Mid-Parental Height Calculator: Four Published Versions of the Target Height Method, and the Range That Matters More Than Any of Them

Four published versions of the parental-height method for a child’s adult height — the Tanner-type 13 cm sex correction, the same with a 4.5 cm secular-trend allowance, the Dutch 2009 regression equations that build in regression towards the mean, and the correction recomputed from the measured 14.6 cm difference between adult men and women in the United States — all four computed, with the spread between them printed. At typical parental heights the spread is about 4.5 cm, and it reaches 10.5 cm for a girl with very short parents, where the Dutch equation drifts furthest from the rest. The prediction interval around any of them is 17 to 25 cm wide, which is nearly four times the disagreement on the narrower published basis and five and a half times it on the wider one, and that is the honest answer: a single centimetre figure for a child’s adult height is the misleading one. Metric and imperial, and no judgement about anybody’s height.

An estimated weight is what you use when a child cannot be weighed. It is an estimate from age or length, it carries a wide error in both directions, and a measured weight always replaces it. Check anything calculated from this figure against the measured weight as soon as one is available.

The four published versions, the two published ranges, and what each constant actually is

The four versions for a boy, across the range of parental heights

The same four versions for a girl

The two published statements of the target range, and what each implies

Where each figure on this page comes from, and what was deliberately left out

Why this page prints a range rather than a centimetre figure for a child’s adult height

There is more than one published version of the parental-height method, and the versions disagree by less than the method’s own uncertainty. That sentence is the whole page. Three of the four versions computed here are the parents’ mean height plus a constant: plus or minus 6.5 cm on the traditional 13 cm sex difference, plus a further 4.5 cm if a secular-trend allowance is carried, and plus or minus 7.3 cm if the constant is recomputed from the 14.6 cm difference actually measured between adult men and women in the United States in 2015 to 2018. The fourth, the Dutch 2009 regression equations, is the only one that does something structurally different. Across typical parental heights the four span about 4.5 cm for a boy and 5.3 cm for a girl. The prediction range around any single one of them is 17 to 25 cm wide. So the disagreement between methods is a quarter to a fifth of the uncertainty inside any one of them, and a reader who chooses carefully between calculators has optimised the small term and ignored the large one.

One widely repeated claim about these versions is simply false, and this page checked it rather than repeating it. The method is written down in several apparently different ways: add 13 cm to the mother’s height for a boy and average with the father’s; or average the two parents and add 6.5; or compute (father + mother + 13)/2. These are the same expression. Applying the correction before averaging and applying it after averaging give identical numbers, provided the constant is halved consistently, and any account of the method that presents them as rival versions is describing an artefact of notation. The real differences between published versions are two: the size of the constant, and whether a secular-trend term is added. The first is worth 0.8 cm between the traditional 13 cm and the measured 14.6 cm, and 0.15 cm between the metric 6.5 cm and the imperial two-and-a-half inches. The second is worth 4.5 cm, and for a girl it does something odd enough to deserve its own sentence: added to a correction of −6.5 cm it leaves −2 cm, so on that version a girl’s predicted adult height is only 2 cm below her parents’ mean rather than 6.5 cm below. That is the largest disagreement between any two published versions of this method, it falls entirely on girls, and it is invisible on any page that computes one version.

The Dutch 2009 equations are the one version that takes regression towards the mean seriously, and they take it towards a Dutch mean. Their coefficients sum to less than one — 0.376 plus 0.411 for a boy — so the prediction moves only about four fifths of the way with the parents and the remainder is carried by the intercept, which encodes the population’s own adult mean. This is the statistically right shape: the children of unusually tall parents are on average closer to the population mean than their parents, and a method that shifts the parents’ mean by a constant cannot represent that. Feed the equations the Dutch adult means of 183.8 and 170.6 cm and they return 183.7 cm for a boy and 170.6 for a girl, reproducing those means and agreeing with the plain method to within 0.03 cm — the two versions cross exactly at the population they were fitted on. Away from it they separate, and the direction depends on which side you are: for parents of 170 and 155 cm the Dutch equation predicts 172.1 cm for a boy against the plain method’s 169.0, because it is pulling towards a population about 15 cm taller. The mother-only version is worse: for a mother of 142 cm it still returns 169.8 cm for a boy, because almost all of the population mean sits in its intercept. The paper that publishes these equations says they can be adapted to another population if that population’s final height is known, and presents no validation outside the Netherlands. No equivalent equation fitted on an Indian or South Asian population could be found for this page, and that gap is recorded rather than filled with a guess.

