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Child Height Predictor Calculator (Khamis-Roche Method)

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Khamis-Roche Adult Height Predictor

Estimate a child's adult height with the Khamis-Roche method, using age- and sex-specific regression coefficients for current height, current weight, and mid-parental height. The method does not require a bone-age X-ray.

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

How It Works

The Khamis-Roche method turns a child's age, sex, current height and weight, and both parents' heights into an adult-height estimate using regression coefficients derived from the Fels Longitudinal Study. The 1994 paper, with coefficients corrected in a 1995 erratum, tabulates separate equations for boys and girls at half-year ages from 4.0 through 17.5. InfantChart linearly interpolates between adjacent table rows for an age such as 10.3 years; this avoids a sudden jump at a half birthday, but it is an implementation choice rather than a step specified in the paper. Across the tabulated ages, the study reported average empirical absolute-error bounds: 50% bounds of about ±2.16 cm for boys and ±1.67 cm for girls, and 90% bounds of about ±5.34 cm for boys and ±4.25 cm for girls (Khamis & Roche, 1994). These are age-averaged study-sample error summaries, not standard errors, normal-distribution confidence intervals, or guarantees for an individual child. The source population was healthy white American children in the Fels cohort; use for other populations or for children with conditions affecting growth is an extrapolation.

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 a predicted height of about 70.43 in, or 178.9 cm.
  6. Report the point estimate as approximately 178.9 cm (5 ft 10 in). For broad context, applying the study's age-averaged male 90% error bound gives about 173.6–184.2 cm, but this is not an individualized confidence interval.

Key Concepts

Adult height reflects heredity, nutrition, health, and maturation. Khamis-Roche represents family stature with the average of the parents' heights and adds the child's current height and weight. It intentionally omits skeletal age, making it convenient when an X-ray is not warranted, but chronological age alone cannot identify whether a child is maturing unusually early or late. The paper's error bounds vary by age and sex; the ±5.34 cm male and ±4.25 cm female figures are averages of the study's 90% error bounds across ages, not fixed personal ranges. Mid-parental height alone (the Tanner shortcut: (mother + father + 13 cm for boys, or −13 cm for girls) / 2) uses less information and can sometimes give a similar result by coincidence.

Applications

  • Family context: explore a broad adult-height estimate while keeping the study's uncertainty and population limits in view.
  • Well-child conversations: use the estimate to prepare questions for a pediatrician, not to screen for a disorder or choose treatment.
  • Method comparison: see why Khamis-Roche can differ from a mid-parental-height shortcut when current height and weight are included.
  • Educational use: demonstrate how age-specific regression combines a child's measurements with family stature.

Common Mistakes

  • Expecting an exact number — the point estimate has uncertainty. The study's age-averaged 90% absolute-error bounds were about ±5.34 cm for boys and ±4.25 cm for girls, but they do not guarantee that range for a particular child.
  • Running the calculator outside ages 4.0–17.5 — the paper does not provide coefficient rows beyond that range, so extrapolation is unsupported.
  • 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 — errors in either parent's height carry into the mid-parent height and therefore the prediction. If possible, measure both parents barefoot against a wall.
  • Assuming the equations are equally validated for every child — they were developed from healthy white American participants in the Fels Longitudinal Study and do not adjust for other population backgrounds or conditions that affect growth.
  • Ignoring unusually early or late maturation — Khamis-Roche does not use Tanner stage or bone age, so a clinician may choose a different evaluation when skeletal maturity is a concern.
  • 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 final adult height from a child's current height and weight, sex, chronological age (4–17.5 years), and both parents' heights. Khamis and Roche published the regression in 1994 and corrected its coefficient tables in a 1995 erratum. It provides a point estimate, not a diagnosis or a guaranteed range, and it is not a substitute for clinical assessment when growth is a medical concern.

How accurate is the Khamis-Roche height predictor?

In the study sample, the error bounds averaged across ages were about ±2.16 cm for 50% of errors and ±5.34 cm for 90% of errors in boys; the corresponding averages for girls were about ±1.67 cm and ±4.25 cm. The paper also reports different bounds by age. These empirical absolute-error bounds are not standard errors or individualized confidence intervals, and performance may differ outside the population in which the equations were developed.

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 rather than extrapolating beyond the table. If growth outside that range is a concern, a clinician can assess it; this calculator cannot supply a validated prediction.

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

Bone-age methods use a hand or wrist X-ray to assess skeletal maturity, information that Khamis-Roche does not use. That can be especially relevant when a child appears to mature unusually early or late. Bone-age interpretation belongs in clinical care; Khamis-Roche is a convenient non-radiographic estimate, not a replacement for a clinician-directed evaluation.

Why do girls and boys use different coefficients?

Girls and boys have different average patterns of growth and maturation. The Khamis-Roche tables therefore provide separate regression coefficients for each sex and each half-year of age. The study also reports separate empirical prediction-error bounds by sex and age.

How much do parent heights matter in the prediction?

