About GrowthPercentile.com
A free, open tool for parents and clinicians. Here's where the data comes from, how percentiles are calculated, and what the numbers mean.
Data Sources
All calculations use official reference data published by two organizations. No proprietary datasets or modifications are applied — the LMS parameters are used exactly as published.
WHO Child Growth Standards (Birth – 5 Years)
The WHO Child Growth Standards are based on the Multicentre Growth Reference Study (MGRS), which followed approximately 8,500 healthy breastfed children from six countries (Brazil, Ghana, India, Norway, Oman, and the United States) between 1997 and 2003. These standards represent how children should grow under optimal conditions regardless of ethnicity or socioeconomic status.
Charts available from WHO data on this site:
- Weight-for-age (wfa) — birth to 60 months
- Head circumference-for-age (hcfa) — birth to 60 months
WHO data was downloaded in tabulated format (monthly intervals) from the official WHO website and converted to JSON using a Python script. The original LMS parameter values are preserved without rounding or modification.
CDC Growth Charts (Birth – 20 Years)
The CDC 2000 Growth Charts are based on data from five US National Health Examination Surveys (NHES) and National Health and Nutrition Examination Surveys (NHANES) collected between 1963 and 1994. These charts describe how American children actually grew — a descriptive reference, not a prescriptive standard.
Charts available from CDC data on this site:
- Weight-for-age, infant (wtageinf) — birth to 36 months
- Length-for-age, infant (lenageinf) — birth to 36 months
- Head circumference-for-age, infant (hcageinf) — birth to 36 months
- Weight-for-length, infant (wtleninf) — 45–103.5 cm
- Weight-for-age (wtage) — 2 to 20 years
- Stature-for-age (statage) — 2 to 20 years
- BMI-for-age (bmiagerev) — 2 to 20 years
- Weight-for-stature (wtstat) — 77–121.5 cm
CDC LMS data was downloaded as CSV files from the CDC website and converted to JSON. Duplicate header rows present in some CDC files were automatically removed during conversion. The original L, M, and S parameter values are preserved exactly.
Which Chart Is Used When?
Following the recommendation of the American Academy of Pediatrics (AAP):
- Birth to 24 months: WHO growth standards are recommended as the primary reference. CDC charts are shown alongside for comparison.
- 2 to 20 years: CDC growth charts are used as the primary reference.
- BMI-for-age: Only CDC charts are applicable, and only from age 2 to 20 years. BMI is not clinically meaningful below age 2.
When both data sources are available for a child's age, both results are displayed. The recommended chart for that age range is clearly marked.
Calculation Methodology: The LMS Method
Both WHO and CDC growth charts use the LMS method developed by Tim Cole (1990). This statistical technique summarizes the distribution of a measurement (weight, height, BMI) at each age using three parameters:
- L (Lambda) — the Box-Cox transformation power that normalizes the data
- M (Mu) — the median value at that age
- S (Sigma) — the generalized coefficient of variation
These three values are pre-computed and published for each age/sex combination in the reference tables. Given a child's measurement, we compute a z-score using the following formula:
When L ≠ 0:
Z = ((X / M)L − 1) / (L × S)
When L = 0:
Z = ln(X / M) / S
Where X is the child's measurement (weight in kg, height in cm, or BMI in kg/m²).
Interpolation
When a child's exact age falls between two reference data points, the calculator uses linear interpolation on the L, M, and S parameters individually, then computes the z-score from the interpolated values. This provides smooth results at any fractional age rather than snapping to the nearest reference point.
Z-Score to Percentile Conversion
The z-score is converted to a percentile using the cumulative distribution function (CDF) of the standard normal distribution. This is implemented with an approximation based on the Abramowitz and Stegun method (Handbook of Mathematical Functions, 1964). A z-score of 0 corresponds to the 50th percentile (median), +1 to approximately the 84th percentile, and −2 to approximately the 2.3rd percentile.
BMI Calculation
Body Mass Index is calculated as:
BMI = weight (kg) / height (m)²
The resulting BMI value is then compared against CDC age-and-sex-specific LMS parameters to produce a percentile. BMI percentiles are only meaningful for children aged 2 to 20 years.
Height Prediction
The height predictor uses two methods:
- Growth curve projection: The child's current z-score on the stature-for-age chart is applied to the age-18 LMS parameters to project an adult height, assuming the child remains on their current growth curve.
- Mid-parental height: A simple genetic estimate using the average of both parents' heights, adjusted ±6.5 cm (2.5 in) for sex. This is a well-established clinical rule of thumb with a prediction range of approximately ±10 cm.
Interpreting Percentile Results
A percentile indicates the proportion of the reference population that a child's measurement equals or exceeds. For example, a child at the 75th percentile for weight weighs more than 75% of children of the same age and sex in the reference population.
| Percentile Range | Z-Score Range | Interpretation |
|---|---|---|
| < 3rd | < −1.88 | Below normal range — discuss with pediatrician |
| 3rd – 15th | −1.88 to −1.04 | Low-normal — may warrant monitoring |
| 15th – 85th | −1.04 to +1.04 | Normal range |
| 85th – 97th | +1.04 to +1.88 | High-normal — may warrant monitoring |
| > 97th | > +1.88 | Above normal range — discuss with pediatrician |
Single readings vs. trends: A single percentile reading is far less informative than a series of readings over time. A child consistently tracking at the 10th percentile is growing normally — they are simply smaller than average. Pediatricians watch for percentile crossing (moving across two or more major percentile lines over several visits), which can indicate a growth concern worth investigating.
BMI Percentile Categories (Ages 2–20)
The CDC defines the following BMI-for-age categories for children and teens:
- < 5th percentile: Underweight
- 5th to < 85th percentile: Healthy weight
- 85th to < 95th percentile: Overweight
- ≥ 95th percentile: Obese
Accuracy & Limitations
- All LMS parameters are sourced directly from the official WHO and CDC published data tables. No values have been modified, rounded, or estimated.
- The z-score to percentile conversion uses a polynomial approximation with maximum error of approximately 7.5 × 10⁻⁸ across the full range.
- Linear interpolation between reference ages introduces a negligible approximation compared to measurement uncertainty in clinical practice.
- All unit conversions (lb ↔ kg, in ↔ cm, oz ↔ g) use exact conversion factors.
- WHO length-for-age and BMI-for-age charts are not currently available on this site (data source was unavailable at launch).
- This calculator does not support corrected age for premature infants — parents of preterm babies should manually calculate corrected age before entering data.
- The height predictor uses growth-curve projection and mid-parental height methods. The Khamis-Roche method is not implemented as the required regression coefficients are not publicly available.
Privacy & Data Handling
GrowthPercentile.com performs all calculations entirely in your browser. No measurement data is transmitted to any server. No cookies are set for tracking purposes. The only data stored locally is an optional visit counter using your browser's localStorage, which you can clear at any time through your browser settings.
References
- Cole TJ. The LMS method for constructing normalized growth standards. Eur J Clin Nutr. 1990;44(1):45-60.
- WHO Multicentre Growth Reference Study Group. WHO Child Growth Standards: Length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age. Geneva: World Health Organization; 2006.
- Kuczmarski RJ, Ogden CL, Guo SS, et al. 2000 CDC growth charts for the United States: Methods and development. Vital Health Stat. 2002;11(246):1-190.
- Abramowitz M, Stegun IA. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Washington, DC: US Government Printing Office; 1964.
- Hermanussen M, Cole TJ. The calculation of target height reconsidered. Horm Res. 2003;59(4):180-183. (Mid-parental height method)