How Tall Will a Child Be? The Arithmetic Is Easy; the Error Bar Is the Story

The formula, and where the constant comes from

Tanner, Goldstein and Whitehouse published the method in 1970 in the Archives of Disease in Childhood, and it has barely changed since. Take the two parents' heights, average them, and then shift the answer by half the average adult height difference between men and women: up for a boy, down for a girl. Tanner used 6.5 cm, which is half of 13 cm. American paediatric practice writes it differently — add 5 inches to the mother's height, then average with the father's for a boy; subtract 5 inches from the father's, then average, for a girl — but that is the same operation with a 2.5-inch shift instead of a 2.56-inch one. For a father of 5'10" and a mother of 5'5", the two routes give 70.0 and 70.06 inches. The difference is a sixteenth of an inch and you should ignore it.

The constant is worth a moment, because it is a population parameter and people treat it as a law of nature. It is half the adult male–female height gap, and that gap is not the same everywhere. Reading the NCD Risk Factor Collaboration's country file for the 1996 birth cohort: France 14.9 cm, Germany 14.0, the Netherlands 13.8, the United States 13.6, Italy 13.2, Spain 13.2. Halve those and you get 7.5, 7.0, 6.9, 6.8, 6.6 and 6.6 cm against Tanner's 6.5. Portugal is the outlier in that file at 9.9 cm, which would halve to 5.0 — though Portugal's own uncertainty intervals (172.9 cm for men, 163.0 for women, each about ±1.4 cm) make it the least certain figure of the seven, so treat it as a caution rather than a correction. The practical reading is that the sex constant is right to within about a centimetre in most of Europe and North America, and that a centimetre is nothing next to the interval that comes in the next section.

The error bar, which is the whole article

Tanner never claimed the target was a prediction. His own paper attached a band of ±3.3 inches to it, described as the spread from the 3rd to the 97th centile of where children of those parents end up. Later work has generally widened rather than narrowed it: the figures you see quoted today are around ±3.5 inches for girls and ±4 inches for boys, and modern re-derivations put the 95% prediction interval close to ±4 inches. Take the wider figure and work it through. Our boy's target was 5'10". Add and subtract 3.9 inches and you get 5'6.1" to 6'1.9". Now score that band against measured adult men — the NCD-RisC file gives a mean of 5'9.7" for American men born in 1996, and measured national growth studies put the standard deviation at about 2.8 inches. The band runs from the 9th centile to the 94th. It contains 84% of adult men.

That is the sentence the whole article exists for. A number that spans 84% of the population is not a prediction about a person; it is a near-tautology dressed as one. Narrow it to Tanner's original ±3.3 inches and the coverage only falls to 77%. The empirical work agrees: Wright and Cheetham measured 419 eight- and nine-year-olds against their parents' reported heights and found 90% of the children within 1.5 standard-deviation scores of the mid-parental figure — about two centile spaces on a growth chart, in either direction. Their more uncomfortable finding was that the method degrades exactly where you most want it: children of very tall or very short parents regress toward the population mean, so for the families most likely to be worried, the mid-parental target is systematically wrong in a predictable direction.

Bone age: what clinics use when they need a real number

The mid-parental target uses no information about the child at all. Bone-age methods do, and that is where their accuracy comes from. A radiograph of the left hand and wrist shows how far the growth plates have matured; comparing it against the Greulich–Pyle atlas, or scoring the individual bones with the Tanner–Whitehouse system, gives a skeletal age that may be a year or two ahead of or behind the calendar. That maturity reading is the missing variable: a child who is short but skeletally young still has growth in front of them, while a child who is tall and skeletally advanced has less left than their current height suggests. The Bayley–Pinneau tables, published in 1952, convert current height and bone age into a predicted adult height, and the Tanner–Whitehouse and Roche–Wainer–Thissen methods do the same with different weightings.

How much better is it? Bramswig and colleagues, in the Journal of Pediatrics in 1990, followed boys and girls with untreated short stature and constitutional delay to their adult heights and compared the predictions: mean errors of −0.8 cm for Bayley–Pinneau and −2.1 and −1.8 cm for the two Tanner–Whitehouse variants. Those are small numbers, and they are also mean errors — the average of over- and under-predictions across a group, which is not the same as the error on one child. Individual errors are several times larger, and every one of these methods performs worse in disease, at the extremes of stature, and in populations unlike the ones it was built on. Bone age is better than mid-parental arithmetic, not exact. And it requires an X-ray, which means it needs a clinical reason: it is a test a paediatric endocrinologist orders when the answer will change what happens next, not something to satisfy curiosity.

There is a middle option worth knowing about. The Khamis–Roche method, published in 1994, predicts adult stature from the child's current height and weight together with the mid-parental height, and needs no radiograph at all. It is more accurate than the mid-parental target alone, because it uses the child, and less accurate than a bone-age method, because it cannot see the growth plates. Most consumer height calculators, including ours, are working in this territory: better than a single line of arithmetic, still nowhere near a clinical assessment.

