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Child Height Predictor Calculator (Khamis-Roche Method)

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Khamis-Roche Adult Height Predictor

Predict your child's adult height with the Khamis-Roche method — one of the most accurate non-invasive height predictions, using age- and sex-specific regression coefficients on current height, current weight, and mid-parental height. No bone-age X-ray required.

Predicted Height (in) = B₀ + b₁ · child height + b₂ · child weight + b₃ · mid-parent height

How It Works

The Khamis-Roche method turns five inputs — child's age, sex, current height, current weight, and the mother's and father's heights — into an adult height prediction using published regression coefficients derived from the Fels Longitudinal Study. For each half-year of age from 4.0 to 17.5, Khamis and Roche fit a linear equation that weights the child's current stature, current weight, and mid-parental height (the average of both parent heights) to estimate adult stature. The calculator linearly interpolates between the two bracketing coefficient rows for fractional ages (e.g., 10.3 years), applies the regression, converts inches to centimeters, and returns a single predicted adult height. The prediction comes with a published standard error: about 2.2 inches (5.6 cm) for boys and 1.7 inches (4.3 cm) for girls. The method does not require skeletal age radiographs, which is why it is widely used in primary-care settings where bone-age assessment is not practical.

Example Problem

A 10-year-old boy is 140 cm tall, weighs 35 kg. His mother is 165 cm and his father is 178 cm. What is his predicted adult height?

  1. Select 'Boy' for gender and enter the child's age (10 years).
  2. Enter the child's current height (140 cm) and current weight (35 kg).
  3. Enter the mother's height (165 cm) and the father's height (178 cm).
  4. The calculator converts centimeters to inches and kilograms to pounds internally, then looks up the Khamis-Roche coefficients for 10-year-old boys (B₀ = −11.038, b₁ = 0.971, b₂ = −0.040, b₃ = 0.459).
  5. Mid-parent height = (165 + 178) / 2 = 171.5 cm = 67.5 in. The regression gives predicted height ≈ 70.0 in ≈ 178 cm.
  6. Report the result: predicted adult height ≈ 178 cm (5 ft 10 in) with a 90% range of roughly 169-186 cm after accounting for the ±5.6 cm standard error.

Key Concepts

Adult height is shaped by three forces: genetics (roughly 60-80% of the variation), nutrition, and overall health. The Khamis-Roche method bakes the genetic component in via mid-parental height and captures the growth-so-far component via the child's current height and weight. It intentionally does not use skeletal age, making it faster and cheaper than radiographic methods like Bayley-Pinneau or Tanner-Whitehouse but slightly less accurate in children who are unusually early or late maturers. The prediction is a point estimate — real children land within roughly ±5.6 cm (boys) or ±4.3 cm (girls) of it about 68% of the time, and within ±11 cm or so 95% of the time. Predictions stabilize as the child ages: a 15-year-old's prediction is far more reliable than a 4-year-old's because there is less remaining growth to estimate. Mid-parental height alone (the classic Tanner formula: (mother + father + 13 cm for boys, −13 cm for girls) / 2) is a rougher shortcut that the Khamis-Roche regression improves on by adding the child's own trajectory.

Applications

  • Well-child visits: pediatricians use height prediction to reassure parents whose child is tracking below or above peers but whose predicted adult height is normal.
  • Growth counseling: families with a short-for-age child can see whether the trajectory converges toward a typical adult height or remains below the 3rd percentile.
  • Sports and athletic potential: parents and coaches weigh predicted adult height against position demands in basketball, volleyball, gymnastics, and rowing.
  • Screening for growth disorders: a predicted adult height more than 2 standard deviations below mid-parental height expectation is a flag for endocrine workup.
  • Planning scoliosis and orthopedic treatment: surgeons use remaining-growth estimates to time bracing or surgery.
  • Educational use: demonstrating how heavily parental height predicts adult height helps set realistic expectations and reduce anxiety about normal variation.

Common Mistakes

  • Expecting an exact number — the Khamis-Roche prediction has a published ±5.6 cm (boys) / ±4.3 cm (girls) standard error and should be read as a range, not a guarantee.
  • Running the calculator for a 2- or 3-year-old expecting a meaningful prediction — the published regression coefficients start at age 4; below that the input fields become unreliable and bone-age methods are more appropriate.
  • Forgetting to measure the child's standing height in the morning — diurnal spinal compression can shorten a measurement by 1-2 cm by evening, enough to shift the prediction.
  • Using estimated or remembered parent heights — a 3 cm error on each parent's height translates directly into about a 1.5 cm error in the prediction. If possible, measure both parents barefoot against a wall.
  • Applying the prediction to a child with a diagnosed growth disorder (growth hormone deficiency, Turner syndrome, chronic disease) — the Khamis-Roche equations were fit to healthy US children and do not adjust for pathology.
  • Treating early or late puberty as invisible — a child well ahead of or behind Tanner-stage norms for their age may end up significantly above or below the point estimate; bone-age radiography gives a better number in those cases.
  • Comparing the predicted adult height to a growth-chart percentile for the child's current age — those are different measurements answering different questions.

