Is the 3rd percentile a cutoff for being too short?

No, and this is worth being precise about. A percentile line on a growth chart is a description of how a reference group is spread, so about 3% of healthy children in that group sit below the 3rd percentile line by construction — the line is a position on a ruler, not a health verdict. What a clinician looks at is something this page does not have: the shape of the child's own growth across several visits, the parents' heights, and the child's history. A height at the 3rd percentile that has tracked along that line for years and a height that has just dropped to it from the 50th are very different findings with the same percentile, and only the second one is a change.

What ages does this cover?

Two to 20 years, for a standing height. Those are the limits of the chart this page carries: the CDC stature-for-age charts run from 24 to 240 months, and the calculator adds the months on top of the years so that a child of 5 years 6 months is placed on the right row. Under 2 the measurement itself changes — children that young are measured lying down, and length measured lying down reads a little more than standing height — and the charts for that age are a separate set. Over 20 the charts stop, because growth has stopped.

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

Because the chart has a row for every half month of age, and because a single box labelled 'Age' invites a parent of a five-month-old to type 5 and receive an answer that is arithmetically correct and completely unrelated to their child. Splitting the age into years and the months since the last birthday removes that possibility. The months are also worth getting right: a boy of 110 cm is at the 59.4th percentile at 5 years 0 months, the 32.8th at 5 years 6 months and the 14.3rd at 6 years. The first half of that year costs 26.6 percentile points and the second half another 18.5, for a height that never changed.

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

The CDC 2000 growth charts, specifically the stature-for-age chart for 2 to 20 years, and the LMS parameters that the CDC publishes alongside it. The reference children were measured in national surveys in the United States, and the charts were issued in 2000 and remain the ones used in the United States for this age range. Two caveats belong with them. A reference population describes a particular group at a particular time, so children in another country or another generation are not exactly that group. And a chart is not a standard: nothing about a child is wrong because a line on a chart says they are unusual.

How much does a measuring error matter?

More than most people expect at these ages. For a boy of 5, heights of 108, 109, 110, 111 and 112 cm come out at the 42.3rd, 50.8th, 59.4th, 67.5th and 74.9th percentile — roughly eight or nine percentile points per centimetre, so a two-centimetre slip moves the answer by 15 to 17 percentile points. Stand the child against a wall without shoes, heels together, back and head against the surface, and look straight ahead rather than up. Measuring in the morning is slightly more repeatable than in the evening, since the spine compresses a little over the day, and repeating the measurement once and taking the closer of the two is more useful than buying a better tape.

Child Height Percentile Calculator

Result

59.4%

Percentile

Z-score: 0.24
Height at the 3rd percentile: 100.1 cm

A height percentile is a position in a lineup of other children — the children of the same age and the same sex. Those lineups are what the CDC growth charts are: for every half month of age from 2 to 20 years, and separately for boys and girls, the charts record three numbers describing how heights are spread at that age, and this calculator carries all 436 rows of them. Type in a height and an age and it returns the share of children that age who are at or below that height, the z-score that share is read from, and the height that marks the 3rd percentile of the chart for that age and sex. What does a height percentile mean, exactly? It means a statement about a group rather than about one child: it says where a single measurement lands among measurements of children the same age, and nothing beyond that. The group is not something you supply — it is a published reference chart — so the question worth asking is which chart, from when, and that answer is on this page. One field deserves care: the charts have a row every half month, and children at this age grow fast enough that half a year moves the same height a long way up or down the lineup.