The target range is the output that matters, and the two published statements of it do not agree. The clinical literature quotes a target range of 8.5 cm either side of the prediction, described as two standard deviations around the target height — which implies a prediction-error standard deviation of about 4.25 cm and a window 17 cm wide. The empirical statement is different: in 419 children aged 8 to 9, 90% of the children’s heights fell within 1.5 standard deviation scores of the mid-parental height. Converting that to centimetres needs a standard deviation of adult height, and with 8.27 cm for men — derived on this page from published United States percentiles and disclosed as a derivation — it gives 12.4 cm either side, a window 24.8 cm wide, implying a prediction-error standard deviation near 7.5 cm. Those two cannot both be right; they differ by about three quarters. A theoretical figure from the published correlations sits between them: with a parent-offspring correlation of 0.58 and a correlation between the parents’ own heights of 0.19, roughly 43% of the variance in a child’s adult height is unexplained by the parents, which corresponds to a residual standard deviation around 4.7 cm. This page prints both published intervals and names the discrepancy, rather than choosing the narrower one because it looks better. Whichever is right, the conclusion is the same: a prediction stated to the nearest centimetre is false precision, and the page’s own headline flag says so.

The method is weakest in exactly the situation that sends people looking for it. The study that produced the 1.5 standard deviation score figure also found that where parents were unusually tall or short, their children were relatively less tall or less short, and that the mid-parental height was then a poor predictor of attained height. Its authors’ conclusion is worth quoting in substance: parental height gives useful guidance for families of average stature but can be misleading when used to assess short children. A parent of average height rarely searches for this calculation. A parent worried that their child is short does, and that is the case where the method is least reliable and where the Dutch and plain versions diverge most. So the page is built to refuse the question it is most often asked. It will not say whether a child is short, it will not screen for a growth disorder, it will not grade or band the prediction, and it will not print a figure for a child to reach. There is no band, no tone and no category anywhere in it, and that is a design decision rather than an omission: a banded output would have to decide what counts as a short prediction, which is a judgement about a child made from two numbers about the parents.

What would actually answer the question, and where those things live. Whether a child’s growth is normal is a question about the child: a measured height, plotted on a growth chart, on more than one occasion, read by somebody who can interpret the track rather than a single point. A child who is on a low centile and staying on it is a different situation from a child crossing centiles downwards, and no prediction from the parents can tell those apart. Growth centile pages are not on this site yet, and this page does not link to pages that do not exist. The clinical investigation that follows a genuine concern is a different thing again and sits on the medical side of this site, at the growth hormone stimulation test page, which exists for clinicians interpreting a test that has already been done. The other paediatric page here is the paediatric weight estimation page, built on the same principle as this one: print every published formula and the distance between them rather than one number that hides it. For adults, body size on this site is the BMI page, which borrows this page’s input-range refusal for the same reason — a height of 69 cm is a units mistake and should be refused rather than answered.

One last thing about the inputs, because it is the largest avoidable error on the page. Self-reported adult height is systematically overstated, and more so by men. An error in a parent’s height passes into the prediction at half its size, so two centimetres of exaggeration by one parent moves the prediction one centimetre, and two centimetres from each moves it two. That is small against a 17 cm range, which is the point: there is no version of being careful with the inputs that makes this method precise, and no version of choosing between the four published methods that does either. Measure the parents if you can, read the range rather than the midpoint, and treat the whole output as a description of a population rather than a statement about one child.

