Worked example: 180 cm, compared against US men
- z = (180 − 175.3) ÷ 7.4 = 4.7 ÷ 7.4 = 0.635
- Percentile = the normal cumulative distribution at z = 0.635 = 73.7
So 180 cm is taller than about 73.7% of US men aged 20 and over, and shorter than about 26.3%. In feet and inches that is 5′ 11″, and the median it is being compared against is 5′ 9″.
The formula, and the population behind it
A percentile is a statement about a population, and it is meaningless without knowing which one. This page uses:
- US adults aged 20 and over, from the NHANES 2015–2018 anthropometric reference data
- Mean standing height 175.3 cm for men and 161.3 cm for women
- Standard deviation 7.4 cm for men and 7.1 cm for women
The calculation is the standard normal score followed by the normal cumulative distribution:
z = (height − mean) ÷ standard deviationpercentile = Φ(z) × 100
where Φ is the cumulative distribution function of the standard normal. The implementation uses the Abramowitz & Stegun 7.1.26 approximation to the error function, accurate to about 1.5 × 10−7 — far more precision than a percentile printed to one decimal place requires.
An honest note about the standard deviation
The two means above are measured and published. The two standard deviations are not. The NHANES reference report gives standard errors of the mean rather than population standard deviations, and 7.4 cm and 7.1 cm are the conventionally quoted figures for this population rather than numbers lifted from that table.
This matters, because the SD is what converts a height difference into a percentile. If the true male SD were 7.0 rather than 7.4, the same 180 cm would come out at 74.9 rather than 73.7. That is a small shift near the middle and a larger one in the tails, so the extreme rows of the table are softer than the middle rows. Every other height percentile tool you will find makes the same assumption; most of them do not say so.
Why a normal distribution, and where it breaks
Adult height is the textbook example of an approximately normal distribution, and for good reason: it is the sum of many small independent genetic and developmental contributions, which is precisely the situation the central limit theorem describes. Within a single adult population of one sex it fits well through the middle of the range.
It fits less well at the edges. Real height distributions are slightly left-skewed — there is a longer tail of unusually short adults than of unusually tall ones, because conditions and circumstances that restrict growth are more common than ones that extend it. The practical effect is that a normal model slightly underestimates how unusual a very short height is and slightly overestimates how unusual a very tall one is. Below the 1st percentile and above the 99th, read the output as an approximation.
Why the whole table is printed
Because a single percentile is a poor way to understand where you sit. “The 74th percentile” means very little on its own; seeing that the 50th is 175.3 cm, the 75th is 180.3 cm and the 90th is 184.8 cm makes the distribution concrete — and shows how tightly packed adult height is. Five centimetres, two inches, covers the entire span from the median to the 75th percentile.
That compression is why height percentiles move so fast. A single inch is worth roughly ten percentile points around the middle of the distribution, so the difference between the answer you get in shoes and the answer you get without them is not trivial.
Measuring accurately
Standing height, shoes off, heels together against a wall, looking straight ahead with the head level. Have somebody else read it; measuring yourself reliably adds a centimetre or more.
You are also genuinely taller in the morning. Spinal discs compress through the day and most people lose one to two centimetres between waking and evening — comfortably enough to move a percentile by ten points. If you are tracking a number, take it at the same time of day.
Limitations, stated plainly
This compares against US adults aged 20 and over. It is not a global comparison: national median heights vary by more than fifteen centimetres, so the same measurement is a very different percentile in the Netherlands than in Guatemala. It is not age-adjusted either — a 25-year-old and an 80-year-old are compared against the same distribution, although average height has risen across generations and people lose height with age, so an older person's percentile against their own cohort would be higher than this shows.
The standard deviations are inferred rather than published, as set out above, and the normal approximation is weakest in the tails.
This is not a growth chart and must not be used as one. Height percentiles for children and adolescents are read against age-specific and sex-specific CDC or WHO growth curves that track a moving target, they are interpreted alongside weight, growth velocity and parental height, and they are a clinical instrument. This page compares an adult against an adult distribution, and it will return a wrong and potentially alarming answer for a child.
Height is descriptive anthropometry here and nothing more. Nothing on this page reads any meaning into a height, and it is not medical advice.