Where a Percentile Comes From: Which Population, Measured When

A percentile is a rank, and a rank needs a crowd

The arithmetic is the least of it. If you know the mean and the standard deviation of a roughly normal distribution, a percentile is one subtraction, one division and one lookup: subtract the mean, divide by the standard deviation, and read the resulting z-score off the normal curve. For a man of 5'11" against an American mean of 5'9.7" with a standard deviation of 2.8 inches, z is +0.46 and the percentile is the 68th. Two lines of work. The part that decides the answer happened long before the arithmetic, when somebody chose which crowd he was being ranked in.

So take one man and change nothing about him except the crowd. The NCD Risk Factor Collaboration pooled 1 472 population-based data sources covering 18.6 million adults to produce mean adult height by country and birth year, which is the cleanest set of comparison groups anyone has published. Scoring our man against the 1996 birth cohort of nine of them — holding the standard deviation constant at 2.8 inches throughout, so that only the mean moves — gives the table above: the 38th percentile in the Netherlands, the 53rd in Germany, the 68th in the United States, the 86th in Portugal, the 99th in Guatemala. He is simultaneously below average and unusually tall, and both statements are correct, because they are answers to different questions.

One methodological note, because it matters. Holding the standard deviation constant is a deliberate simplification: it isolates the effect of the reference's centre from the effect of its spread. The figure used, 2.8 inches for men, is not invented — the fifth Dutch growth study measured 7.1 cm in men and 6.3 cm in women, and measured national studies land close to those numbers wherever they exist. Real datasets differ a little in spread as well as in centre, so treat the percentiles here as clean illustrations of one mechanism rather than as official figures for any country.

Measured when: a reference has a date on it

The reference population is not only a place, it is a time. The same NCD-RisC file, read down the years for one country, shows how fast the ground moves. Our 5'11" man against American men of successive birth cohorts: the 91st percentile against those born in 1896, the 69th against those born in 1946, the 68th against those born in 1996. American growth flattened after the war, so the last two are close together. Run the same exercise in France and the movement is dramatic: the 97th percentile against the 1896 cohort, the 92nd against 1926, the 83rd against 1946, the 69th against 1966, the 52nd against 1996. Nothing about the man changed across those five rows. He simply stopped being unusual.

This is also why serious reference tables are stratified by age band rather than lumped into one adult figure. Two different things pull the older bands down. One is the cohort effect just described: a 75-year-old was born into a shorter generation, and always was shorter. The other is real loss of stature with age, from intervertebral disc compression and changes in spinal curvature, which is why a national anthropometric report such as the NCHS series prints separate rows for 20–39, 40–59 and 60 and over rather than a single mean. Scoring an older adult against a whole-population mean quietly rewards them for both effects at once.

Measured how: the self-report problem

There is a third question hiding behind the first two: did someone hold a ruler, or did someone answer a question? The gap is measured and it goes one way. Connor Gorber and colleagues, reviewing validation studies in Obesity Reviews in 2007, found height overestimated in 11 of 12 population studies among men, by 0.2 to 0.9 inches, and in 10 of 12 among women, by 0.2 to 0.9 inches. In the American NHANES data the average overstatement is about half an inch for men and a quarter of an inch for women, and it grows with age and in shorter people — that is, it is largest exactly where it is most misleading.

Now propagate that into a percentile. A reference built from self-reported heights has a mean about half an inch too high. Our 5'11" man, scored against a measured American mean, is the 68th percentile; scored against the same population's self-reported mean, he is the 61st. Seven percentile points, from a measurement convention, in a direction nobody flags. It works the other way too — if he reported his own height with the same generosity and was then scored against a measured reference, he would gain about the same amount. The lesson is not that self-reported surveys are worthless, since for many purposes a systematic half-inch does no harm. The lesson is to make sure the person and the reference were measured the same way.

Sex, and why the two distributions are kept apart

Adult height references are always split by sex, and the reason is that the two distributions differ by about the same amount as a whole standard deviation. In the 1996 birth cohort the gap between men and women runs from roughly 4 inches in Portugal to close to 6 inches in France, and mixing the sexes into one reference would produce a distribution with two humps that no percentile could sensibly describe. So a woman is ranked among women. Run our exercise on the female side: a woman of 5'5" is the 28th percentile against Dutch women, the 45th against German women, the 51st against French women, the 52nd against Italian women, the 59th against American women, the 60th against Spanish women and the 62nd against Portuguese women. Same span of references, same mechanism, same conclusion.

