Child Height Percentile Calculator — Growth Chart Tool

Formula

How this is calculated

The calculator looks up the reference median height (μ) and standard deviation (σ) for the given age and sex from an internal table calibrated to the CDC 2000 Growth Charts (Kuczmarski et al., Vital and Health Statistics, Series 11, No. 246). For ages between the 2-year anchor points in the table, both μ and σ are linearly interpolated. The z-score is computed as (height − μ) / σ, and the percentile is derived using the standard normal cumulative distribution function Φ(z) implemented with the Abramowitz & Stegun polynomial approximation (maximum error < 1.5 × 10⁻⁷).

For height-for-age at ages 2–20, the distribution is approximately normal (the Box-Cox L parameter is close to 1), so the Gaussian approximation is accurate in the middle of the distribution. The classification thresholds follow commonly cited pediatric convention: below P5 is considered short stature, P5–P95 is the normal range, and above P95 is tall stature. A height below P3 in a previously growing child warrants evaluation by a pediatrician to rule out growth hormone deficiency, hypothyroidism, or other conditions.

Limitations: reference values in the internal table are approximate (calibrated to published CDC charts but not the official digital dataset); clinical growth assessment should use the official CDC Growth Chart percentile calculators or WHO Anthro software. Height measurement technique matters — always measure standing height in the same way. Parental target height and growth velocity (rate of change over time) are clinically important but not captured here.