A z-score tells you how many standard deviations (SDs) your baby's measurement is from the median for their age and sex. A z-score of 0 is the median, the 50th percentile. A z-score of −2 is about the 2.3rd percentile, and +2 is about the 97.7th. A 12-month-old girl who weighs 7.9 kg (17 lb 7 oz) has a weight-for-age z-score of about −1.0, the 15th percentile on the WHO growth standards. She's smaller than average and well inside the normal range.
Z-scores and percentiles describe the same spot on the chart in different units. US pediatricians mostly use percentiles; the WHO and growth specialists prefer z-scores, especially near the edges of the chart. The WHO's weight-for-age z-score charts show the median (0) and lines at ±2 and ±3.
Z-score to percentile conversion table
Every z-score matches exactly one percentile, because growth z-scores follow the standard normal distribution (CDC). Negative z-scores (below the median) are on the left, their positive mirror images on the right.
| Z-score | Percentile | Z-score | Percentile | On the chart |
|---|---|---|---|---|
| −0.5 | 30.9th | +0.5 | 69.1st | |
| −0.67 | 25th | +0.67 | 75th | CDC lines |
| −1 | 15.9th | +1 | 84.1st | |
| −1.04 | 15th | +1.04 | 85th | WHO lines |
| −1.28 | 10th | +1.28 | 90th | CDC lines |
| −1.5 | 6.7th | +1.5 | 93.3rd | |
| −1.64 | 5th | +1.64 | 95th | CDC lines |
| −1.88 | 3rd | +1.88 | 97th | WHO lines |
| −2 | 2.3rd | +2 | 97.7th | The usual cutoffs (printed as 2nd and 98th on US WHO charts) |
| −2.5 | 0.6th | +2.5 | 99.4th | |
| −3 | 0.13th | +3 | 99.87th | WHO severe cutoffs; WHO percentiles stop here |
Source: standard normal distribution (CDC); lines and cutoffs from the CDC, WHO and WHO/UNICEF.
To convert any z-score, enter =NORM.S.DIST(z, TRUE) in Excel or Google Sheets and multiply by 100; =NORM.S.INV(percentile/100) goes the other way.
Notice how unevenly the percentiles move. Going from 0 to −1 drops 34 percentile points. Going from −2 to −3, the same one-SD step, drops just over 2.
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What a z-score means for your baby
An SD measures how spread out healthy babies' measurements are. About 68 in 100 healthy children fall between −1 and +1, and about 95 in 100 between −2 and +2 (WHO/UNICEF).
- Negative means below the median, not "bad." A z-score of −1 is about the 16th percentile: roughly 1 in 6 healthy babies measure less.
- The size of the number is the distance from the middle. −0.3 is close to average; −2.5 is far from it.
- Each measurement gets its own z-score: weight, length, head circumference and weight-for-length.
The trend matters more than any single value. Here's the girl from the opening, followed from birth:
Weight-for-age, girls, birth to 12 months
Her z-score is −1.0 at birth (the 16th percentile), −1.1 at 6 months (the 14th) and −1.0 at 12 months (the 15th). A z-score that holds steady means a baby is growing along their own curve.
A z-score that keeps falling is what "crossing percentile lines" looks like in numbers. Falling across two major lines is the usual trigger for a closer look (AAFP); on a WHO chart, falling from the 50th line to below the 15th is a drop of more than 1 z-score. See babies who drop on the growth chart.
Why doctors and the WHO use z-scores
Percentiles are easier to explain. Z-scores do several things percentiles can't.
1. Equal steps. Each z-score unit is the same statistical distance. For 12-month-old girls, the median weight is 8.9 kg (19 lb 12 oz), a z-score of −1 is 7.9 kg (17 lb 8 oz), −2 is 7.0 kg (15 lb 8 oz) and −3 is 6.3 kg (13 lb 13 oz). Each step down is a similar amount of weight, roughly 0.8 to 1 kg (about 2 lb), yet the percentile steps shrink from 34 points to 13.6 and then 2.1. Near the edge of the chart, a tiny percentile change can hide a real change in size.
