Head Circumference Percentile Calculator (WHO)

Quick Answer

Head circumference percentile = Φ(z) × 100, where z = (measurement ÷ M) − 1, divided by S, using the WHO head-circumference-for-age tables. A boy of 4 months measuring 41.5 cm sits on the 45.6th percentile, a z-score of −0.11, against a median of 41.6 cm for that age.

Diagram of how a head circumference percentile is worked out: the measurement, age and sex are looked up in the WHO head-circumference-for-age table to get the median M and spread S, converted to a z-score, then read off as a percentile, with the WHO chart lines from minus 3 SD to plus 3 SD — Measurement, age and sex give the WHO median and spread for that exact day; those turn the measurement into a z-score, and the z-score into a percentile on the −3 SD to +3 SD chart lines.

How the percentile is worked out

The calculator uses the WHO Child Growth Standards head-circumference-for-age tables and the standard LMS method. Each day of age carries three parameters: L (a skew power), M (the median) and S (the coefficient of variation).

In both the boys’ and girls’ head-circumference tables L is constant at 1, so the general LMS formula collapses to a plain z-score about the median:

z = (measurement ÷ M) − 1, divided by S
percentile = Φ(z) × 100 — the share of children below that z-score on the normal curve.
Reversing it gives any chart line: measurement = M × (1 + S × z).

That reverse step is what fills the ladder under the result: it prints the head circumference for every whole standard-deviation line at your child’s exact age, with your own measurement slotted into position.

The WHO chart lines

WHO prints its growth charts with whole standard-deviation lines rather than round percentiles, so those are the lines shown here. Their percentiles are not chosen — each is just Φ(z) for that z-score:

Line	Percentile	Meaning
−3 SD	0.1st	1 in 1,000 measure smaller
−2 SD	2.3rd	about 2 in 100 measure smaller
−1 SD	15.9th	about 16 in 100 measure smaller
0 SD	50th	the median
+1 SD	84.1st	about 16 in 100 measure larger
+2 SD	97.7th	about 2 in 100 measure larger
+3 SD	99.9th	1 in 1,000 measure larger

Between −2 SD and +2 SD sit roughly 95 children in 100. UK-WHO paper charts label some lines as decimals for the same reason — the 0.4th and 99.6th centile lines are two-thirds of a standard deviation outside the 2.3rd and 97.7th.

How to use the calculator

Pick the sex.
Boys and girls have separate WHO tables, and the difference is real — about 0.6 cm at birth. Choosing the wrong one shifts the percentile noticeably.
Enter the age and pick the unit.
Days, weeks, months or years. Use days or weeks for a newborn, months after that. A month here is 365.25 ÷ 12 days, which is how the WHO tables are keyed.
Enter the measurement in cm or inches.
Type the number and switch the unit beside it. Results appear in both units either way.
Read the percentile and the ladder.
You get the exact percentile, the z-score, the nearest WHO line, the median for that exact age, and the full −3 SD to +3 SD ladder with your child’s row marked.

Measuring it properly

Technique moves the number more than most parents expect, so it is worth getting right. RCPCH guidance for health professionals states: “When measuring the head circumference use a narrow tape, either paper or plastic.”

Pass the tape around the widest part of the head — above the eyebrows and ears, and around the back where the skull sticks out most. Keep it flat against the scalp rather than angled, and take the largest of three readings.

A soft cloth tape that has stretched with use, or a tape sitting too low at the back, are the two usual reasons a reading looks out of line with the last one. Re-measure before reading anything into a single surprising number.

Worked example

A boy of 4 months measuring 41.5 cm — the calculator’s own default, so you can open it and check every figure below.

Output	Value
Percentile	45.6th
Z-score	−0.11 SD
Nearest chart line	0 SD (50th)
Median for that age	41.6 cm

So this baby sits a tenth of a standard deviation below the median — for practical purposes, on the middle line. The ladder for that exact age:

Line	Head circumference
−3 SD · 0.1st	38.0 cm (15.0 in)
−2 SD · 2.3rd	39.2 cm (15.4 in)
−1 SD · 15.9th	40.4 cm (15.9 in)
this baby	41.5 cm (16.3 in)
0 SD · 50th	41.6 cm (16.4 in)
+1 SD · 84.1st	42.8 cm (16.9 in)
+2 SD · 97.7th	44.0 cm (17.3 in)
+3 SD · 99.9th	45.2 cm (17.8 in)

Notice how tight the bands are: the whole normal range at this age spans about 4.8 cm between the 2.3rd and 97.7th lines. That is why a half-centimetre measuring error matters, and why the trend across visits tells you far more than any single reading.

Median head circumference by age

The 50th centile, straight from the WHO tables. A child well above or below these can be growing perfectly normally if they track along their own line.

Age	Boys (50th)	Girls (50th)
Birth	34.5 cm	33.9 cm
3 months	40.5 cm	39.5 cm
4 months	41.6 cm	40.6 cm
6 months	43.3 cm	42.2 cm
12 months	46.1 cm	44.9 cm
2 years	48.3 cm	47.2 cm
5 years	50.7 cm	49.9 cm

A guide, not medical advice. This calculator reproduces the WHO tables and nothing more — it does not decide whether a measurement needs looking at. A single reading matters far less than the pattern across visits, and head shape and technique both move the number. Take any worry to your health visitor, GP or paediatrician, especially if the measurement crosses chart lines between visits.

Head size is one strand of growth. For the same child’s weight against the UK-WHO charts, the baby weight percentile calculator works the same way on the weight-for-age tables.

Head circumference percentile: FAQ

It is your baby’s rank out of 100 against WHO reference children of the same age and sex. On the 45th percentile, about 45 in 100 measure smaller and 55 measure larger. Anywhere between the 2.3rd and 97.7th lines — that is −2 SD to +2 SD — covers roughly 95 in 100 healthy children, so a number well away from 50 is common and not by itself a problem.

There is no single normal figure — it changes with every week of age and differs by sex. On the WHO standard the median is 34.5 cm for a newborn boy, 41.6 cm at 4 months, 46.1 cm at 12 months and 50.7 cm at 5 years. Enter an exact age above and the calculator prints the median for that day along with the full −3 SD to +3 SD ladder.

Not on its own. A baby who sits steadily on the 2nd centile and grows along it is following their own pattern. What health professionals watch is the trend across visits rather than any single reading, and measuring technique alone can move the number by half a centimetre. This calculator is a guide, not medical advice — take any concern to your health visitor, GP or paediatrician.

RCPCH guidance for health professionals says: “When measuring the head circumference use a narrow tape, either paper or plastic.” Pass it around the widest part of the head — above the eyebrows and ears, and around the back where the skull sticks out most — keep it flat, and take the largest of three readings. A stretched cloth tape or a tape sitting too low is the usual reason a reading looks wrong.

Because the WHO head-circumference-for-age standard itself runs to 5 years, and this calculator loads the whole range — 1,856 days. Many tools only load the birth-to-24-months table, so they simply cannot answer for a 3, 4 or 5 year old. Nothing extra is estimated here: the data for a 5 year old is WHO’s own published table.

Yes. Switch the unit beside the measurement box to in and type inches; every result, including the chart-line ladder, is shown in both centimetres and inches. The conversion is exact at 2.54 cm per inch, so the same head entered either way returns the same percentile.