What is my child’s weight percentile?

How it works

1. Age in months. Enter the age as years and months (months may have decimals), or as a birth date and a measurement date:

• age in months = 12 × years + months, or
• age in months = (measurement date − birth date, in days) ÷ 30.4375.

No answer if the measurement date is before the birth date, or if the age is over 240 months (20 years).

2. The chart. Under 24 months the calculator uses the WHO weight-for-age standard; from 24 months to 240 months, the CDC 2000 weight-for-age chart. These are the tables named in the sources, used exactly as published:

• WHO: one row per whole month, 0 to 24, with L, M and S for boys and for girls.
• CDC: rows at 24 months, then at 24.5, 25.5, 26.5 and so on up to 239.5, then at 240 months.

3. L, M and S at the age. At a table age the row is used as it is. Between two table ages a₀ < a < a₁, each of L, M and S is read on a straight line: L = L₀ + (a − a₀) ÷ (a₁ − a₀) × (L₁ − L₀), and the same for M and S.

4. The z-score and percentile (the LMS method, as the CDC data files describe it), with the weight x in kilograms:

• z = ((x ÷ M)^L − 1) ÷ (L × S), or z = ln(x ÷ M) ÷ S if L is 0;
• percentile = Φ(z) × 100, where Φ is the standard normal cumulative distribution.

The percentile is rounded half up to one decimal place (the decimal value decides), and then kept between 0.1 and 99.9: a percentile that rounds above 99.9 shows as 99.9, and one that rounds below 0.1 shows as 0.1. The z-score is shown to two decimal places.

5. Other rows.

• Median weight at this age = M.
• 5th and 95th percentile weights = M × (1 + L × S × z)^(1/L) with z = −z₉₅ and +z₉₅, where z₉₅ = Φ⁻¹(0.95), the exact inverse normal value 1.6448536269514727… (the engine uses the nearest double, 1.6448536269514729).
• Screening range, read from the shown percentile p: on the WHO chart (under 24 months), "Below the 2.3rd percentile" if p < 2.3, "Above the 97.7th percentile" if p > 97.7, otherwise "Between the 2.3rd and 97.7th percentiles"; on the CDC chart, the same with 5 and 95 ("5th", "95th"). These are the cut-offs the CDC suggests for screening (MMWR 2010).
• Age: the age in months rounded half up to one decimal place, written as years and months ("4 years 2.5 months", "9 months", "12 years").
• Growth chart: "WHO weight-for-age (birth to 24 months)" or "CDC weight-for-age (2 to 20 years)".

The chart on the page shows the standard normal curve with the area to the left of the child’s z-score shaded: that area is the percentile.

Rounding. Every “rounded half up” on this page reads the decimal value: a result within 1e-9 (relative) of a half counts as the half. For example, 80 ÷ 1.6², which a computer stores as 31.249999999999993, rounds to 31.3.

Assumptions

• Φ is computed with Marsaglia’s series (J Stat Softw 2004), which matches the exact value to within 5e-15; percentiles beyond z = ±8 show as 0.1 or 99.9.
• Weights are without clothes or shoes. The WHO standard describes healthy breastfed babies; the CDC chart describes US children measured from 1963 to 1994.
• A single percentile is a snapshot. Doctors look at the pattern over several visits.
• This calculator gives general information. It is not medical advice or a diagnosis; talk to your child’s doctor about their growth.

Worked examples by hand

A 6-month-old boy who weighs 6.611702 kg (14.6 lb). The WHO boys’ row for month 6 is L = 0.1257, M = 7.934, S = 0.10958. (6.611702 ÷ 7.934)^0.1257 = 0.977343; minus 1 = −0.022657; ÷ (0.1257 × 0.10958 = 0.013774) gives z = −1.6449. Φ(−1.645) = 0.0500, so the percentile is 5.0, the table’s own 5th percentile. It is between the 2.3rd and 97.7th percentiles. The median is 7.934 kg, and the 5th and 95th percentile weights are 6.612 and 9.482 kg.

A girl of 9 years 6.5 months (114.5 months) who weighs 40.9331551 kg (90.2 lb). The CDC girls’ row for 114.5 months is L = −0.902197638, M = 31.0403221, S = 0.191041375. (40.9331551 ÷ 31.0403221)^−0.902197638 = 0.779116; minus 1 = −0.220884; ÷ (−0.902197638 × 0.191041375 = −0.172357) gives z = 1.2816, so the percentile is 90.0, the table’s 90th percentile. It is between the 5th and 95th percentiles.

A boy born January 15, 2024, weighed at 30 lb (13.608 kg) on July 15, 2026. The dates are 912 days apart, so the age is 912 ÷ 30.4375 = 29.963 months, which shows as 2 years 6 months. It falls between the CDC boys’ rows for 29.5 and 30.5 months, 0.463 of the way along; the straight line gives L = −0.378371, M = 13.488022, S = 0.109220. z = ((13.608 ÷ 13.488)^−0.378371 − 1) ÷ (−0.378371 × 0.109220) = 0.0808, and the percentile is 53.2.