2. Values beyond the edge of the chart. The WHO publishes percentiles only between z-scores of −3 and +3, the 0.13th to 99.87th percentiles (WHO). Z-scores keep going. A 9-month-old boy who weighs 6.2 kg (13 lb 11 oz) is below the 1st percentile, which says little. His z-score, about −3.25, shows how far below the chart he is: past the −3 line the WHO uses for severe underweight. Our guide to baby percentiles shows how z-scores can also reveal catch-up growth that percentiles hide.
3. Comparing different measurements. Every indicator uses the same unit, so z-scores line up side by side. Take a 12-month-old boy who weighs 8.9 kg (19 lb 10 oz), is 77.0 cm (30.3 in) long and has a head circumference of 46.0 cm (18.1 in):
- Length-for-age: +0.5 (the 70th percentile)
- Head circumference-for-age: −0.05 (the 48th)
- Weight-for-age: −0.7 (the 23rd)
- Weight-for-length: −1.3 (the 10th)
On one scale the picture is clear: he's long, with an average head and a lean build for his length, and all four are well within ±2. To line up your own child's measurements this way, get every WHO z-score at once.
4. Measuring change. Subtracting z-scores shows how far a child has moved against the standard. One UK study counted a rise of more than 0.67 in weight z-score between birth and age 2 as clinically significant catch-up growth (Ong et al., 2000).
5. Describing populations. Z-scores can be averaged, so national nutrition surveys report the mean z-score as well as the share of children below −2 (WHO/UNICEF).
WHO z-score cutoffs: stunting, underweight, wasting and overweight
The WHO defines growth problems in children under 5 with z-score cutoffs (WHO):
| Term | Measured by | Cutoff | Severe |
|---|---|---|---|
| Stunting | Length/height-for-age | Below −2 | Below −3 |
| Underweight | Weight-for-age | Below −2 | Below −3 |
| Wasting | Weight-for-length/height | Below −2 | Below −3 |
| Overweight | Weight-for-length/height | Above +2 | Above +3 |
Sources: WHO Nutrition Landscape Information System; severe categories from the WHO/UNICEF 2019 recommendations.
US pediatricians use the same ±2 cutoffs. On the WHO charts used under age 2 in the US, the lines labeled 2nd and 98th are really the 2.3rd and 97.7th percentiles (z-scores of −2 and +2), which the CDC recommends for flagging unusually low or high growth (CDC). From age 2, US children move to the CDC charts; see WHO vs CDC growth charts.
How z-scores are calculated: the LMS method
The WHO stores each growth standard as three numbers for every age (or length):
- L, a power that corrects for skew (lopsidedness)
- M, the median
- S, the spread, as a coefficient of variation
A measurement X becomes a z-score with one formula: z = ((X ÷ M)^L − 1) ÷ (L × S). This is the LMS method (Cole & Green, 1992), which the WHO's curves simplify to (WHO). Our step-by-step percentile guide works an example by hand.
- Length is symmetric. Length follows a normal distribution, so L = 1 and the SD lines are evenly spaced (WHO MGRS Group, 2006). For 9-month-old girls, the median is 70.1 cm (27.6 in) and one SD is about 2.4 cm (1 in), so a 1 cm measuring error shifts the z-score by about 0.4.
- Weight is skewed. There's a longer tail of heavy babies, so weight SD lines spread wider above the median than below. For 12-month-old girls, the steps below the median shrink (about 1.0, 0.9 and 0.8 kg) while those above grow (about 1.2, 1.4 and 1.6 kg).
Free tool
WHO Z-Score Calculator
Get WHO z-scores for weight, length or height, weight-for-length, BMI and head size from birth to 5 years.
A z-score is a screening number, not a diagnosis
The ±2 cutoffs are statistical: by design, they flag about 2.3% of healthy children at each end. The WHO and UNICEF note that children beyond them are counted as malnourished "even if they are apparently 'healthy' individuals with no growth impairment" (WHO/UNICEF).
So one z-score never makes a diagnosis. Your pediatrician will weigh it against the trend over several visits, weight-for-length, your family's build, your baby's birth size, feeding, development and an exam. Babies born early are plotted by corrected age through age 2 (AAP). If the evaluation does find a lasting problem with weight gain, see what a failure-to-thrive diagnosis means.
If your baby's z-score is below −2 or above +2, ask what it means for your child and when to recheck. For low numbers, see baby in a low percentile; for high ones, baby always in a high percentile. To read the whole chart, see how to read a child growth chart.
