How this is calculated

This calculator uses the Khamis-Roche method, published by Harry Khamis and Alex Roche in Pediatrics in 1994. Where a bone age is not available, it is what most paediatric growth software falls back on.

The parental average tells you roughly where a family sits in the height distribution, and not much else. A child who is already tall for their age, or already heavy for their age, is carrying information those two numbers cannot hold. Khamis and Roche went to the Fels Longitudinal Study — children measured repeatedly from infancy to adulthood — and fitted a separate regression for each sex at each half-year of age, with three predictors: the child's current stature, the child's current weight, and the mid-parent stature.

The equation

For a given sex and age, the prediction is a weighted sum:

Adult height (in) = B₀ + (b₁ × child's height) + (b₂ × child's weight) + (b₃ × mid-parent height)

Mid-parent height here is just (mother's height + father's height) ÷ 2, with no sex adjustment. That adjustment is already built into which coefficient table gets used.

If you are checking the arithmetic, watch the units: the regression was fitted in inches and pounds. Metric entries have to be converted going in and converted back coming out, and feeding centimetres and kilograms straight into these coefficients produces nonsense. The published tables also stop at half-year steps between 4.0 and 17.5 years, so an age in between — 8.2 years, say — is handled by interpolating linearly between the rows for 8.0 and 8.5, as clinical implementations do. Opening “Show the arithmetic” in the result panel prints the coefficients actually used.

One correction still trips up calculators elsewhere online. The weight coefficients printed in the 1994 paper were wrong, and were fixed in an erratum the following year. This calculator uses the corrected 1995 coefficients.

A worked example

A girl aged exactly 10.0, 54 in tall and 70 lb, whose mother is 64 in and father 70 in — so a mid-parent height of 67 in. The coefficient row for girls at 10.0 years is B₀ −0.33468 … in full:

B₀ (intercept)0.335
0.82771 × 54 in (her height)44.696
−0.07397 × 70 lb (her weight)−5.178
0.37312 × 67 in (mid-parent)24.999
Predicted adult height64.9 in — 5 ft 4.9 in, or 165 cm
90% band (±1.7 in for girls)63.2 – 66.6 in

Two things are worth noticing. The weight term is negative — at a given height, a heavier ten-year-old is predicted to finish slightly shorter, because extra weight at this age tends to go with earlier maturation and therefore less growing time left. And the mid-parental method for the same family gives (64 + 70 − 5.1) ÷ 2 = 64.4 in, a range of 61.1 to 67.8 in once its own spread is carried — within half an inch of the Khamis-Roche figure, which sits comfortably inside it. That agreement is reassuring but not meaningful in itself: the two methods agree far more often than they are both right, because both are anchored to the same parental heights.

How accurate is it?

Reported 90% error bounds are ±2.1 inches (5.3 cm) for boys and ±1.7 inches (4.3 cm) for girls: nine children in ten finish that close to the predicted figure. It is a good deal tighter than the parental average on its own, and it is still a range. A calculator that hands you one confident number to the nearest centimetre is overselling what three measurements can tell it.

Accuracy is not even across childhood, either. At 4 the equation leans hard on the parents and on a body with years of unpredictable puberty ahead of it; at 16 it is mostly confirming a height already reached. Roughly 10 to 14 is where pubertal timing takes over, and pubertal timing is the one thing the equation has no way of reading.

The mid-parental range shown alongside it

For comparison, the result panel also shows the older mid-parental target height described by Tanner and colleagues, which uses nothing but the parents:

  • For a boy: (mother's height + father's height + 13 cm) ÷ 2
  • For a girl: (mother's height + father's height − 13 cm) ÷ 2

The 13 cm (5.1 in) is the average adult height difference between men and women, and it is Tanner's published figure rather than the rounded 5 inches the arithmetic is often written with.

What that gives you is a midpoint, and a midpoint on its own is misleading. Two parental heights, with nothing measured from the child, carry a spread of roughly ±8.5 cm (±3.3 in) — about two standard deviations. So the panel shows a band rather than a single number, because the band is what the method actually supports. Read it as a reference point rather than a rival answer: when the Khamis-Roche prediction falls outside it, the gap is measuring how far this child has already diverged from the family average.