Frequently asked questions

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References

1. Tanner JM, Goldstein H, Whitehouse RH. Standards for children’s height at ages 2 to 9 years allowing for height of parents. Arch Dis Child 1970;45(244):755–62. The origin of the mid-parent height idea in clinical growth assessment. The paper presents centile standards for boys’ and girls’ heights at ages 2 to 9 with parents’ height allowed for, using mid-parent height, defined there as the average of father’s and mother’s height, and reports correlation coefficients at successive ages from 1 month to 9 years. It notes that allowing for parental height substantially sharpens interpretation: a child on the 3rd centile of a conventional chart can be anywhere from the 1st to the 20th centile once the parents are taken into account. WHAT COULD NOT BE ESTABLISHED: whether this paper contains the 13 cm sex correction or the 8.5 cm target range that are universally quoted to it. Neither appears in the accessible text, which describes parent-adjusted centile charts rather than an adult-height prediction formula. Both are therefore attributed on this page to the sources that state them, and not asserted as Tanner’s.
2. Tornese G. The ABCD of target height. Minerva Endocrinol 2022;47(4):377–8. The source of the 13 cm correction as implemented here: in girls the father’s height minus 13 cm is averaged with the mother’s height, and in boys the mother’s height plus 13 cm is averaged with the father’s. Also the source of the target-range statement this page uses on its wider basis — that 90% of children’s height is within 1.5 standard deviation scores, approximately two centile lines, of the mid-parental height — and of the catalogue of further corrections that exist: one for secular trend, one based on the average height standard deviation score of the parents, and a revision considering assortative mating and the parent-offspring correlation. It also names Galton’s 1886 method, the plain average of the parents’ heights, which this page prints as a labelled non-prediction.
3. Wright CM, Cheetham TD. The strengths and limitations of parental heights as a predictor of attained height. Arch Dis Child 1999;81(3):257–60. PMID 10451401. 419 children aged 8 to 9. The empirical source for the interval: 90% of the children’s heights fell within 1.5 standard deviation scores, about two centile spaces, of their mid-parental heights. And the source of the limitation this page leads on: where parents were unusually tall or short, their children were relatively less tall or less short respectively, and the mid-parental height was a poor predictor of attained height. The authors conclude that mid-parental height provides useful guidance for average-statured families but can be misleading when used to assess short children, which is the single most important sentence for a reader of a page like this one. WHAT COULD NOT BE ESTABLISHED: the full text was not readable from here, so the residual standard deviation and the correlation coefficients the paper reports are not quoted on this page.
4. van Dommelen P, Schönbeck Y, van Buuren S. A simple calculation of the target height. Arch Dis Child 2012;97(2):182, published online 18 December 2011. doi:10.1136/archdischild-2011-301095. The source of three things on this page. The conventional formula including its secular-trend term, stated as target height for boys = (father + mother + 13)/2 + 4.5 = mid-parental height + 11 and for girls = (father + mother − 13)/2 + 4.5 = mid-parental height − 2, with 13 as the mean adult male-female height difference and 4.5 described as an estimate in centimetres for the secular trend. The Dutch 2009 regression equations: boys 44.5 + 0.376 × father + 0.411 × mother, girls 47.1 + 0.334 × father + 0.364 × mother, with mother-only forms 99.9 + 0.492 × mother for boys and 96.3 + 0.436 × mother for girls, all in centimetres. And the correlations behind them: in Dutch children a parent-parent correlation of 0.19 and a parent-offspring correlation of 0.58. The paper states that the correlation adjustments shrink the 95% confidence interval from ±2.0 SD to ±1.6 SD, and that the formulas can easily be adapted to other populations if the final height of that population is known. WHAT COULD NOT BE ESTABLISHED: a source for the 4.5 cm, which the paper does not give; the sample size and population description, which are not in the accessible text; and the confidence interval in centimetres, which is given only as a ratio in standard-deviation units, so this page states the ratio and labels any conversion of it as an inference.
5. CHECK PERFORMED ON THE DUTCH EQUATIONS, recorded because it is the main reason this page is confident it transcribed them correctly. A population-calibrated regression should reproduce its own population’s mean when fed that population’s mean inputs. Dutch adult mean heights in the relevant period were about 183.8 cm for men and 170.6 cm for women. The boys’ equation returns 44.5 + 0.376 × 183.8 + 0.411 × 170.6 = 183.73 cm, and the girls’ equation returns 47.1 + 0.334 × 183.8 + 0.364 × 170.6 = 170.59 cm. The mother-only forms return 183.84 and 170.68 at the same mean mother’s height. All four reproduce the Dutch adult means to within 0.1 cm, and all four agree with the plain mid-parental method to within 0.03 cm at that point, which is the behaviour the equations must have if the coefficients are right.
6. Hermanussen M, Cole TJ. The calculation of target height reconsidered. Horm Res 2003;59(4):180–3 — named on this page and deliberately not computed. It is the revision that accounts for assortative mating and the parent-offspring correlation, and its form is given in the 2012 paper above as target height in standard deviation scores = r(parent, offspring) × √2 / (1 + r(parent, parent)) × mid-parental height in standard deviation scores. Two reasons for leaving it out, both recorded rather than worked around. It needs the mean and standard deviation of adult height for the reader’s own population in order to convert heights to standard deviation scores and back, and no such figures for an Indian population could be sourced here on terms this site can use. And the published form does not make clear whether the mid-parental standard deviation score it takes is the plain average of the two parents’ scores or a standardised mid-parent score: on the first reading the implied regression slope is 2 × 0.58/1.19 = 0.975, and on the second 0.58 × √2/1.19 = 0.689. Those give materially different predictions for every set of parents, so an implementation would be guessing. The Dutch 2009 equations are on the page instead, as the published closed form that embodies the same correction without needing either the population constants or the disambiguation.
