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 at the midpoint of the completed month for the selected CDC sex reference.
- S: the generalized coefficient of variation at that age and sex.
The calculator uses the full monthly CDC reference data. Enter whole completed years and extra completed months; a blank extra-month field means zero. The lookup uses the midpoint of that month (for example, 8 years 0 months uses 96.5 months). BMI is weight in kg divided by standing height in metres squared. At or below the 95th BMI percentile it uses LMS; above it, the CDC 2022 extended method uses P = 90 + 10 × Φ((BMI − P95) / σ). Its inverse is BMI = P95 + σ × Φ⁻¹((P − 90) / 10). Other inverse results use the LMS equation. Reference values are not recommended growth or weight targets. Height and weight estimates outside the published 3rd–97th curves extrapolate the reference model.
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 | 3rd percentile reference |
| -1.04 | 15th | Below average |
| 0.00 | 50th | Median for age and sex |
| 1.04 | 85th | Above average |
| 1.64 | 95th | 95th percentile reference |
| 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 percentile with kg, the calculator selects the girls' CDC row at 96.5 months. A weight of 25.7 kg gives a z-score of about −0.0129 and the 49.49th percentile. This is close to the reference median.
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 accepts ages 2 years 0 months through 19 years 11 months (24 to 239 completed months). It uses CDC 2000 height and weight references and the CDC 2022 extended BMI method. For children under 2 years, CDC recommends WHO growth standards; use an age-appropriate tool and clinical guidance.
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 reading cannot assess growth or health. A clinician interprets the pattern over time, measurement quality, medical history and other findings. BMI categories are screening categories, not diagnoses.
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. The selection identifies the CDC reference used for the estimate. Percentiles compare with that reference population, not every child today.