What the method cannot do

The Fels cohort was almost entirely white and American, and its children grew up in the middle of the twentieth century; the equations carry that with them. They also assume a healthy child growing normally. Chronic illness, a nutritional deficit, an endocrine disorder, a family pattern of constitutional delay — none of these appears anywhere in the model, and for a child with one of them the prediction is far shakier than the range makes it look.

The clinical gold standard: bone age

When a doctor needs a genuinely accurate estimate — usually to investigate delayed or precocious puberty — formulas are set aside in favour of a hand and wrist X-ray, read against the Greulich-Pyle atlas.

What this reveals is the state of the growth plates, the cartilage zones near the ends of the long bones where new bone is laid down. A radiologist compares their maturation against standard images to establish skeletal age, which can run ahead of or behind chronological age. As sex hormones peak towards the end of puberty, those plates fuse into solid bone — and once fused, linear growth stops permanently. Knowing how much growth plate remains is far more informative than any formula.

What actually influences whether you reach your potential

Puberty timing

This is the biggest source of variation, and the most misunderstood. Children who enter puberty early hit their growth spurt sooner and shoot ahead of classmates — but their growth plates also fuse earlier, cutting the total time available to grow.

Children with constitutional delay — the classic "late bloomers" — spend years being the shortest in their year group, then keep growing steadily after their peers have stopped. They frequently catch up entirely, and sometimes overtake their earlier predicted percentile. If you are 14 and shorter than everyone, that is genuinely not the end of the story.

Sleep

The pituitary gland releases the great majority of human growth hormone in pulses during stage N3 slow-wave sleep — the deepest part of the night. Chronic sleep deprivation or fragmented sleep suppresses that nocturnal release, and it does so precisely during the years when it matters most. Of everything on this page you can actually control, sleep is the one with the clearest mechanism.

Nutrition

Bone elongation is expensive. Sustained calorie restriction — from severe dieting, from intense athletic training without matching intake, or from an eating disorder — makes the body divert energy away from growth. Adequate protein matters, and so do vitamin D, calcium and zinc, which are required co-factors for bone mineralisation and cell division; zinc deficiency in particular blunts growth directly.

This is worth stating plainly to any teenager reading: undereating during your growing years can cost you height you don't get back. If food and body image are difficult for you right now, that is worth telling someone about — a parent, a doctor, or a school nurse.

Medical conditions and medications

Conditions causing malabsorption — undiagnosed coeliac disease, inflammatory bowel disease — can stunt growth, sometimes with poor growth as the first visible sign. So can endocrine problems such as hypothyroidism or growth hormone deficiency. Long-term high-dose oral corticosteroids, prescribed for severe asthma or autoimmune disease, suppress growth velocity as a known side effect.

All of these are things a doctor can identify and, in many cases, treat.

When to actually see a doctor

Rather than watching a calculator, see your doctor if any of these apply:

  • Growth has clearly slowed or stopped compared with previous years
  • A child is much shorter or taller than expected for the family
  • Puberty has started very early (before 8 in girls, 9 in boys) or has not begun by 13 in girls or 14 in boys
  • Growth is accompanied by fatigue, persistent digestive symptoms, or unexplained weight loss

A doctor plotting height over time on a growth chart learns more from two measurements a year apart than any formula can tell you from a single day.

One last thing, for the teenagers

Height gets a great deal of attention during adolescence and very little afterwards. It is almost entirely outside your control, it is a poor predictor of health, happiness or anything else that matters, and the timing differences that feel enormous at 14 have usually evened out by 20. Sleep well, eat properly, and let your growth plates do their work.

Questions people actually ask about this

How tall will my child be?

The most accurate estimate available without an X-ray comes from the Khamis-Roche equation above, which combines the child’s current height and weight with the average of both parents’ heights, weighted by coefficients specific to age and sex. It is accurate to roughly 2.1 inches for boys and 1.7 inches for girls, meaning nine children in ten finish within that band. Treat it as a range, not a number.

What is the Khamis-Roche method?

A regression published in 1994 and corrected by a 1995 erratum, derived from the Fels Longitudinal Study — children measured repeatedly from infancy into adulthood. It predicts adult stature from four things: the child’s height, the child’s weight, the mid-parental height, and an age- and sex-specific set of coefficients. It applies between ages 4 and 17½.