Boys: height by age at the 3rd, 50th and 97th percentile

Age (years)	3rd percentile (cm)	50th percentile (cm)	97th percentile (cm)
2	79.9	86.5	93
3	88.1	95	102.6
4	94.3	102.2	110.2
5	100.1	108.9	117.5
6	105.9	115.4	124.8
7	111.7	121.8	132
8	117.3	127.9	139
9	122.2	133.5	145.4
10	126.5	138.6	151.3
11	130.6	143.5	157
12	135.4	149.1	163.4
13	141.5	156.1	171
14	148.2	163.8	178.5
15	154.4	169.9	184
16	158.7	173.5	187
17	161.2	175.3	188.6
18	162.5	176.2	189.4
19	163.1	176.6	189.9
20	163.3	176.8	190.2

The middle column is the median height for boys of that age — half are taller, half shorter. The two outer columns are where the chart's 3rd and 97th percentile lines sit, so about 3% of boys that age are shorter than the first number and about 3% are taller than the last. Between them lies the middle 94%. The charts below are the same ones the calculator reads: every value here was produced by the same two formulas that fill the result panel, so entering a number from the 3rd percentile column returns a percentile of 3. Note that the table is coarser than the calculator — the chart itself has a row every half month of age, while these rows are whole years, which is why a result computed for a 5-year-6-month-old will not match the 5-year row exactly.

Girls: height by age at the 3rd, 50th and 97th percentile

Age (years)	3rd percentile (cm)	50th percentile (cm)	97th percentile (cm)
2	78.4	85	91.5
3	86.6	93.9	101.5
4	92.8	100.8	109.2
5	99.1	107.7	117
6	105.5	114.7	124.9
7	111.6	121.5	132.4
8	117.1	127.6	139.1
9	121.7	132.9	145.1
10	125.8	138	151
11	130.5	144	157.8
12	137.1	151.2	164.9
13	144	157.2	170
14	148	160.4	172.8
15	149.7	161.9	174.1
16	150.4	162.5	174.8
17	150.7	162.9	175.1
18	150.9	163.1	175.3
19	151	163.3	175.4
20	151.1	163.3	175.5

These are the same three columns for girls, and they are a separate chart rather than a row in the boys' one, because girls and boys of the same age are not spread the same way. Compare the two medians at 5 years: 108.9 cm for boys against 107.7 cm for girls, a gap of just over a centimetre. At 14 the two medians are three centimetres apart, but the gap widens to about 13 cm by 18, because girls of 14 are nearly finished growing while boys of the same age are not. That is the whole reason the sex is a required field on this page: it selects which of the two charts the height is read against, and the same 125.8 cm is the 3rd percentile of a 10-year-old girl and just under the 3rd percentile of a 10-year-old boy.

Formula

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

height: The child's standing height. This is the only measurement you take — everything else on this page comes out of the chart (cm)
age: How old the child is, counted to the month. Age and sex together pick out one row of the chart; neither number is used in the arithmetic below
sex: Boys and girls have separate charts, because at the same age their heights are spread differently — at 5 years the median is about 109 cm for boys and about 108 cm for girls
M: The median height for that row: half of the children of that age and sex are shorter than M, half are taller
S: How spread out the heights are in that row, written as a fraction of the median rather than in centimetres
L: A power that stretches the scale so the spread becomes symmetric. It changes with age, and at some ages it is negative
z: How far the height 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 height that sits at a given percentile — the same formula read backwards. This page uses it once, for the third result: the height of the 3rd percentile line for this age and sex (cm)

Use it when you have a standing height for a child between 2 and 20 years old and want to know where that height sits. It is not the tool for a child under 2, where the measurement is taken lying down rather than standing and the charts are a different set. It is not a way to track growth either: tracking means several measurements over time and the shape of one child's own line, which a single height cannot show. It will not say whether a child is short in any clinical sense — what separates a child who is simply small for their age from one who is growing slowly is the pattern across visits together with the parents' heights and the child's own history, and this page receives none of that. It does not project adult height, and it does not read weight: the weight side of the same idea is a BMI-for-age chart, which is how weight status is read for children over 2.

