What the mid-parental formula can't tell you about your own child
Add the two parents' heights, add 13 cm if it's a boy, halve it. That is the mid-parental target. Almost every calculator on the web stops there. So does the one on the front page of this site, which I wrote, so I should say what it actually does: one set of parents gets one number, and every child those parents have gets that same number. Mother 165 cm, father 175 cm, boy: 176.5 cm. The shortest boy in his class and the tallest boy in his class both get 176.5.
The band usually printed around it is plus or minus 8.5 cm, so those parents read 168.0 to 185.0. Seventeen centimetres. Every boy of those two parents is handed the same seventeen.
The child's own measurement moves it. Below are nine children who all have those parents, run through the engine the iPhone app uses: CDC LMS stature tables, age in months, height today, and a stated puberty stage.
| Child | Age | Height now | Percentile now | Predicted adult | Range | Range width |
|---|---|---|---|---|---|---|
| boy | 8 | 120 | 8th | 172.4 | 168.9 – 175.9 | 7.0 |
| boy | 8 | 128 | 51st | 176.7 | 173.2 – 180.2 | 7.0 |
| boy | 8 | 137 | 94th | 181.4 | 177.9 – 184.9 | 7.0 |
| boy | 12 | 135 | 3rd | 169.0 | 165.9 – 172.1 | 6.1 |
| boy | 12 | 145 | 29th | 174.5 | 171.5 – 177.6 | 6.1 |
| boy | 12 | 155 | 79th | 179.8 | 176.7 – 182.9 | 6.1 |
| girl | 10 | 128 | 6th | 157.9 | 154.9 – 161.0 | 6.1 |
| girl | 10 | 138 | 50th | 163.4 | 160.3 – 166.5 | 6.1 |
| girl | 10 | 146 | 88th | 167.6 | 164.5 – 170.6 | 6.1 |
Look at the three eight-year-old boys. The one at the 8th percentile comes out at 172.4 cm. The one at the 94th comes out at 181.4. Nine centimetres between them, from parents the formula treats as one case. Their ranges are 7.0 cm wide. A boy who has sat on the 8th percentile for eight years has already told you something about where he is going, and the seventeen-centimetre window stops being an honest description of what we know. By twelve the ranges come down to 6.1 cm, because there is less growing left to be wrong about.
Where this breaks: it assumes the child stays on roughly the curve he is on now. A child crossing percentiles is the interesting case and the arithmetic has nothing useful to say about him. Take that one to a doctor.
Method: every row is predictAdultHeight from Height Predictor's own
engine, the same code the iPhone app runs. Percentiles and projections come from the CDC 2000 LMS
stature-for-age tables (2 to 20 years), the prediction blends the child's own projected curve with
the mid-parental target on a weight that rises with age and puberty stage, and heights are
reported to one decimal. The plus-or-minus 8.5 cm figure is the band commonly published with
the Tanner mid-parental target; see Wright CM, Cheetham TD, The strengths and limitations of
parental heights as a predictor of attained height, Arch Dis Child 1999.
Height Predictor on the App Store
The parents-only calculator on this site is free and needs no account.