed.

How a measurement becomes a centile: L, M and S

Growth data are not symmetric. At any given age, children stretch further above the median than below it, so you cannot simply subtract the mean and divide by the standard deviation. The LMS method, set out by Cole and Green in Statistics in Medicine in 1992, handles that by storing three smoothed numbers for every age and sex. M is the median. S is the coefficient of variation, the spread expressed as a fraction of the median. L is a Box-Cox power that says how much skew has to be removed before the distribution becomes normal — and when L is negative, as it is for BMI throughout childhood, it is encoding a long right tail.

With those three in hand, the conversion is one line: z = ((X/M)^L − 1) / (L·S) when L is not zero, and z = ln(X/M) / S in the special case where it is. The z-score is a distance from the median expressed in standard deviations of the transformed distribution, and the centile is just that z read off the normal curve — z = 0 is the 50th, z = 1 the 84th, z = 1.645 the 95th, z = 2 the 98th. Everything after the LMS step is ordinary statistics. The chart-specific knowledge lives entirely in those three numbers, which is exactly why swapping charts swaps the answer.

One boy, worked end to end

Take a boy who has just turned 8, measuring 4 feet 2 inches and weighing 65 pounds. His BMI is 703 × 65.0 ÷ 50.4² = 18.0 kg/m² — the clinical unit is metric everywhere, including in the United States. Now open the WHO 2007 reference for BMI-for-age, boys, and read the row for month 96: L = −1.4629, M = 15.7368, S = 0.09526. Substitute. X/M = 18.0 ÷ 15.7368 = 1.143816. Raise that to the power L: 1.143816^(−1.4629) = 0.821544. Subtract one: −0.178456. Divide by L·S = −1.4629 × 0.09526 = −0.139356. The result is z = 1.2806, and the area of the normal curve below 1.2806 is 0.8998 — the 90th centile.

It is worth checking that the machinery reproduces the published tables rather than approximating them. Run the LMS formula backwards at the same age — X = M(1 + L·S·z)^(1/L) — and it returns 13.302 at z = −2, 15.737 at the median, 17.437 at z = +1, 19.675 at z = +2 and 22.785 at z = +3. Those are exactly the values WHO prints in its own standard-deviation columns for month 96. The same check against the CDC file reproduces its published 85th and 95th percentiles at 17.96 and 20.07. The arithmetic is not an approximation of the chart; it is the chart.

Two charts, two answers for the same child

Now read the identical measurement on the CDC 2000 chart. Its BMI-for-age file for boys gives, for the age band that begins the day a boy turns 8, L = −3.18305795, M = 15.78231007, S = 0.102091189. The medians barely differ — 15.78 against WHO's 15.74 — but L and S do, and that is enough. X/M = 1.140517, raised to L gives 0.658023, minus one is −0.341977, divided by L·S = −0.324962 gives z = 1.0524, which is the 85th centile. The same boy, measured once, is on the 90th centile on one chart and the 85th on the other.

The gap widens as you move up the distribution, because the two charts disagree most about the upper tail. At this age the WHO 85th centile sits at a BMI of 17.51 and the CDC's at 17.96; the 95th sits at 18.80 against 20.07; the 97th at 19.37 against 21.24. For a child of 4 feet 2 inches, the 95th centile is 68 pounds on the WHO chart and 73 pounds on the CDC one — five pounds of daylight between two official answers to the same question. A boy at a BMI of 20.0 is above the 98th centile on the WHO reference and below the 95th on the CDC one. Neither chart is wrong. They were built to answer different questions.

Standard or reference: should, or did

The distinction is doing all the work, and it is usually skipped. A standard is prescriptive: it describes how children ought to grow under conditions taken to be good. The WHO charts were built that way — the reference infants were breastfed by design, all of them for twelve months and predominantly so for at least four, and the sample was drawn across continents under conditions chosen to support healthy growth. A reference is descriptive: it records how the children of a particular country, in a particular period, actually did grow. The CDC 2000 charts are built from United States national survey data, and they describe an American population as it was, including the part of the distribution that had already begun to shift upwards.

That is why the CDC's upper centiles sit higher than the WHO's, and why the difference is small at the median and large in the tail. It is also why the CDC has since revisited its own upper tail: in December 2022 it published extended BMI-for-age charts that reach a BMI of 60 and add curves at the 98th, 99th, 99.9th and 99.99th percentiles, built on a reference that includes children with obesity measured between 1999 and 2016. The CDC's own recommendation, set out in MMWR in 2010, is to use the WHO standard for children under 24 months in the United States and the CDC charts from 2 to 19 years — an explicit acknowledgement that the two instruments are for different jobs.

