Z-scores

Z-scores and percentiles from LMS reference parameters, with WHO's restricted extrapolation.

Z-score: 1.11
Percentile: 87th
Median: 9.4 kg

Illustrative LMS parameters (L 0.2, M 9.4, S 0.11), not a published growth reference.

Installation

bunx shadcn@4.22.1 add https://organui.com/r/z-scores.json

This adds lib/z-scores.ts, with no dependencies.

Usage

import { formatPercentile, lmsZScore, zToPercentile } from "@/lib/z-scores"

// L, M and S for the child's age and sex, from your reference tables.
const z = lmsZScore(10.6, [0.2, 9.4, 0.11], { restricted: true }) // 1.11
formatPercentile(zToPercentile(z!)) // "87th"

API Reference

Z-scores exports
Export	Description
`lmsZScore(value, lms, { restricted? })`	The z-score of a measurement. restricted applies WHO's extrapolation beyond ±3 SD, which WHO uses for weight-based indicators. Null for a non-positive value.
`lmsValue(lms, z)`	The measurement at a z-score, for drawing curves.
`zToPercentile(z)`	The standard normal cumulative distribution as a percentile, accurate to 1.5e-7.
`percentileToZ(percentile)`	The z-score of a percentile between 0 and 100.
`formatPercentile(percentile)`	Ordinals such as "34th", with "<0.1st" and ">99.9th" at the ends.

Notes

The file ships no reference data. Take L, M and S from the standard you use, such as WHO or CDC, under its terms; the growth chart's page says where to get them.

The growth chart uses this file for its z-scores and percentiles.