WHO Weight-for-Age Z-Score Calculator

The World Health Organization growth standards describe how children should grow under good nutrition and care, based on the Multicentre Growth Reference Study (2006). The weight-for-age z-score says how far a child’s weight sits from the median for their age and sex, in standard deviation units.

The LMS formula

Child weight is skewed, with a longer tail on the heavy side, so the WHO does not use a plain mean and standard deviation. For every month it publishes three numbers: L (the skew), M (the median) and S (the spread). Then

z = ((weight ÷ M)^L − 1) ÷ (L × S)

Beyond 3 standard deviations either way the WHO stops trusting the skew curve and extends the scale in a straight line, using the distance between the 2 and 3 SD weights. This calculator does the same, and uses the official monthly L, M and S values from birth to 60 months, with a straight line between months for an age in between.

A z-score of 0 means the child is exactly at the median. Z = +1 is about the 84th percentile, and Z = −2 about the 2.3rd percentile, the conventional cut-off for underweight.

WHO interpretation:

• Z above +2: heavier than expected for age. The WHO does not use weight-for-age to judge overweight; weight-for-length or BMI-for-age does that job.
• −2 to +2: within the normal range
• −3 to −2: underweight
• Below −3: severely underweight

Severe acute malnutrition is diagnosed from weight-for-length, mid-upper arm circumference or swelling of both feet, not from weight-for-age, but a reading below −3 always needs prompt assessment.

Worked example: a 12-month-old boy weighing 9.6 kg. The WHO values at 12 months are L = 0.0644, M = 9.6479 kg and S = 0.10925.
z = ((9.6 ÷ 9.6479)^0.0644 − 1) ÷ (0.0644 × 0.10925) = −0.0003205 ÷ 0.0070357 = −0.05, the 48th percentile. Right at the median.

Limitations:

• For ages beyond 60 months, BMI-for-age replaces weight-for-age as the better indicator.
• Weight-for-age alone does not separate wasting (low weight-for-length, recent weight loss) from stunting (low length-for-age, long-term undernutrition). A short, well-nourished child and a thin child of normal length can share the same weight-for-age.
• Premature infants need their age corrected for gestation up to 2 years; the standards apply to term infants from birth.

Routine well-child visits track z-scores over time. A falling trend across visits is more concerning than a single low number with a steady curve. For a baby’s weight and length on one chart, see the Infant Growth Percentile Tracker, which uses the same WHO values and gives the same answer for weight.