7. Fryar CD, Carroll MD, Gu Q, Afful J, Ogden CL. Anthropometric reference data for children and adults: United States, 2015–2018. National Center for Health Statistics, Vital and Health Statistics Series 3, Number 46, January 2021. Source of the measured sex difference this page uses as its fourth version: men aged 20 and over had a mean standing height of 175.9 cm with 5th and 95th percentiles of 162.1 and 189.3, and women aged 20 and over a mean of 161.3 cm with 5th and 95th percentiles of 149.8 and 172.5. The difference of means is 14.6 cm, giving a correction of plus or minus 7.3 against the traditional 6.5. A United States Government work, which is this project’s preferred route where a figure exists in more than one place. DERIVATION DISCLOSED: the adult-height standard deviations this page uses to put the 1.5 standard deviation score interval into centimetres, 8.27 cm for men and 6.90 for women, are not published in that report; they are computed here as the 5th-to-95th percentile span divided by 3.29. The men’s figure is inflated by pooling all ages above 20, which mixes a secular trend with age-related height loss, so the within-age standard deviation is smaller, nearer 7 cm — which would put the interval at about ±10.5 cm rather than ±12.4. Both readings are stated where the figure is used.
8. Khamis HJ, Roche AF. Predicting adult stature without using skeletal age: the Khamis-Roche method. Pediatrics 1994;94(4):504–7. PMID 7936860. Named on this page to correct a common misunderstanding: this method does not require a skeletal age, and not requiring one is the point of it. It is left out of this page for two other reasons. It takes the child’s own current height and weight as inputs, which this page does not ask for and which would make it a different calculator. And it is driven by a table of coefficients indexed by the child’s age separately for each sex, which on this site is treated as expression rather than as a method — a fitted equation may be used, a published table is not reproduced. Bayley-Pinneau requires a skeletal age from a hand radiograph; Tanner-Whitehouse requires a skeletal age and is in addition a commercially licensed method with licensed reference material. Neither is on this page.
9. LICENSING POSITION taken for this page, recorded because it determined what the page contains. The four versions computed here are arithmetic or published regressions, and both are used freely: a fitted regression is a method and its coefficients are facts about data, which is this project’s standing position. Three things are treated as expression and are not reproduced: the Khamis-Roche coefficient table, the Tanner-Whitehouse scoring method and its reference material, which are commercially licensed in any case, and any growth-reference centile data. The adult-height means and percentiles come from a United States Government work in preference to equivalent figures from elsewhere, which is this site’s standing preference. No World Health Organization growth material is used: its licence is NonCommercial and this site is commercial. No guidance from the United Kingdom national institute is used: its open content licence is United Kingdom-only and forbids display of the licensed information next to advertising, and this site carries advertising. The two child growth-centile pages planned for this plugin are not built, are blocked on reference data, and are referred to in prose here without being linked, because a link to a page that does not exist is a dead link.
10. Derivations and checks performed for this page rather than taken from a source, recorded so they can be checked. (1) The three renderings of the sex correction are algebraically identical: (F + M + 13)/2, (F + M)/2 + 6.5 and ((M + 13) + F)/2 all give the same number for every pair of parental heights, so the widely repeated claim that applying the correction before or after averaging gives different answers is false. (2) The spread between the four versions is 4.5 cm for a boy and 5.3 cm for a girl at parental heights near average, rising to 6.9 cm for a boy at parental heights of 150 and 140 cm and 10.5 cm for a girl with the same parents, where the Dutch equation drifts furthest above the three constant-shift versions. Near average parental heights the extra 0.8 cm in girls is entirely the secular-trend version, where +4.5 against a correction of −6.5 leaves −2; at the extremes it is the Dutch equation that sets the spread in both sexes. (3) Changing the sex-difference constant from 13 to the measured 14.6 cm moves the prediction by 0.8 cm; the imperial two-and-a-half-inch form of the rule is 6.35 cm against the metric 6.5, worth 0.15 cm. (4) The Dutch 2009 equation crosses the plain method at the Dutch population means, agreeing to 0.03 cm there, sits 3.1 cm above it at parental heights of 170 and 155 cm, and 2.2 cm below it at 195 and 180. Its mother-only form returns 169.8 cm for a boy whose mother is 142 cm, which is 14.8 cm above the plain method, and is printed on the page as a warning row for that reason. (5) The two published intervals imply prediction-error standard deviations of about 4.25 cm (±8.5 as two standard deviations) and about 7.5 cm (±12.4 as a 90% interval), which disagree by about three quarters; the figure implied by the published correlations, with roughly 43% of variance unexplained and an adult-height standard deviation near 7 cm, is about 4.7 cm and sits between them. (6) The ratio of interval WIDTH to method spread at the page’s default inputs is 17.0/4.5 = 3.8 on the narrower published basis and 24.8/4.5 = 5.5 on the wider one. Both are printed, and they are the figures the page uses to say that choosing between methods is the second-order question. Expressed as half-widths the same ratios are 1.9 and 2.8.

CalcEngines health calculators are for education and for checking arithmetic that has already been decided elsewhere. They are not medical advice, they do not decide what to give, and they do not replace the judgement of a doctor, nurse, midwife or dietitian who knows the person in front of them. Every figure depends on the values you enter and on the assumptions stated on the page — check it against the prescription, the product label and your local policy before acting on it.