Calculate your child’s height, weight, and BMI percentile by age and sex using CDC growth chart data.
Child Growth Percentile Formula
A growth percentile is found with the LMS method used by the CDC growth charts. Each measurement is first turned into a z-score, and the z-score is then converted to a percentile using the standard normal distribution.
Z = ((X / M)^L - 1) / (L * S) when L is not 0
Z = ln(X / M) / S when L = 0
The percentile is the area under the standard normal curve to the left of Z, multiplied by 100. To work backward from a percentile to a measurement, the same parameters are rearranged:
X = M * (1 + L * S * Z)^(1 / L)
- Z: the z-score, or number of standard deviations from the median for that age and sex.
- X: the child’s measurement (height in cm, weight in kg, or BMI in kg/m2).
- L: the power in the Box-Cox transformation, which corrects for skew in the distribution.
- M: the median measurement for the child’s exact age and sex.
- S: the generalized coefficient of variation at that age and sex.
The calculator looks up the L, M, and S values for the child’s age in months and sex, fills in the measurement you enter, and returns the z-score and percentile. For BMI mode it first computes BMI from height and weight, then applies the same formula to the BMI value. The reverse mode asks for a target percentile, converts it to a z-score, and solves for the matching measurement.
Z-Score and Percentile Reference
The z-score from the formula maps to a single percentile. The values below show how common z-scores line up with percentiles, and the weight-status bands the CDC uses for BMI-for-age.
| Z-score | Percentile | Meaning |
|---|---|---|
| -1.88 | 3rd | Low end of the typical range |
| -1.04 | 15th | Below average |
| 0.00 | 50th | Median for age and sex |
| 1.04 | 85th | Above average |
| 1.64 | 95th | High end of the typical range |
| BMI-for-age percentile | CDC weight status |
|---|---|
| Less than 5th | Underweight |
| 5th to less than 85th | Healthy weight |
| 85th to less than 95th | Overweight |
| 95th or higher | Obesity |
Example Problems
Example 1. A girl is 8 years old and weighs 25.7 kg. Using weight-for-age mode in metric units, the calculator finds the L, M, and S values for a girl at 96 months. The median weight is about 25.6 kg, so 25.7 kg gives a z-score near 0.02 and a percentile of about 51. She weighs slightly more than half of girls her age.
Example 2. A boy is 12 years old, 58 inches tall, and weighs 90 pounds. In BMI-for-age mode with US units, the calculator converts the height and weight, computes a BMI of about 18.8 kg/m2, and returns roughly the 65th percentile. That falls in the healthy weight band, since it is below the 85th percentile.
Frequently Asked Questions
What ages does this calculator cover? It covers children and teens from 2 through 20 years, the range of the CDC 2000 growth charts for height, weight, and BMI. For infants under 2 years, clinicians usually use the WHO growth standards instead, so use a birth-to-24-month tool for that age group.
Is a high or low percentile a problem? Not by itself. A percentile only describes where a child falls compared with others of the same age and sex. A single value at the 10th or 90th percentile can be perfectly healthy. Growth that is tracking steadily along a percentile over time matters more than any one reading, and a sudden jump or drop across percentiles is what usually prompts a closer look.
Why do boys and girls use different numbers? Height, weight, and BMI distributions differ by sex at every age, so the CDC publishes separate L, M, and S parameters for boys and girls. Selecting the correct sex is required for an accurate percentile.