How accurate is a height predictor?

Khamis-Roche carries a 90% error band of about ±2.1 inches for boys and ±1.7 inches for girls. The simpler mid-parental method is considerably looser — roughly two thirds of children finish within 2 inches and almost all within 4. Neither can read pubertal timing, which is the single largest unknown between about 10 and 14.

Which method should I use?

Khamis-Roche if you have the child’s current height and weight, because those two measurements carry real information the parental average cannot. Use the mid-parental estimate when you only know the parents, or as a sanity check. If the prediction falls outside the mid-parental range altogether, the child is unusual for their family in a way worth mentioning to their doctor rather than resolving with a calculator.

Can a child grow taller than predicted?

Yes — about one child in ten finishes outside the band, and that is the equation working as designed rather than failing. Late developers are the commonest reason: a child who starts puberty at 15 keeps growing well past friends who started at 12 and have already fused their growth plates. The prediction has no way of knowing which of those a given ten-year-old will turn out to be.

Why does my child’s weight make the prediction shorter?

Because the weight coefficient is negative at most ages. At a given height, a heavier child tends to mature earlier, and earlier maturation means less growing time before the growth plates close. It is not a statement about health, and it is not a reason to change anything about how a child eats — it is the regression capturing a real average pattern in the Fels data.

At what age does a height prediction become reliable?

It tightens steadily with age, for an uninteresting reason: by 15 or 16 the equation is largely confirming a height already reached. Between roughly 10 and 14 is the loosest stretch, because that is when pubertal timing dominates and the equation cannot see it. A prediction at 4 leans almost entirely on the parents and on a body with a decade of unknowns ahead of it.

Do these equations apply to every child?

Less well than the tidy numbers suggest. They were derived from the Fels Longitudinal Study, a mostly white American cohort measured through the mid-twentieth century, and they know nothing about ethnicity, chronic illness, growth-affecting medication, or a family history of late growth. They are a reasonable orientation for most children and a poor one for any child whose growth is already a clinical question — that belongs with their doctor and a growth chart, not a web page.

References

  1. Khamis HJ, Roche AF. Predicting adult stature without using skeletal age: the Khamis-Roche method. Pediatrics. 1994;94(4 Pt 1):504–507. PMID: 7936860 The method this calculator implements, including the sex- and age-specific coefficient tables.
  2. Khamis HJ, Roche AF. Predicting adult stature without using skeletal age: the Khamis-Roche method [erratum]. Pediatrics. 1995;95(3):457. Corrects the weight coefficients printed in the 1994 tables. These are the values used here.
  3. Roche AF, Wainer H, Thissen D. The RWT method for the prediction of adult stature. Pediatrics. 1975;56(6):1027–1033. The earlier Fels-derived method that Khamis-Roche was designed to simplify by removing the need for a bone age.
  4. Tanner JM, Goldstein H, Whitehouse RH. Standards for children's height at ages 2–9 years allowing for heights of parents. Arch Dis Child. 1970;45(244):755–762. doi:10.1136/adc.45.244.755 The mid-parental target height shown alongside the main prediction.
  5. Greulich WW, Pyle SI. Radiographic Atlas of Skeletal Development of the Hand and Wrist. 2nd ed. Stanford, CA: Stanford University Press; 1959. The atlas against which bone age is assessed — the clinical alternative described below.
  6. Bayley N, Pinneau SR. Tables for predicting adult height from skeletal age. J Pediatr. 1952;40(4):423–441. doi:10.1016/S0022-3476(52)80205-7 The bone-age-based prediction tables used clinically once an X-ray has been taken.
  7. Takahashi Y, Kipnis DM, Daughaday WH. Growth hormone secretion during sleep. J Clin Invest. 1968;47(9):2079–2090. doi:10.1172/JCI105893 Established that growth hormone is released mainly during deep slow-wave sleep.
  8. Marshall WA, Tanner JM. Variations in pattern of pubertal changes in girls. Arch Dis Child. 1969;44(235):291–303. · Variations in the pattern of pubertal changes in boys. Arch Dis Child. 1970;45(239):13–23. The staging work underlying the discussion of early and late puberty.
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