Which chart your country actually uses

Because there is no single chart, a centile only means something once you know which one produced it. Portugal's Direção-Geral da Saúde adopted the WHO curves in its Programa Nacional de Saúde Infantil e Juvenil. The United Kingdom uses the RCPCH UK-WHO charts, which run the WHO standard from two weeks to four years and continue on the UK90 national reference thereafter. France replaced the curves in the carnet de santé in April 2018 with new national references built by the AFPA and CRESS-Inserm from around five million measurements on 261,000 children. Germany's Arbeitsgemeinschaft Adipositas im Kindes- und Jugendalter recommends the Kromeyer-Hauschild reference published in 2001, drawn from roughly 17,000 boys and 17,000 girls across seventeen German studies and updated for the 15-to-18 range in 2015. Italy has the SIEDP charts of Cacciari and colleagues, based on some 70,000 children measured between 1994 and 2004.

The practical rule follows directly. Whatever tool you use, including this one, note which chart it applied before you compare its output to anything — a number in a health record, a figure a relative remembers, a centile from an app that defaults to a different reference. Comparing centiles computed on different charts is like comparing two prices without checking the currency, and the difference is not always small.

Trajectory is the signal; one reading is not

Growth is read as a line, not a dot. The expected pattern is tracking: a child stays roughly parallel to a centile over months and years, and where that line sits is largely a family characteristic rather than a verdict. The RCPCH guidance behind the UK-WHO charts puts it plainly — weight is most likely to track within one centile space, the gap between two adjacent printed centile lines, and babies do not all grow at the same rate, especially in the first year. Wobble is normal. What is watched for is a sustained departure from the child's own line.

The threshold that matters is crossing, in either direction. RCPCH describes a sustained drop through two or more centile spaces as unusual — fewer than 2% of infants — and something that requires assessment, and lists crossing two or more spaces, along with measurements below the 0.4th or above the 99.6th centile, among the reasons to consider referral. Two points to keep hold of: the concern runs both ways, upwards as well as downwards, and it is the movement that carries the information, not the height of the line it started on. A child tracking steadily along the 9th centile is doing something ordinary; a child who moves from the 75th to the 25th over a year is telling you something, whatever their absolute number.

This is also the reason a calculator cannot do the clinical part. It can compute one point accurately, and that is genuinely useful — it saves you reading a line off a chart by eye. It cannot see the previous six points, it does not know the child's family, their history, their puberty stage or how they were measured, and it does not know that BMI is a proxy for body composition rather than a measurement of it. Take the number to the person who has the rest.

Frequently asked questions

Is a high centile a bad result?

A centile is a rank, not a grade. It says what proportion of the reference population measured at or below your child, and nothing about whether that is good or bad. Half of all healthy children are below the median by definition, and both extremes are equally uncommon. Only a clinician looking at the whole picture, including several measurements over time, can say whether a value means anything.

Why does this calculator give a different centile from my child's health record?

Almost always because the two used different charts. Our worked example gives the 90th centile on the WHO 2007 reference and the 85th on the CDC 2000 chart for the same boy on the same day, and national references differ again. Check which reference each one applied before treating the difference as an error — and if it still looks wrong, the health record and the clinician who keeps it are the authority, not a web page.

My child moved from the 50th centile to the 25th. Should I worry?

Take it to your clinician rather than deciding here. What they look at is whether the change is sustained and how far it goes: RCPCH guidance describes weight as most likely to track within one centile space, and a sustained drop through two or more spaces as unusual — fewer than 2% of infants — and warranting assessment. A single measurement can move by several centiles on measurement error alone, which is exactly why one reading is not a trend.

What is a z-score, and why do clinicians use it instead of a centile?

A z-score is the same information on a different scale: how many standard deviations the measurement sits from the median, computed as ((X/M)^L − 1) / (L·S). Centiles bunch up at the extremes — the difference between the 99th and the 99.9th is large in z but small in centiles — so z-scores stay readable out in the tails and can be averaged and compared arithmetically. Both are computed from the same L, M and S.

Can I compare my two children's centiles?

Only if both were computed on the same chart, and even then the comparison says little. Centiles are already adjusted for age and sex, so a boy on the 40th and a girl on the 60th are each ranked within their own reference group — the numbers are not a contest between them. Siblings routinely sit on different centiles for entirely ordinary reasons, and each child's own trajectory is the thing worth following.

Does a small measuring error really change the centile?

More than people expect, because BMI divides by height squared. On our 8-year-old at a BMI of 18.0, measuring him half an inch shorter or taller moves the result from roughly the 92nd centile to roughly the 87th. Half a kilo of weight does something similar. Measure without shoes, at the same time of day, on the same scale — and treat any single point as approximate.