Child Weight Percentile Calculator

z = ((weight ÷ M)^L − 1) ÷ (L · S) · percentile = Φ(z) × 100% · X = M · (1 + L · S · z)^(1 ÷ L)

weight

The child's weight, as read off a scale. This is the only measurement you take — everything else on this page comes out of the chart (kg)

age

How old the child is, counted to the month. Age and sex together pick out the rows of the chart, and the calculator averages the two rows either side of that age; neither number appears in the arithmetic below

sex

Boys and girls have separate charts, because at the same age their weights are spread differently — at 5 years the median is about 18.4 kg for boys and about 17.9 kg for girls

M

The median weight for that age: half of the children of that age and sex weigh less than M, half weigh more

S

How spread out the weights are in that row, written as a fraction of the median rather than in kilograms

L

A power that stretches the scale so the spread becomes symmetric. It changes with age, and on the weight chart it is negative at every single age

z

How far the weight sits from the median, measured in units of that spread — negative below the median, positive above it

Φ

The share of a normal curve that falls at or below z. This is the step that turns a distance into a percentile

percentile

That share written as a percentage. It is the number most people came for, and it is also what tells you where the 3rd percentile line sits

X

The weight that sits at a given percentile — the same formula read backwards. This page uses it once, for the third result: the weight of the 3rd percentile line for this age and sex (kg)

Use it when you have a weight for a child between 2 and 10 years old and want to know where that weight sits. It is not the tool for a child under 2, where the charts are a different set built for a measurement taken lying down. It is not a way to track growth either: tracking means several weighings over time and the shape of one child's own line, which a single weight cannot show. It will not say whether a child is underweight in any clinical sense — that reading takes a growth curve across visits, the child's own history and, above age 2, a height as well. Above 10 years this page stops, and the reason is the one worth remembering: weight without height stops separating a heavy child from a tall one once children start their growth spurt at different ages. For weight status past that point, and for any child over 2, the tool is a BMI-for-age chart.

1. A boy of 5 years 0 months who weighs 18 kg

   1. Find the row: 60 months, boys. There L = −0.998049, M = 18.392523, S = 0.129467 — and the 3rd percentile line for that row is 14.8 kg
   2. Divide the weight by the median: 18 ÷ 18.392523 = 0.978659
   3. Raise that to the power L: 0.978659 ^ −0.998049 = 1.021764, so the top of the fraction is 1.021764 − 1 = 0.021764
   4. Multiply L by S for the bottom: −0.998049 × 0.129467 = −0.129214
   5. Divide: z = 0.021764 ÷ −0.129214 = −0.17
   6. Read the normal curve at −0.17: 0.43312 of boys of that age weigh this much or less, so the percentile is 43.3

   The median 5-year-old boy weighs 18.4 kg, so 18 kg lands just under the middle of the lineup — the 43.3rd percentile, a little below the 50th. Note where the negative sign went: L is negative, so raising a ratio below 1 to the power L brings it back above 1, and the whole fraction comes out negative. That is the same answer the subtraction would have given, since dividing by a negative L · S flips the sign back.

2. The same weight at 5 years 6 months

   1. Find the rows: 66 months falls between the chart's 65.5-month and 66.5-month rows for boys, and the calculator averages the two. That gives L = −1.031643, M = 19.525968, S = 0.134287, with the 3rd percentile line at 15.6 kg
   2. Divide the weight by the median: 18 ÷ 19.525968 = 0.921849
   3. Raise that to the power L: 0.921849 ^ −1.031643 = 1.087573, so the top of the fraction is 1.087573 − 1 = 0.087573
   4. Multiply L by S for the bottom: −1.031643 × 0.134287 = −0.138536
   5. Divide: z = 0.087573 ÷ −0.138536 = −0.63
   6. Read the normal curve at −0.63: 0.26365 of boys of that age weigh this much or less, so the percentile is 26.4

   Six months older and not a gram heavier, and the same 18 kg drops from the 43.3rd percentile to the 26.4th. That is the whole reason this page asks for the age in months: half a year of growing moves the median up by more than a kilogram, so a weight that was unremarkable in the spring can sit low by the autumn without anything about the child having changed. It is also the clearest case of why the comparison group matters — a percentile is a position among children of one exact age, not a property of the weight itself.

3. A girl of 10 years 0 months who weighs 23.9 kg

   1. Find the row: 120 months, girls — the last age this page covers. There L = −0.850952, M = 32.891303, S = 0.195577, and the 3rd percentile line is 23.9 kg
   2. Divide the weight by the median: 23.9 ÷ 32.891303 = 0.726636
   3. Raise that to the power L: 0.726636 ^ −0.850952 = 1.312238, so the top of the fraction is 1.312238 − 1 = 0.312238
   4. Multiply L by S for the bottom: −0.850952 × 0.195577 = −0.166427
   5. Divide: z = 0.312238 ÷ −0.166427 = −1.88
   6. Read the normal curve at −1.88: 0.03032 of girls of that age weigh this much or less, so the percentile is 3.0

   This one is worth reading twice: the input is a number taken straight off the 3rd percentile column of the girls' table below, and the third result hands the same number back. That is the check that the table and the result panel are the same machine — both columns come out of the two formulas above, so a value on the 3rd percentile line has to return a percentile of 3, and does. It is also the page's own boundary: at 10 years a girl's median weight is 32.9 kg, and 23.9 kg is far enough below it that the percentile is a single digit.