Frequently Asked Questions

What is the Khamis-Roche height predictor?

The Khamis-Roche method estimates a child's final adult height from current height and weight, sex, age (4–17.5 years), and the heights of both parents. It is a regression-based prediction published by Khamis and Roche in 1994 and remains one of the most widely-cited non-invasive height predictors in pediatric research. The model reports a point estimate with a standard error of about ±5.6 cm for boys and ±4.3 cm for girls — useful for family curiosity, but not a substitute for a clinical bone-age assessment when there is a specific medical question.

How accurate is the Khamis-Roche height predictor?

The published standard error is about 2.2 inches (5.6 cm) for boys and 1.7 inches (4.3 cm) for girls. That means about 68% of children end up within that range of the prediction and about 95% within roughly twice that. Khamis-Roche is considered one of the most accurate non-invasive prediction methods and is widely cited in pediatric research as the reference against which other regressions are compared.

What age range does the Khamis-Roche method support?

The original Khamis and Roche (1994) paper published coefficients for ages 4.0 through 17.5 years in half-year increments. The calculator enforces that range. For children younger than 4, the coefficients have not been validated and a pediatric endocrinologist should be consulted for a reliable prediction. For teens older than 17.5, most growth has already occurred and current height is close to the final answer.

How does Khamis-Roche compare to the bone-age (Bayley-Pinneau) method?

Bone-age methods (Bayley-Pinneau, Tanner-Whitehouse, Roche-Wainer-Thissen) read skeletal maturity from a hand X-ray and typically achieve slightly better accuracy than Khamis-Roche, especially in children with unusually early or late puberty. The trade-off is the radiation exposure, cost, and trained-radiologist interpretation. Khamis-Roche was designed specifically to give pediatricians a near-equivalent prediction without ordering an X-ray.

Why do girls and boys use different coefficients?

Girls and boys follow different growth curves. Girls typically enter puberty 1-2 years earlier and finish growing 2-3 years earlier than boys. Their predicted adult height averages about 12-13 cm shorter. The Khamis-Roche method fits a separate regression for each sex and each half-year of age to capture those divergent trajectories, which is why the coefficients (and the resulting standard error) differ between girls and boys.

How much do parent heights matter in the prediction?

Mid-parental height (the average of mother and father) is the single strongest predictor in the equation — it carries most of the genetic signal. A 10 cm swing in mid-parental height typically moves the predicted adult height by about 5-6 cm, depending on the child's age. That said, the child's own current height and weight refine the estimate materially, especially after age 10 when growth velocity and pubertal timing start to diverge between children with similar parents.

Can puberty or growth plate status change the prediction?

Yes — indirectly. The Khamis-Roche equations do not read bone age or Tanner stage, so a 12-year-old already well into puberty and a 12-year-old still in pre-puberty receive the same prediction from the same measurements, even though the first child has much less remaining growth. If a child is clearly early or late for their chronological age, a bone-age X-ray typically gives a better prediction. Growth plate closure around age 14-16 in girls and 16-18 in boys marks the end of longitudinal growth.

When should I see a pediatric endocrinologist instead of relying on this calculator?

Consider a referral if a child's current height is below the 3rd percentile for age and sex, if their growth velocity has dropped below 4-5 cm per year between ages 4 and puberty, if the predicted adult height is more than 8-10 cm below mid-parental expectation, or if there is a family history of growth hormone deficiency, Turner syndrome, skeletal dysplasia, or other disorders affecting stature. An endocrinologist can order bone-age radiography, growth hormone stimulation testing, and karyotyping to refine the prediction and identify treatable causes.

Reference: Khamis HJ, Roche AF. Predicting adult stature without using skeletal age: the Khamis-Roche method. Pediatrics. 1994;94(4):504-507. https://pubmed.ncbi.nlm.nih.gov/7936860/

Worked Examples

Preschool screening

Where is a 4-year-old girl headed if she is 100 cm and her parents are 160 cm and 175 cm?

