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What a growth percentile actually means

The number is a position, not a score

Almost every parent meets percentiles the same way: someone reads a number off a chart at a checkup, and the number sounds like a mark out of a hundred. It is not one. A percentile is a rank position inside a reference group, and the reference group is a specific, published set of children, not the children in your town or your family.

If a 9 month old girl weighs on the 30th percentile, the statement being made is: line up 100 girls of exactly that age from the reference population, sorted lightest to heaviest, and she stands about 30th from the light end. Around 30 weigh less than she does, and around 70 weigh more. That is the entire claim. It contains no judgement about whether she is thriving, no comparison to her siblings, and no target.

The 50th percentile gets mistaken for a goal more than any other number, because “average” sounds like where a child ought to be. It is only the middle of the line. Half of a perfectly healthy reference population sits below it by definition, and it would be a strange world if they did not.

Where the line of 100 children comes from

The chart is not a tally of real children re-counted each year. Both the World Health Organization and the US Centers for Disease Control and Prevention took large measurement studies, fitted smooth mathematical curves through them, and published the curves as parameters. Everything a growth chart shows is those curves being evaluated.

Each published curve is stored as three numbers at each age, known as the LMS parameters:

• M is the median, the value at the 50th percentile at that age.
• S is the coefficient of variation, roughly how spread out the population is around the median at that age.
• L is a power that accounts for skew, because measurements like weight are not symmetric around the middle: there is more room to be heavy than to be light.

Those three numbers per age are all the data a growth chart needs. Everything else is arithmetic.

From a measurement to a percentile, in two steps

The arithmetic runs in two steps, and both are worth seeing once, because seeing them takes some of the mystique out of the number.

Step one turns the measurement into a z-score. A z-score says how many standard deviations from the median a value sits, after the skew has been accounted for:

z = ((X / M) ^ L - 1) / (L * S)

where X is the measurement. In the one special case where L is exactly zero, the formula takes its limit form, z = ln(X / M) / S. A z of 0 means the measurement is exactly the median. A z of +1 means it is one standard deviation above. A z of -1.5 means one and a half below.

Step two turns the z-score into a percentile, by asking what share of a standard normal distribution falls below that z. A z of 0 gives 50 percent. A z of +1 gives about 84 percent. A z of -2 gives about 2 percent.

That is the whole calculation. It is the same calculation whether a clinician does it with a chart, a hospital system does it in software, or this site’s chart tool does it in your browser.

Why the tails behave strangely, and why that matters

Because the second step runs through a normal distribution, percentiles are not evenly spaced in measurement units. Near the middle of the chart, a small change in weight moves the percentile a lot. Out in the tails, a much larger change in weight moves it barely at all.

Concretely, on the WHO weight standard for boys at 12 months: the published 25th percentile is 9.0 kg and the 75th is 10.4 kg, so the whole middle half of the reference population fits inside 1.4 kg. Down at the bottom, the 3rd percentile is 7.8 kg and the 10th is 8.4 kg, only 0.6 kg apart in rank terms that are more than twice as wide.

Run the same 300 grams through both ends and the asymmetry is obvious. Adding 300 g to a boy sitting exactly on the median at 12 months moves him about eleven percentile points, from the 50th to roughly the 61st. Adding the identical 300 g to a boy sitting on the 3rd percentile moves him about three points, to roughly the 6th. The first child changed rank on the difference between a full stomach and an empty one. The second gained real weight and barely moved.

This is the single most useful thing to know about percentiles, and the reason a z-score is often the better number to watch than a percentile. The z-score is linear where the percentile is not. Clinicians frequently track z-scores for exactly that reason, and this site prints both.

What a percentile is not

It is worth being blunt about the boundaries, because the number invites all three of these readings and supports none of them.

• It is not a health measure. The reference population is a population, and every position in it is occupied by real, healthy children. A percentile describes where a measurement sits. It says nothing on its own about whether a child is well.
• It is not a target. There is no percentile a child is supposed to be on. Children arrive on the chart wherever their genetics, their birth, and their history put them.
• It is not a single reading’s story. Growth is read over time, in context, alongside everything else a clinician knows about a child. One dot is a dot.

That last point is why this site draws a chart rather than printing a verdict. Plotting several measurements shows you the shape of what has actually happened, which is a far more honest thing to look at than one number in isolation.

What to do with the number

Look at it. Understand what it is measuring. Then take any question it raises to the person whose job that is.

Percentiles describe position in a reference population, not health; growth patterns are for your pediatrician to read. If you want the source material, the CDC’s growth chart pages publish the charts and the technical notes behind them.

If you want to see the mechanics for yourself, the reference tables page shows the actual L, M and S values this site uses, month by month, with the file each one came from.

Keep going: plot a measurement, read the published reference tables, or browse the other guides.