Worked examples

A boy of 5 years 0 months, 110 cm tall
1. Find the row: 60 months, boys. There M = 108.90 cm, S = 0.042541, L = 1.260744 — and the 3rd percentile line for that row is 100.1 cm
2. Divide the height by the median: 110 ÷ 108.90 = 1.010079
3. Raise that to the power L: 1.010079 ^ 1.260744 = 1.012723, so the top of the fraction is 1.012723 − 1 = 0.012723
4. Multiply L by S for the bottom: 1.260744 × 0.042541 = 0.053633
5. Divide: z = 0.012723 ÷ 0.053633 = 0.24
6. Read the normal curve at 0.24: 0.59376 of children that age are at or below 110 cm, so the percentile is 59.4
The median height for a boy of exactly 5 is 108.9 cm, so 110 cm sits a little above the middle of the lineup, and the 3rd percentile line is 100.1 cm — nearly 10 cm below him. That gap is the thing this page exists to make visible: the same 110 cm belongs to a different place in the lineup at a different age. Six months later, at 5 years 6 months, 110 cm is the 32.8th percentile, and at 6 years it is the 14.3rd. Nothing about the child changed in that example except the row of the chart his age points at, which is why the age is worth entering exactly.
A girl of 10 years 0 months, 125.8 cm tall
1. Find the row: 120 months, girls. There M = 137.99 cm, S = 0.048612, L = 0.273317, and the 3rd percentile line is 125.79 cm
2. Divide: 125.8 ÷ 137.99 = 0.911659
3. Raise to the power L: 0.911659 ^ 0.273317 = 0.975038, so the top of the fraction is 0.975038 − 1 = −0.024962
4. Multiply L by S: 0.273317 × 0.048612 = 0.013286
5. Divide: z = −0.024962 ÷ 0.013286 = −1.88
6. Read the normal curve at −1.88: 0.030139 of girls that age are at or below 125.8 cm, so the percentile is 3.0
This height was chosen because it is the 3rd percentile line itself: the exact value on that line is 125.79 cm, and entering the rounded 125.8 gives back 3.0%. That round trip is the quickest way to check that the page and the chart below agree — put in any number from the 3rd percentile column and the percentile reading should come back at 3. Note the sign of z: −1.88 means below the median, and the 3rd percentile line is 1.88 spread units below the middle. Below this line sits about 3% of the reference girls — which is a statement about the chart, not about the child.
A boy of 2 years 0 months, 93 cm tall
1. Find the row: 24 months, boys — the first row of the chart, so no interpolation is involved. There M = 86.45 cm, S = 0.040322, L = 0.941524, and the 3rd percentile line is 79.9 cm
2. Divide: 93 ÷ 86.45 = 1.075739
3. Raise to the power L: 1.075739 ^ 0.941524 = 1.071156, so the top of the fraction is 0.071156
4. Multiply L by S: 0.941524 × 0.040322 = 0.037964
5. Divide: z = 0.071156 ÷ 0.037964 = 1.87
6. Read the normal curve at 1.87: 0.969557 of boys that age are at or below 93 cm, so the percentile is 97.0
93 cm is the top line of that first row — the 97th percentile for a 2-year-old boy — so this is the mirror of the previous example: 1.87 spread units above the middle instead of below it. The gap between the two outer columns of the table is what a percentile is doing at this age: at 2 years the 3rd percentile line is 79.9 cm and the 97th is 93.0 cm, so the whole middle 94% of boys spans about 13 cm. At 20 years the same two columns are 163.3 cm and 190.2 cm. A centimetre is therefore worth a great deal at the young end, and almost nothing at the old end.

Limitations

Two things limit what a percentile from this page can mean, and neither is a fault in the arithmetic. The first is the measurement. A standing height taken at home carries a few millimetres of technique — shoes on, heels apart, chin up, back not against the wall — and at the ages where children grow fastest a centimetre is worth several percentile points. For a boy of 5, heights of 108, 109, 110, 111 and 112 cm come out at the 42.3rd, 50.8th, 59.4th, 67.5th and 74.9th percentile: about eight to nine points per centimetre. So the difference between the 50th and the 60th percentile can be the difference between measuring well and measuring carelessly, and a height taken in the morning is a little more than one taken in the evening. The second limit is the comparison group. The charts behind this page come from a reference population of children measured in the United States in surveys around the turn of the century; that group is a reference, not a standard of what a child ought to be, and children elsewhere or in other generations will not match it exactly. A single height is also a single point: it cannot separate a child who is small for their age from one who is growing slowly, because that distinction lives in the shape of a curve across several visits. Children born early are not corrected here for how early they were, and this page says nothing about weight — for children over 2 that is read from a BMI-for-age chart. 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.

