LMS Z-score and Percentile
Use L, M and S from the same vetted table, measure, age, sex and population. The units of X and M must match. Reference values are never automatically chosen.
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Calculation, provenance and source limitations
Equation
For L ≠ 0, Z = ((X/M)^L − 1)/(L × S); for L = 0, Z = ln(X/M)/S. Percentiles are derived from the standard normal CDF. X, M and S must be positive; L may be any finite number.
Worked CDC example
CDC 2000 male infant at age 9 months: X = 9.7 kg, L = −0.1600954, M = 9.476500305 kg, S = 0.11218624; Z approximately 0.2074 SD, percentile approximately 58.2151%.
Use and limitations
This is generic arithmetic only: no built-in age/sex reference table is selected. It does not implement WHO corrections, CDC 2022 extended BMI percentiles, diagnostic interpretation, or treatment thresholds. Tail calculations beyond ±3 SD may require source-specific handling. Use only correctly sourced, licensed population-specific coefficients.
Source and review
Method and example checked 2026-11-10.