Calculate height velocity
Why velocity is the sensitive indicator
A single height centile tells you where a child stands. Velocity tells you where they are going, and it tells you sooner. A child can sit on a perfectly normal centile while their growth rate has already halved; the centile will not reveal the problem until months later, when the lines have been crossed. Paediatric endocrinologists therefore call growth velocity the most sensitive auxological indicator: it is the earliest quantitative sign of growth hormone deficiency, hypothyroidism, chronic disease and the effects of high-dose steroids.
The arithmetic is simple: subtract the earlier height from the later one and divide by the years between. The clinical skill lies in everything around the arithmetic: measuring both heights with the same careful technique, spacing the measurements sensibly, and interpreting the result against what is expected at that age and pubertal stage.
What counts as normal at each age
Growth velocity follows a predictable curve. Infants grow explosively, about 25 cm in the first year, slowing to about 12 cm in the second. From roughly age 4 to the start of puberty, healthy children grow at a steady 5 to 6 cm per year with little variation; this flat prepubertal phase is what makes a low velocity so conspicuous. Then puberty brings the spurt: peak velocity averages 8 to 9 cm per year in girls around age 12 and 9 to 10 in boys around age 14, before growth decelerates to zero as the growth plates fuse.
The reference data in this calculator comes from Kelly and colleagues (Journal of Clinical Endocrinology and Metabolism, 2014), who published age-specific means and standard deviations for velocity in 6 to 18 year olds. For example, the mean velocity for 10-year-old boys is about 5.5 cm per year, rising to about 7.7 at 13 and falling to 2.7 by 16. The calculator converts the measured velocity to a z-score and percentile against the nearest age row.
Technique: where velocity calculations go wrong
Velocity magnifies measurement error, which is its Achilles heel. A 0.5 cm error on each of two measurements three months apart creates up to 4 cm per year of phantom velocity. Three rules keep it honest. First, use the same stadiometer, the same technique and ideally the same measurer. Second, space measurements 6 to 12 months apart; intervals under 6 months should be interpreted very cautiously and never used alone to start investigations. Third, measure at a similar time of day, because children are measurably taller in the morning than the evening as the spinal discs compress through the day.
Record the dates, not just the ages. "Six months ago" is not a date, and rounding the interval introduces exactly the kind of error velocity is meant to detect. This calculator annualises using the exact day count divided by 365.25.
Worked examples
Example 1. A boy measured 120.5 cm on 1 April 2025 and 126.8 cm on 1 April 2026: 6.3 cm over exactly one year, velocity 6.3 cm per year. At a midpoint age of 10, the Kelly mean for boys is 5.5 with SD 1.18, giving a z-score of about +0.7: around the 75th percentile, normal.
Example 2. A girl measured 140.0 cm and then 142.0 cm twelve months later at age 9: velocity 2.0 cm per year. Against the Kelly mean of 5.9 (SD 1.23) for 9-year-old girls, the z-score is about -3.2: frankly low, and an indication for paediatric assessment whatever the centile.
Example 3. A boy measured 150.0 cm and 158.5 cm a year apart at age 13.5: velocity 8.5 cm per year. The Kelly mean at 13 is 7.7 (SD 2.4): z-score about +0.3, normal for mid-puberty. Context is everything: the same velocity at age 8 would be strikingly abnormal.
When low velocity needs investigation
A persistently low velocity, roughly below the 3rd percentile for age or under 4 to 5 cm per year in a prepubertal child over a proper 6 to 12 month interval, deserves workup. The differential is broad: inadequate nutrition, chronic systemic disease (renal, gastrointestinal, cardiac, pulmonary), hypothyroidism, growth hormone deficiency, skeletal dysplasias, and medication effects, particularly prolonged high-dose glucocorticoids. Constitutional delay of growth and puberty is the common benign mimic in teenagers: slow now, but with delayed bone age and a normal eventual height.
Bone age X-ray is usually the next step after confirming the velocity, because it distinguishes constitutional delay (delayed bone age) from growth hormone deficiency and hypothyroidism (also delayed) versus familial short stature (normal bone age, normal velocity). Velocity finds the problem; bone age characterises it.
Laboratory investigation follows the history rather than preceding it, but typically includes thyroid function, coeliac screening, full blood count, renal function and IGF-1, with growth hormone stimulation testing reserved for specialist centres when the auxology points that way. Throughout, the most important test remains the next careful height measurement: treatment decisions in growth are made on confirmed trends, never on a single interval.
Key takeaways
- Height velocity is the most sensitive early indicator of growth disorders.
- Measure 6 to 12 months apart with identical technique; short intervals magnify error enormously.
- Prepubertal children grow about 5 to 6 cm per year; pubertal peaks reach 8 to 10.
- Interpret against age and puberty stage: 8 cm per year is normal at 13 and alarming at 8.
- A persistently low velocity needs paediatric assessment even when the centile still looks normal.
Frequently asked questions
How far apart should the two measurements be?
Six to twelve months is ideal. Shorter intervals magnify measurement error: a 0.5 cm error over 3 months becomes nearly 2 cm per year of apparent velocity. Longer than a year risks averaging across different growth phases, especially around puberty. Always use exact dates.
My child's velocity is normal but the centile is low. Is that okay?
Usually yes. A normal velocity on a low centile means the child is growing well along their own curve, which is typical for children of short parents. The concerning pattern is the reverse: a falling centile or a low velocity, which means the child's own growth has slowed.
Does the time of day really matter?
Yes, measurably. Children are tallest in the morning and lose up to 1 to 2 cm through the day as intervertebral discs compress. For velocity work, measure at a similar time of day each visit, and be extra careful with short intervals where diurnal variation becomes a large fraction of the apparent growth.
What velocity suggests growth hormone deficiency?
No single cutoff diagnoses it, but a velocity persistently below the 3rd percentile for age, or under about 4 cm per year in a prepubertal child over a 6 to 12 month interval, is the classic auxological trigger for investigation. The workup then includes bone age, thyroid function, IGF-1 and often GH stimulation testing under specialist care.
Can velocity be too high?
Yes. Consistently excessive velocity can signal precocious puberty, hyperthyroidism, or over-treatment, and paradoxically it can reduce final adult height if bone age advances faster than height accrues. Unusually fast growth with signs of early puberty deserves assessment just as slow growth does.