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Child Growth Percentile Calculator

Find a child's height-for-age, weight-for-age and BMI-for-age percentiles from the CDC growth charts for ages 2 to 20.

Level: Grade 12 to college

  • Common Core standard HSS.ID.A.4Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
Printable worksheet

Child Growth Percentile Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Units
Sex

The CDC charts are separate for boys and girls.

Months past the last birthday, from 0 to 11.

Result

Height-for-age percentile

52.7

On the CDC charts, a boy aged 5 years is at the 53rd percentile for height, the 53rd for weight and the 56th for BMI-for-age. A percentile compares one child with a reference group and is not a diagnosis. Talk to your child's doctor about any growth questions.

Weight-for-age percentile
53.4
BMI-for-age percentile
55.5
BMI
15.6 kg/m²
Height z-score
0.07
Weight z-score
0.09
BMI z-score
0.14
Median (50th percentile) height for a boy this age
42.9 in
Median (50th percentile) weight for a boy this age
40.5 lb

See the step-by-step solution ↓

Step-by-step solution

  1. Find the age in months, because the CDC tables go month by month

    5 years×12+0=60 months

  2. Change height to centimeters and weight to kilograms, the units in the CDC tables (1 in = 2.54 cm, 1 lb = 0.45359237 kg)

    43 in×2.54=109.22 cm; 41 lb×0.45359237=18.597 kg

  3. Read the CDC height-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

    z=(109.22 cm108.9024)1.260744−11.260744×0.042541=0.069

  4. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

    Φ(0.069)×100=52.7

  5. Read the CDC weight-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

    z=(18.6 kg18.3925)−0.998049−1−0.998049×0.129467=0.085

  6. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

    Φ(0.085)×100=53.4

  7. Find BMI (body mass index): weight in kilograms divided by height in meters, squared

    18.597 kg(1.0922 m)2=15.59 kg/m²

  8. Read the CDC BMI-for-age values for a boy of this age. M is the middle (median) value, and L and S set the curve's shape and spread

    z=(15.59 kg/m²15.4246)−2.578974−1−2.578974×0.075757=0.139

  9. Turn the z-score into a percentile using the bell curve. It is the share of children in the reference group who measured less

    Φ(0.139)×100=55.5

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

Please note: This calculator gives a general screening estimate, not a diagnosis. Talk to a qualified healthcare professional about your individual health.

What this calculator does

See where your child's height and weight fall on the CDC growth charts. These are the charts many US pediatricians use from age 2 to 20. A percentile tells you how a measurement compares with a large reference group of children of the same age and sex. For example, the 60th percentile for height means about 60 out of 100 children in that group were shorter.

Enter your child's age, sex, height and weight. The calculator works out three percentiles: height-for-age, weight-for-age and BMI-for-age. BMI (body mass index) compares weight with height. It uses the CDC's own published tables and shows every step. A percentile is a comparison, not a verdict on health. Talk to your child's doctor about any questions on growth.

Where it's used

Why this math matters outside the classroom:

  • Well-child visits. A nurse finds that a 5-year-old boy who is 110 cm tall sits near the 59th percentile on the CDC height chart.
  • Statistics class. Students turn a z-score of 1.0 into a percentile with the normal curve and get about 84.
  • Reading a median. A parent sees that the CDC median height for a 12-year-old boy is about 149 cm, the 50th percentile.
  • Skewed data. Nutrition students see how the L value reshapes lopsided weight data into a bell curve before z is found.
  • Public health research. Researchers turn thousands of survey measurements into z-scores so children of different ages can be compared on one scale.

Grade level and standards: Grade 12 to college; Common Core State Standards for Mathematics HSS.ID.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose US units (inches and pounds) or metric units (centimeters and kilograms).
  2. Choose boy or girl, since the CDC charts are separate for each.
  3. Enter the age in years, plus any months past the last birthday.
  4. Enter the height and weight, then read the three percentiles and the median for that age.

What the inputs mean

Sex
The CDC charts are separate for boys and girls.
Age (years)
The charts cover ages 2 to 20 years. For children under 2, doctors in the US usually use the WHO charts, which this calculator does not include.
Plus months
Months add precision, because children grow quickly. Six months can move a young child's percentile noticeably.
Height
Measure standing, without shoes, back against a wall. The CDC charts for ages 2 to 20 use standing height, not length lying down.
Weight
Weigh in light clothing, without shoes. A home scale is fine for a rough check, but clinic measurements are more consistent.