Frequently asked questions

What does a height percentile mean?: It is the share of children of that age and sex whose height is at or below this one. A boy of 5 at the 59.4th percentile is taller than about 59% of boys of exactly that age, and shorter than the other 41%. Two wordings in that sentence matter. 'At or below' is one of them: the figure is not the share of children whose height is exactly 110 cm, which would be a much smaller number. The other is that this is a statement about a group. It says where one measurement lands in a lineup of measurements, and it says nothing about the child who produced it — not how they will grow, not what they eat, not anything a percentile was never built to carry.
Is the 3rd percentile a cutoff for being too short?: No, and this is worth being precise about. A percentile line on a growth chart is a description of how a reference group is spread, so about 3% of healthy children in that group sit below the 3rd percentile line by construction — the line is a position on a ruler, not a health verdict. What a clinician looks at is something this page does not have: the shape of the child's own growth across several visits, the parents' heights, and the child's history. A height at the 3rd percentile that has tracked along that line for years and a height that has just dropped to it from the 50th are very different findings with the same percentile, and only the second one is a change.
What ages does this cover?: Two to 20 years, for a standing height. Those are the limits of the chart this page carries: the CDC stature-for-age charts run from 24 to 240 months, and the calculator adds the months on top of the years so that a child of 5 years 6 months is placed on the right row. Under 2 the measurement itself changes — children that young are measured lying down, and length measured lying down reads a little more than standing height — and the charts for that age are a separate set. Over 20 the charts stop, because growth has stopped.
Why do you ask for age in years and months separately?: Because the chart has a row for every half month of age, and because a single box labelled 'Age' invites a parent of a five-month-old to type 5 and receive an answer that is arithmetically correct and completely unrelated to their child. Splitting the age into years and the months since the last birthday removes that possibility. The months are also worth getting right: a boy of 110 cm is at the 59.4th percentile at 5 years 0 months, the 32.8th at 5 years 6 months and the 14.3rd at 6 years. The first half of that year costs 26.6 percentile points and the second half another 18.5, for a height that never changed.
Which chart is this based on, and is it still current?: The CDC 2000 growth charts, specifically the stature-for-age chart for 2 to 20 years, and the LMS parameters that the CDC publishes alongside it. The reference children were measured in national surveys in the United States, and the charts were issued in 2000 and remain the ones used in the United States for this age range. Two caveats belong with them. A reference population describes a particular group at a particular time, so children in another country or another generation are not exactly that group. And a chart is not a standard: nothing about a child is wrong because a line on a chart says they are unusual.
How much does a measuring error matter?: More than most people expect at these ages. For a boy of 5, heights of 108, 109, 110, 111 and 112 cm come out at the 42.3rd, 50.8th, 59.4th, 67.5th and 74.9th percentile — roughly eight or nine percentile points per centimetre, so a two-centimetre slip moves the answer by 15 to 17 percentile points. Stand the child against a wall without shoes, heels together, back and head against the surface, and look straight ahead rather than up. Measuring in the morning is slightly more repeatable than in the evening, since the spine compresses a little over the day, and repeating the measurement once and taking the closer of the two is more useful than buying a better tape.

References

Growth Charts — Percentile Data Files with LMS Values — US CDC, National Center for Health Statistics — the source data file behind the percentile chart on this page (stature-for-age, ages 2–20, one L / M / S set per half-month of age)
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, not from weight-for-age

Related calculators

Child Weight Percentile CalculatorA child's weight percentile for age and sex.BMI CalculatorBody mass index with WHO category bands, in metric or imperial.Age CalculatorWork out your exact age in years, months, days and seconds.Percentile CalculatorValue at a percentile you choose, with its two neighbours.