Growth percentile calculator: the LMS method, explained

Reference tables pending verification

The WHO and CDC publish their growth charts as tables of L, M and S by age and sex. Those tables have not yet been downloaded into this site and checked against their own printed medians, so this page will not print a centile for a child. We would rather show you nothing than show you a number we have not verified - on a growth chart, a confident wrong answer is the worst thing we could do. The arithmetic below is complete and tested, and you can check it against a chart you have to hand.

How this site verifies reference data

Worked example: 107.8143 against a median of 100 with S = 0.04worked example

97.0th centile

Z-score: 1.881standard deviations from the median
Median on this chart (M): 100from the example values
Chart convention for this age: CDC
Reference tables: pending verificationno centile is shown for a child until they are checked

A centile is a position among peers, not a grade. About 97 of every 100 children of the same age and sex on this reference chart measured less, and about 3 measured more. Children on the 10th and the 90th centile can both be growing exactly as they should; what a clinician reads is the shape of the curve across several visits, not any single point.

MeasurementThe WHO standards cover the first 24 months; the CDC charts run from 2 to 20 years.

Chart

Boys and girls have separate charts because the growth patterns differ.

Age (months)240 months is 20 years, the top of the CDC charts.Measurement (kg)Measured, not estimated - small children are genuinely hard to measure accurately.

I have the L, M and S values from a published chart

Both the WHO and the CDC publish these three numbers for every age and sex. Enter the row for your child’s age and this page will do the arithmetic on it - which is the whole of what a centile calculator does, minus the table we have not yet verified.

L (power)M (median)S (coefficient of variation)

Everything you type here is computed in your browser. Nothing you enter is stored on a server, sent anywhere, or shared — there is no account and no health data to leak.

Centile values for the L, M and S above (worked example while the tables are pending)
Centile	Z-score	Measurement
3th	-1.88	92.8
10th	-1.28	95
25th	-0.67	97.3
50th	0	100
75th	0.67	102.7
90th	1.28	105.3
97th	1.88	107.8

These rows demonstrate the maths on the example L, M and S values, not on a published chart. Enter a real row from a WHO or CDC table above to see it applied to one.

The sources this defers to

WHO Child Growth Standards (0-24 months) — the L, M and S tables for the first two years
CDC growth charts: percentile data files (2-20 years) — the L, M and S tables for children and adolescents
NHS: your baby's weight and height — how centile charts are read in practice, and why crossing lines matters more than one point

For an estimate that needs no chart at all, the height predictor works from two parents’ heights - with a 17 cm band around the answer.

A growth percentile calculator turns a child's height or weight into a centile using the LMS method Cole published in 1990, with the reference tables the WHO and CDC publish by age and sex. Enter an age, a sex and a measurement to see where it falls, and what a centile does not mean.

LMS z-score (Cole) — Z = ((X / M)^L - 1) / (L x S), and Z = ln(X / M) / S when L = 0. Verified 2026-07-30 against Cole, Eur J Clin Nutr 1990 (the LMS method) (The z-score is exact arithmetic given L, M and S; all of the uncertainty lives in the reference table those three come from, and in whether that table describes the child in front of you.)
Centile from a z-scoreconvention — centile = 100 x standard normal CDF of Z. Verified 2026-07-30 against Cole, Eur J Clin Nutr 1990 (the LMS method) (The normal CDF is evaluated with the Zelen and Severo rational approximation (Abramowitz and Stegun 26.2.17, absolute error under 7.5e-8) and inverted with Acklam's approximation (relative error under 1.15e-9). Both are far more precise than the tenth of a centile anything here displays.)

Everything you type here is computed in your browser. Nothing you enter is stored on a server, sent anywhere, or shared — there is no account and no health data to leak.

Frequently asked questions

What does a growth percentile actually mean?

It is a position among peers, not a grade. The 25th centile means that of 100 children of the same age and sex on that reference chart, about 25 measured less and about 75 measured more. Children at the 10th and the 90th centile can both be growing exactly as they should.

How is a percentile calculated?

By the LMS method Cole published in 1990. Each age and sex has three published values - L, M and S - and the measurement becomes a z-score as ((X divided by M) to the power L, minus 1) divided by L times S. The centile is the standard normal distribution of that z-score.

Which reference chart should be used?

The WHO Child Growth Standards cover 0 to 24 months and describe how children grow in good conditions; the CDC 2000 charts cover 2 to 20 years and describe how a US reference population did grow. The CDC recommends the WHO standards under two years in the US.

Where do the reference tables on this page come from?

From the WHO and CDC files themselves, downloaded rather than typed in. Each stored table is then checked by running its L, M and S back through this site's own maths and comparing the result to the 3rd, 50th and 97th centiles those same bodies publish separately. A table that disagrees is not shipped.

Should a change in percentile worry me?

That is a question for a clinician, who will look at the shape of the curve across several measurements rather than at any single point. Small movements between visits are ordinary, partly because measuring a small child accurately is genuinely difficult.

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The next number

No body metric means much on its own. Here is what this one feeds into.

Child height predictorWhat the parents' heights point at, with the 17 cm band that comes with it.

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