The equation uses the average of the two parents' heights. Its effect is the age- and sex-specific parent-height coefficient multiplied by a change in that average, so it is not a fixed one-for-one adjustment. Current height and weight also contribute, with coefficients that change across the half-year table rows.

Can puberty or growth plate status change the prediction?

Yes. The equations do not use bone age or Tanner stage, so two children with the same chronological age and measurements receive the same estimate even if their skeletal maturity differs. Early or late maturation can therefore make the estimate less representative; a clinician can decide whether a bone-age assessment or other evaluation is appropriate.

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

Talk with a pediatrician if a child's growth slows unexpectedly, crosses percentile lines downward, differs substantially from the family pattern, or comes with symptoms or a condition that can affect growth. This calculator cannot diagnose a cause or determine whether specialist referral, bone-age imaging, or laboratory testing is appropriate.

References:

Khamis HJ, Roche AF. Predicting adult stature without using skeletal age: the Khamis-Roche method. Pediatrics. 1994;94(4):504-507. https://publications.aap.org/pediatrics/article/94/4/504/59488/Predicting-Adult-Stature-Without-Using-Skeletal

Khamis HJ, Roche AF. Erratum: Predicting adult stature without using skeletal age: the Khamis-Roche method. Pediatrics. 1995;95(3):457. https://publications.aap.org/pediatrics/article/95/3/457/59792/ERRATUM

Worked Examples

Preschool example

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

A clinician or parent wants a rough adult-height estimate for a healthy 4-year-old girl. The point estimate uses her current measurements and parental heights; it does not measure skeletal age or pubertal timing.

  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: B₀ = −8.13, b₁ = 1.248, b₂ = −0.194, b₃ = 0.448
  4. Prediction ≈ 161.7 cm (5 ft 4 in)

predicted adult height ≈ 161.7 cm (5 ft 4 in).

In the original validation study, the 90% prediction-error bound for girls averaged about ±4.25 cm across the studied ages. Accuracy varies by age and individual, so this is not a guarantee for one child.

Mid-childhood comparison

A 10-year-old boy is 140 cm and 35 kg. His parents are 165 cm and 178 cm. How tall will he be?

This is the page’s original metric example, recalculated directly from the same Khamis-Roche function used by the calculator. It is also a useful comparison with the simpler Tanner mid-parental shortcut.

  1. Knowns: age 10.0 yr, sex boy, current height 140 cm, current weight 35 kg
  2. Mother 165 cm, father 178 cm → unadjusted mid-parent height 171.5 cm (67.5 in)
  3. Khamis-Roche coefficients for 10-year-old boys: B₀ = −11.04, b₁ = 0.971, b₂ = −0.040, b₃ = 0.459
  4. Khamis-Roche prediction ≈ 178.9 cm (5 ft 10 in)
  5. Tanner mid-parental shortcut: (165 + 178 + 13) / 2 = 178.0 cm

Khamis-Roche predicts 178.9 cm versus 178.0 cm from the Tanner shortcut—a difference of only 0.9 cm.

The two methods happen to agree closely in this case. That 0.9 cm gap is much smaller than the original study's average male 90% prediction-error bound of about ±5.34 cm, so this example does not usefully demonstrate the methods separating.

Late adolescent

What adult height is estimated for a 15-year-old boy at 170 cm whose parents are 168 cm and 185 cm?

This endpoint estimate uses the boy’s current height and weight together with both parental heights. Pubertal stage and bone age are not inputs, so the result should not be read as a modeled growth schedule.

  1. Knowns: age 15.0 yr, sex boy, current height 170 cm, current weight 60 kg
  2. Mother 168 cm, father 185 cm → unadjusted mid-parent height 176.5 cm (69.5 in)
  3. Khamis-Roche coefficients for 15-year-old boys: B₀ = −5.13, b₁ = 0.638, b₂ = −0.007, b₃ = 0.495
  4. Prediction ≈ 180.4 cm (5 ft 11 in); difference from current height 10.4 cm

predicted adult height ≈ 180.4 cm (5 ft 11 in), a 10.4 cm difference from current height.

The original study's male 90% prediction-error bound averaged about ±5.34 cm across ages; it did not establish that uncertainty narrows steadily with age. Bone-age assessment may be more informative when maturation timing is a clinical concern.

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, taken from the Khamis and Roche (1994) tables with the coefficient corrections published in the 1995 erratum.

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. The published tables list coefficients at half-year ages. When an age falls between those rows (for example, 10.3 years), InfantChart linearly interpolates the coefficients. That interpolation is an InfantChart implementation choice, not a procedure specified in the original paper.

The original validation study reported empirical prediction-error bounds, not a single universal range for every child. Averaged across the studied ages, about 90% of prediction errors fell within approximately ±5.34 cm for boys and ±4.25 cm for girls. Accuracy and the reported bounds vary by age and sex, so these averages are not guaranteed ranges for a particular child.

The equations were developed from white American children in the Fels Longitudinal Study who did not have conditions known to affect growth. Performance may differ for other populations, children who mature unusually early or late, or children with growth-affecting medical conditions.

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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