A pediatrician wants a conservative read on adult height for a healthy 4-year-old girl during her well-child visit. Predictions at age 4 carry the widest confidence interval — the remaining 14 years of growth leave more room to diverge — but the regression still picks up the genetic signal from parent heights.

  1. Knowns: age 4.0 yr, sex girl, current height 100 cm, current weight 16 kg
  2. Mother 160 cm, father 175 cm → mid-parent height 167.5 cm (65.9 in)
  3. Khamis-Roche coefficients for 4-year-old girls: B\u2080 = \u22128.13, b\u2081 = 1.248, b\u2082 = \u22120.194, b\u2083 = 0.448
  4. Prediction \u2248 162 cm (5 ft 4 in)

predicted adult height \u2248 162 cm (5 ft 4 in), roughly the 50th percentile for US adult women.

At age 4 the \u00B14.3 cm standard error is a floor — in practice the real range is wider because pubertal timing is still unknown. Treat as a ballpark, not a commitment.

Mid-childhood (imperial units)

A 10-year-old boy is 4 ft 7 in and 77 lb. His parents are 5 ft 5 in and 5 ft 10 in. How tall will he be?

A parent comparing their son against classmates wants a simple prediction using the units their pediatrician used. The calculator converts 4 ft 7 in = 55 in = 140 cm and 77 lb = 35 kg internally, then applies the 10-year-old-boy coefficients.

  1. Knowns: age 10.0 yr, sex boy, current height 55 in (140 cm), current weight 77 lb (35 kg)
  2. Mother 65 in (165 cm), father 70 in (178 cm) \u2192 mid-parent 67.5 in
  3. Khamis-Roche coefficients for 10-year-old boys: B\u2080 = \u221211.04, b\u2081 = 0.971, b\u2082 = \u22120.040, b\u2083 = 0.459
  4. Prediction \u2248 178 cm (5 ft 10 in)

predicted adult height \u2248 5 ft 10 in (178 cm), matching his father almost exactly.

Predictions around age 10 start to firm up, but a child who is clearly ahead of or behind typical puberty for their age can still diverge by \u00B16 cm.

Late adolescent

How much more will a 15-year-old boy at 170 cm grow if his parents are 168 cm and 185 cm?

A late-blooming 15-year-old boy is already 170 cm but has not yet hit a growth spurt. His mother is 168 cm and his father is 185 cm — the father's height in particular suggests upside. The calculator picks up both the mid-parent signal and the fact that the boy is relatively short for parents his size.

  1. Knowns: age 15.0 yr, sex boy, current height 170 cm, current weight 60 kg
  2. Mother 168 cm, father 185 cm \u2192 mid-parent 176.5 cm (69.5 in)
  3. Khamis-Roche coefficients for 15-year-old boys: B\u2080 = \u22125.13, b\u2081 = 0.638, b\u2082 = \u22120.007, b\u2083 = 0.495
  4. Prediction \u2248 180 cm (5 ft 11 in) \u2014 about 10 cm of growth remaining.

predicted adult height \u2248 180 cm (5 ft 11 in), with roughly 10 cm of catch-up growth still projected.

At 15 the standard error narrows to roughly \u00B14 cm. If bone age lags chronological age materially, an endocrinologist can refine the estimate upward.

How the prediction is calculated

The Khamis-Roche method is a linear regression fit separately for each sex and each half-year of age from 4.0 to 17.5. For a given child, the calculator pulls four coefficients from a published table — an intercept B₀, a child-stature weight b₁, a child-weight weight b₂, and a mid-parent-stature weight b₃ — and combines them with the child's measurements:

Predicted adult height (in) = B₀ + b₁ · H + b₂ · W + b₃ · M

Where:

  • H — the child's current height in inches.
  • W — the child's current weight in pounds.
  • M — mid-parent height in inches, defined as (mother height + father height) / 2.
  • B₀, b₁, b₂, b₃ — the regression coefficients for this child's sex and age, read from the Khamis-Roche (1994) table.

Because the coefficients were fit in imperial units, the calculator converts any centimeters and kilograms you enter to inches and pounds first, runs the regression, and converts the result back. For fractional ages (e.g., 10.3 years) it linearly interpolates between the two bracketing half-year coefficient rows. The published standard error — the typical gap between prediction and eventual adult height — is about 5.6 cm for boys and 4.3 cm for girls.

The calculator intentionally does not show a literal “show your work” substitution for these coefficients: the four regression weights are not meaningfully pedagogical on their own (they are statistical fits, not physical quantities), and the parent-friendly version of the math is the explanation above.

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