Children keep out-growing the target

There is a bias built into the method that no error bar covers. Mid-parental height assumes the child will grow up in the same conditions as the parents did, and for most of the last century that has been false. Take the NCD Risk Factor Collaboration's country file and compare the 1966 birth cohort — roughly today's parents — with the 1996 cohort, roughly today's young adults. French men gained 3.2 cm in one generation, Spanish men 3.0, Italian men 2.8, Portuguese men 2.2. Women gained too: 3.3 cm in Italy, 2.1 in Spain, 2.0 in Portugal. A mid-parental target computed in France or Spain has therefore been running two or three centimetres low, systematically, for as long as the trend has held.

The trend is not universal and it is not permanent, which is the interesting part. Over the same generation, German men gained 1.4 cm and German women 0.1 cm; Dutch men gained 0.7 and Dutch women 0.1; American men lost 0.2 cm and American women 0.4. The Netherlands is the documented case: Schönbeck and colleagues, in Pediatric Research in 2013, titled their paper on the fifth Dutch growth study "the world's tallest nation has stopped growing taller", and the flat line since has held. So in the United States and the Netherlands the mid-parental method is roughly unbiased, and in southern Europe it still runs low. Over a full century the numbers are startling — Spanish men gained 14.3 cm between the 1896 and 1996 birth cohorts, Portuguese men 14.0, French men 13.3, American men only 6.1 — but the generational figure is the one that matters when you are looking at one child and their two parents.

Predicting an adult height is not monitoring growth

These are two different activities and they get confused constantly. Predicting adult height asks a question about a single point far in the future, and the answer comes with the interval you have just seen. Monitoring growth asks whether a child is following their own line, and the answer comes from repeated measurements plotted over months and years. The second is what clinics actually do, and it is far more informative, because the signal is in the slope rather than in any single point. A child who has tracked steadily along the 25th centile since infancy is usually fine, whatever a prediction says. A child who was on the 75th at three and is on the 25th at six is a question, even though both readings are unremarkable on their own.

That is why the growth-centile article in this section spends its time on how a centile is computed and what a series of them means, and why the paediatric charts published by the Royal College of Paediatrics and Child Health and by national health services are designed as sequences of plotted dots rather than as prediction machines. If you have come here because a number worried you, the useful next step is not a better calculator. It is the growth record you already have, in front of the person who keeps it.

Frequently asked questions

Is the mid-parental formula accurate?

It is arithmetically exact and predictively very weak. The formula itself has no error — averaging two heights and adding 2.5 inches is not something that can go wrong. The published interval around the result is about ±4 inches at 95%, which around a typical target covers roughly 84% of adult men. It is a screening range, useful for noticing a child growing far outside their family pattern, not a forecast of an individual's adult height.

My child's prediction came out shorter than I expected. Should I worry?

Not on the strength of the number. A mid-parental target moves by a full inch if one parent's height was measured in shoes, and the interval around it is four inches wide in each direction. What does deserve attention is a change in a child's own growth line — a child who has drifted downward across centile lines over a year or two, or who has clearly stopped keeping up with classmates. That is a conversation with your paediatrician or family doctor, who will want the measurement record rather than a calculation.

Why do bone-age methods need an X-ray?

Because the thing they measure — how far the growth plates have closed — is only visible on a radiograph. A hand-and-wrist film shows the maturation stage of a couple of dozen bones, and that is what tells you how much growing is left, independently of how tall the child is today. It is a low-dose examination, but it is still an examination: it is ordered by a clinician when the answer will change management, not out of curiosity. The Khamis–Roche method exists precisely as a middle path for cases where no radiograph is justified.

Will my child be taller than the target because of the secular trend?

On average, in some countries, by a small amount. Comparing the 1966 and 1996 birth cohorts in the NCD-RisC data, men gained 3.2 cm in France, 3.0 in Spain, 2.8 in Italy and 2.2 in Portugal in one generation. In the United States and the Netherlands the trend has flattened — American men in that comparison were 0.2 cm shorter, not taller. So a two-to-three-centimetre upward correction is defensible in southern Europe and not in the US. It is also swamped by the ±10 cm interval, so it changes the average and not what you should expect for one child.

Do the parents' heights need to be measured, or is what they say good enough?

Measured is better, and the reason is documented. Validation studies consistently find that adults overestimate their own height — in NHANES data, men by about half an inch and women by about a quarter of an inch, with the overestimate larger in older and shorter people. Two parents each half an inch generous shift the mid-parental figure by half an inch, and the shift is always in the same direction. It is small against the interval, but it is free to avoid: measure both, without shoes, against a wall.

Does nutrition or sport change a child's adult height?

At the level of populations, unambiguously — the century of gains in the NCD-RisC data is largely a nutrition and childhood-illness story, and it is why Spanish men gained 14 cm in a hundred years while American men gained 6. At the level of one adequately fed child, there is no evidence that extra food, a supplement or a particular sport adds height, and some sports select for a body type rather than producing it. If you are concerned about a child's diet, that is a question for a doctor or a registered dietitian, and it is a question about health rather than about centimetres.