Percentile or z-score: the same information, differently packed

A z-score says how many standard deviations from the mean you are; a percentile says what fraction of the reference is below you. They are the same fact, and you can convert one into the other exactly: z = 1 is the 84.1st percentile, z = 2 the 97.7th, z = 3 the 99.87th. The reason clinical and statistical work prefers the z-score is that the percentile scale is savagely non-linear at the edges. Around the median, with a standard deviation of 2.8 inches, moving one percentile costs 0.07 inches. At the 90th percentile it costs 0.16 inches. At the 97th, 0.48 inches. Going from the 99th to the 99.5th costs 0.7 inches — four times the width of the entire step from the 50th to the 51st.

That compression is why growth charts and laboratory reports switch to standard deviations once they leave the middle of the range, and why the UK-WHO paediatric charts space their printed lines two-thirds of a standard deviation apart rather than at round percentile values. It is also why a percentile in the high nineties should be read gently: the difference between the 98th and the 99.5th is a couple of centimetres of body and an enormous difference in how the number sounds.

What the number is not

It is worth saying plainly, because height attracts more nonsense than almost any other measurement. A percentile of adult height is a description of a reference population, not a property of a person and certainly not a score. Height is overwhelmingly inherited, modified in childhood by nutrition and illness — which is why the century of gains in the NCD-RisC data tracks public health so closely — and fixed by early adulthood. There is nothing in it to be earned or lost, and the arithmetic on this page is interesting for what it says about references, not about bodies.

The one place where adult stature does carry a signal is change. Losing height over years is a real clinical observation rather than a percentile question, and it belongs with a doctor. So does an unusual stature in someone still growing, which is the domain of the growth charts rather than of an adult reference table. Everything else here is a fact about which crowd you were put in.

Frequently asked questions

Which reference should a height percentile calculator use?

Whichever one it tells you it is using. There is no universally right answer — a percentile against the population you live among answers a different question from a percentile against the population you were born into, and both are legitimate. What is not legitimate is a calculator that returns a percentile without naming the reference, the sex, the age band and the year the data were collected, because those four choices between them can move the answer by fifty points.

Why does my percentile change so much between websites?

Almost always the reference, not the arithmetic. Different sites use different national datasets, different birth cohorts, different age bands and — the one nobody discloses — sometimes a self-reported survey rather than a measured one. In the worked example on this page, changing only the country moved one man from the 38th percentile to the 99th; switching a measured reference for a self-reported one moved him seven points on its own. If two calculators disagree, compare their stated references before assuming one is broken.

Is a z-score better than a percentile?

Better for arithmetic, worse for conversation. They carry identical information — z = 2 is always the 97.7th percentile — but the z-score keeps its resolution at the extremes, where the percentile scale runs out of room. Between the 99th and the 99.5th percentile there are 0.7 inches of body; between the 50th and the 51st, 0.07 inches. That is why clinicians track z-scores and charts show percentiles: one is for calculating with, the other for showing to a human being.

Do people really get taller every generation?

They did, for about a century, and in many places they have stopped. In the NCD-RisC data, men born in 1996 are 14.3 cm taller than Spanish men born in 1896, 14.0 cm in Portugal, 13.3 cm in France, but only 6.1 cm in the United States, where the trend flattened after the war. The Dutch, the tallest population measured, plateaued too — the fifth Dutch growth study reported it in 2013. So the answer depends on the country and the period, which is exactly the point of this article.

Does the same reference problem apply to BMI percentiles?

It applies harder. Body weight has shifted far faster than height over the last fifty years, so a BMI percentile is even more sensitive to which decade the reference was collected in — a child on the 85th centile of a 1970s reference and a child on the 85th centile of a current one are not the same child. It is also why adult BMI uses fixed thresholds rather than percentiles, and why paediatric BMI uses percentiles against a dated reference that has to be named. Same principle, larger consequences.