Formula and method

z = ((X ÷ M)^L − 1) ÷ (L × S)
percentile = Φ(z) × 100
BMI = weight (kg) ÷ height (m)²
X = the child's measurement   M = median for that age and sex
L = curve shape   S = spread   Φ = bell-curve share below z

The CDC describes each growth curve with three numbers for each month of age. M is the median, the middle value: half of the reference children were below it. S describes how spread out the measurements are. L corrects for curves that are lopsided, which matters most for weight and BMI.

The first formula turns the child's measurement into a z-score. A z-score counts how far a value sits from the middle, in standard steps. Zero is exactly at the median. Then the bell curve, also called the normal distribution, turns the z-score into a percentile.

The CDC lists values at ages such as 101.5 and 102.5 months. For an age in between, the calculator takes the point on a straight line between the two rows.

Worked example

A girl is 8 years 6 months old, 50 in tall and weighs 60 lb.

  1. Age in months: 8 × 12 + 6 = 102 months.
  2. Height in centimeters: 50 × 2.54 = 127 cm.
  3. CDC values for girls at 102 months: L = −0.004119, M = 130.3361 cm, S = 0.046304.
  4. z = ((127 ÷ 130.3361)^−0.004119 − 1) ÷ (−0.004119 × 0.046304) = −0.560.
  5. The bell curve puts 28.8% of the reference group below z = −0.560, so the height-for-age percentile is 28.8.
  6. Weight (27.216 kg) and BMI (16.87) work the same way, giving percentiles of 49.8 and 65.2.

Result: Height-for-age is at the 28.8 percentile, weight-for-age at 49.8 and BMI-for-age at 65.2. The median height for a girl of this age is 51.3 in.

Understanding the result

There is no "right" percentile. A child at the 20th percentile and a child at the 80th can both be growing well. Doctors usually care most about whether a child follows roughly the same curve over time.

A big jump or drop across several curves between visits is the kind of change worth asking about. So is a reading near the edges of the charts. Talk to your child's doctor rather than reading too much into a single number.

Height and weight percentiles don't have to match. A tall, slim child might be at the 80th for height and the 40th for weight.

Assumptions and limitations

  • The reference group is the one behind the CDC 2000 growth charts, based on US children measured in national surveys.
  • L, M and S change in a straight line between the half-month ages in the CDC table.
  • US units are converted exactly: 1 in = 2.54 cm and 1 lb = 0.45359237 kg.
  • It does not diagnose anything or label weight status. Only your child's doctor can interpret growth in context.
  • Percentiles below the 3rd or above the 97th lie beyond the curves the CDC draws, so they are less precise.
  • For very high BMI values, the CDC also publishes extended BMI-for-age charts. This calculator uses only the original 2000 tables.
  • It doesn't cover children under 2, and it doesn't use special charts made for some medical conditions.

Frequently asked questions

What does a growth percentile mean?

It is the share of children of the same age and sex in the reference group who measured less. At the 70th percentile for weight, about 70 out of 100 weighed less and about 30 weighed more. It compares; it doesn't judge.

Is a low or high percentile a problem?

Not on its own. Healthy children are found all across the chart. Doctors look at the pattern over several visits, the parents' heights and the child's overall health. If you're worried, talk to your child's doctor.

Why does my doctor's chart show a slightly different number?

Small differences usually come from the exact age used, rounding, or how the measurement was taken. Some clinics also use other charts, such as the WHO charts. A difference of a few percentile points is normal.

What is BMI-for-age?

BMI compares weight with height. In children it changes a lot with age, so the number alone isn't compared with adult ranges. Instead it's turned into a percentile among children of the same age and sex.

Sources

How this calculator is checked

Method: CDC 2000 growth charts LMS method: z = ((X/M)^L − 1)/(L·S), or ln(X/M)/S when L = 0, and percentile = Φ(z) × 100. L, M and S for ages 24–240 months from the CDC's own data files statage.csv, wtage.csv and bmiagerev.csv (https://www.cdc.gov/growthcharts/data/zscore/, downloaded 2026-10-26, SHA-256 hashes in src/lib/health/cdc-growth.ts), linearly interpolated between table ages. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-26. Found a problem? Tell us.

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