Child BMI-for-Age Calculator
Calculate Body Mass Index (BMI) and the corresponding age- and sex-specific percentile for children and adolescents aged 2–19 years using CDC growth chart LMS parameters.
Formula
Step 1 – BMI:
BMI = weight (kg) / height² (m²)
Step 2 – Z-score via CDC LMS method (Box-Cox power transformation):
If L ≠ 0: Z = [ (BMI / M)L − 1 ] / (L × S)
If L = 0: Z = ln(BMI / M) / S
where L (Box-Cox power), M (median), and S (coefficient of variation) are age- and sex-specific parameters from the CDC 2000 growth charts, linearly interpolated to the child's exact age in months.
Step 3 – Percentile:
Percentile = Φ(Z) × 100, where Φ is the standard normal CDF.
Step 4 – Weight Status (CDC thresholds):
- Underweight: < 5th percentile
- Healthy Weight: 5th – <85th percentile
- Overweight: 85th – <95th percentile
- Obese: ≥ 95th percentile
Healthy weight range is back-calculated from the 5th and 85th percentile BMI values (Z = −1.6449 and +1.0364) at the child's current height using the inverse LMS formula: BMI = M × (1 + L × S × Z)1/L.
Assumptions & References
- LMS parameters are sourced from the CDC 2000 Clinical Growth Charts for children aged 2–20 years (Kuczmarski et al., 2002).
- Parameters are linearly interpolated between 6-month tabulated values to the child's exact age in months.
- The standard normal CDF is approximated using the Horner-form Hart (1968) rational approximation (max error < 1.5 × 10⁻⁷).
- BMI-for-age percentile is not a diagnostic tool; clinical assessment by a qualified healthcare provider is required.
- This calculator applies to children aged 2–19 years only. Adult BMI thresholds (≥20 years) differ and are not used here.
- Imperial inputs are converted: 1 lb = 0.453592 kg; 1 in = 0.0254 m.
- References:
- CDC Growth Charts: https://www.cdc.gov/growthcharts/
- Kuczmarski RJ et al. (2002). 2000 CDC Growth Charts for the United States. Vital Health Stat 11(246).
- Must A, Dallal GE, Dietz WH (1991). Reference data for obesity: 85th and 95th percentiles of BMI. Am J Clin Nutr 53:839–846.