The mid-parental height formula averages the heights of the two parents and adjusts the average by 13 cm according to the child's sex. The result is reported as the child's target adult height. For a boy: father's height plus mother's height plus 13 cm, divided by two. For a girl: the same sum minus 13 cm, divided by two.
The 13 cm adjustment is the average difference between adult male and female height in the populations on which the formula was developed. Pediatric guidance places a range of about plus or minus 10 cm, or four inches, around the target. A boy with a 178 cm target therefore has a range of 168 cm to 188 cm.
Origin of the formula
Tanner, Goldstein and Whitehouse published the method in 1970 to assess whether a child's current height was consistent with the parents' heights. Their standards covered children aged 2 to 9 years and were developed from British families. The method was designed to answer whether a child's present height is unusual given the parents, not to predict adult height. Its use as an adult-height predictor came later.
The 13 cm adjustment and the two-standard-deviation range are population values from that study. They have been broadly confirmed in later cohorts, but no part of the formula was fitted to predict an individual child's adult height.
Why the range is wide
The formula uses two inputs, both describing the parents, and none describing the child.
Most of the variation in adult height is therefore outside the formula. Siblings with the same parents commonly differ by 10 cm as adults. Nutrition, illness and the timing of puberty all affect the outcome, and none of them is represented. Parents also tend to overstate their own heights, which shifts the target without changing the reported range.
The 10 cm range is the observed spread of adult heights among children for whom only the parents' heights are known.
The predictor's primary estimate
The child height predictor reports the corrected Khamis-Roche estimate first. That equation uses the child's exact age, current height, current weight, and the average of the parents' heights. Including the child's own measurements reduces the error, because a child's current percentile carries information that the parents' heights do not.
Khamis and Roche (1994) reported average 90% absolute-error bounds of 2.10 inches for boys and 1.68 inches for girls across ages 4 to 17.5, about half the width of the mid-parental range. The calculator adds and subtracts the published bound for the child's sex. Error is smallest in mid-childhood and largest during puberty, when children of the same age differ most in maturation.
The equation was fitted to 223 boys and 210 girls from the Fels Longitudinal Study in southwest Ohio, all White. The calculator reports this on the result page. For a child from a different population, the error is likely to exceed the published figure, and no validated correction is available.
Where the mid-parental range remains useful
The formula's original purpose still applies. A child's current height percentile on the CDC 2000 reference may be far from the range implied by the parents' heights. That difference is a reason to talk to the child's pediatrician, whatever any adult-height estimate says. A child at the 5th percentile whose parents are near the 75th percentile presents a different picture from a child at the 5th percentile whose parents are near the 10th.
The predictor shows the mid-parental range alongside the Khamis-Roche estimate for this reason. When the two agree, the estimate is better supported. When they differ by more than the Khamis-Roche error bound, the child's own growth is moving the estimate away from the family average. The Khamis-Roche estimate is then the more informative of the two.
Limits of both methods
Neither method is diagnostic. A result outside the expected range is a reason to have growth assessed with serial measurements and, if a clinician considers it appropriate, a bone-age X-ray. Bone-age methods predict adult height more accurately than either formula and are the standard approach when the question has clinical importance.
Both methods assume typical growth. A child with a known growth condition, a chronic illness affecting growth, or unusually early or late puberty is outside the populations on which the formulas were developed. The predictor states this before reporting a result.