Three things limit what a percentile from this page can mean, and none of them is a fault in the arithmetic. The first is the measurement, and it bites harder here than it does for height. A weight is easier to take than a standing height — no technique, no posture — but it moves far more: clothing, a meal, a full bladder, a bout of sickness with diarrhea, and a different scale all shift it. Near the middle of the lineup, one kilogram is worth a lot. For a boy of 5 these weights come out at these percentiles: 17 kg at the 26.3rd, 18 kg at the 43.3rd, 19 kg at the 59.8th, 20 kg at the 73.3rd and 21 kg at the 83.1st — about sixteen points per kilogram, so the distance from the 43rd percentile to the 60th is one kilogram, which is less than what a heavy sweater and a winter coat will add. Weigh a child at the same time of day, in the same clothes, on the same scale, and read the percentile as a range rather than a digit. The second limit is the comparison group. These charts come from a reference population of children measured in the United States in surveys around the turn of the century; the group is a reference, not a standard of what a child ought to weigh, and children elsewhere or in other generations will not match it exactly. A single weight is also a single point: it cannot separate a child who is light for their age from one who is losing weight, because that distinction lives in the shape of a line across several weighings. The third limit is the one that decides the age range on this page. Weight alone does not say what a child is made of — a heavy child may be tall, or solidly built, or carrying extra fat, and weight-for-age tells these apart no better than a single number can. Up to about 10 years the difference rarely matters, which is why the reference stops there: beyond it, children enter their growth spurt at different ages and a child who is simply tall starts to look heavy on this chart. Above 10 years, and for any child over 2, weight status is read from a BMI-for-age percentile, which brings height into the same figure. Finally, a percentile is not a percentage: the 3rd percentile is not 3% below normal, it is a position that about 3% of the reference children fall below, and it is not a cutoff for anything.

What does a weight percentile mean?

It is the share of children of that exact age and sex who weigh the same or less. A 5-year-old boy at the 43.3rd percentile weighs more than about 43% of boys of exactly his age, and less than the other 57%. Two things in that sentence carry weight. The first is the phrase same or less: the figure is not the share of children who weigh exactly 18 kg, which would be a much smaller number, but the share the chart's line has already passed. The second is that this is a statement about a group. It says where one measurement lands among the measurements of children the same age; it says nothing about the child who produced it, and nothing about where that measurement will be next year.

Is a low percentile the same as underweight?

No, and the difference is worth holding on to. By construction about 3% of the reference children sit below the 3rd percentile line, and another 3% above the 97th — those children are not all ill, they are the tails of any distribution. What matters clinically is a child's own line over time and, above age 2, their weight together with their height. A heavy child who is tall and a light child who is short can sit at the same weight percentile and be in completely different places once height is brought in, which is exactly what a BMI-for-age chart does. Treat this page as a reading of one measurement against a reference, not as a diagnosis of an underweight child.

Why does this stop at 10 years?

Because weight on its own stops being informative around the growth spurt. WHO publishes weight-for-age reference data only up to age 10, with the explanation that beyond that point the measure does not distinguish between height and body mass in an age period where many children are experiencing the pubertal growth spurt — a child may look heavy on this chart while in fact being just tall. The data behind this page (CDC 2000) does run to 20 years, but the arithmetic would be right and the reading would be wrong, so the age field will not accept more than 10 years 11 months. Above that, use BMI-for-age.

Why do you ask for age in years and months separately?

Because the chart's rows are half a month apart and the difference between ages is large enough to matter. At 5 years a boy's median weight is 18.4 kg; at 5 years 6 months it is 19.5 kg. The same 18 kg is the 43.3rd percentile at the first age and the 26.4th at the second — a change of seventeen points with nothing about the child changing. The calculator takes the months field and averages the two chart rows either side of the resulting age, so a child of 5 years 6 months is read against a blend of the 65.5-month and 66.5-month rows.

Which chart is this based on, and is it still current?

The weight-for-age tables of the CDC 2000 growth charts, the same reference the child height page on this site uses, taken from the published data files that carry the L, M and S values for each half-month of age. They remain the reference used in the United States for children over 2, and are one of the two sets the World Health Organization points to for this age range. They describe a reference population rather than a target: a child at the 15th percentile is not behind, they are one of the fifteen in a hundred who are lighter than the rest, and a child who holds that line across a year is growing the way that line says.

How much does the measurement itself matter?

More than most people expect. Take a boy of 5: 17 kg is the 26.3rd percentile, 18 kg is the 43.3rd, 19 kg is the 59.8th. One kilogram moves him roughly sixteen percentile points near the middle, so the whole span from the 40th to the 60th percentile is about a kilogram — less than a winter coat and a pair of shoes. Weigh in the morning, before breakfast, in the same light clothing, on the same scale, and read the result as a band rather than a single number. The wider the gap between the percentile and the last one you recorded, the more it is worth checking that the two measurements were taken the same way before reading anything into the change.

• Growth Charts — Percentile Data Files with LMS Values — US CDC, National Center for Health Statistics — the source data file behind the table on this page (weight-for-age, ages 2–20, one L / M / S set per half-month of age)
• Weight-for-age (5–10 years) — Growth reference data for 5–19 years — World Health Organization — the reason this page stops at 10 years. WHO publishes weight-for-age only to age 10, because the measure does not distinguish between height and body mass in an age period where many children are experiencing the pubertal growth spurt, and a child may appear to have excess weight while in fact being just tall
• 2000 CDC Growth Charts for the United States: methods and development — Kuczmarski RJ, Ogden CL, Guo SS et al. — Vital and Health Statistics, Series 11, No. 246, 2002 (how these charts were built, and the reference population behind them)
• Smoothing reference centile curves: the LMS method and penalized likelihood — Cole TJ, Green PJ — Statistics in Medicine, 1992, 11(10):1305–1319 (the LMS method itself: L is the Box-Cox power, M the median and S the coefficient of variation; both formulas on this page are it)
• Child and Teen BMI Calculator — US CDC — above age 2 a child's weight is read from the BMI-for-age percentile, which is the tool that takes height into account