How to Calculate Growth Velocity

Doctors track a child's growth velocity to make sure he is developing normally.
••• baby image by Diane Stamatelatos from

If you are the parent of a young child, perhaps one of the first things that dawned on you, and continued to startle you over time, was just how quickly children can grow. And naturally, parents want to know that their children are growing ​enough –​ that is, if their growth velocity is sufficient, even allowing for children probably destined by genetics to be short adults.

Knowing that a young child is within the normal height range at any time is not always enough to be reassured, because this can occur in a child whose growth was normal or even rapid for a time and then slowed down; it can also happen in children who were born large but have "lost ground" for their age ever since. For this reason, knowing the ​rate​ of growth is important.

A ​height velocity​ calculator and similar tools can help with this task, as parents can compare their kids' values to established norms that have been generated using extensive population data.

How Children Develop and Grow

Infants grow very rapidly in both absolute and percentage (that is, as a function of overall size) terms. A normal-sized newborn typically increases in length by 30 percent in the first five months and by more than 50 percent by their first birthday.

  • An infant grows on average an astonishing 25 cm (10 in) in its first 12 months.

Overall, healthy infants and children grow about 2.5 cm (1 in) a month between birth and 6 months, 1.3 cm (1/2 inch) a month from 7 to 12 months, and about 7.6 cm (3 in) a year between one and 10 years of age. There is more natural variation in growth velocity in the first year (mostly because of premature births) than afterward, when growth velocity is roughly constant until puberty.

Height Velocity Equation

Researchers have developed equations for software programs to keep track of whether a child's growth velocity is "normal." First, a curve of age vs. normal growth velocity for the child's sex is consulted. Then, researchers can plot curves above and below normal, or average, by some factor that captures healthy growth.

Say you want a curve corresponding to a given height ​percentile​ (top or bottom 10 percent, 20 percent, 30 percent and so on). The height velocity formula for generating these curves is

HV- \text{percentile} = M(1 + LSZ)^{1/L}

where ​HV​ is height velocity, ​M​ is the median (average), ​L​ is a quality called skewness, ​S​ is variability and ​Z​ is the chosen standard deviation from the mean. A broader choice of ​Z​ widens the definition of what is considered "normal" for growth velocity purposes, which can vary from source to source.

Peak Height Calculator

It is possible given a variety of inputs to get a good estimate of peak height velocity, or the age at which height is increasing most rapidly. Unlike the previous calculations, though, this one applies to adolescents, who experience a ​growth spurt​ with the onset of puberty in both sexes.

Prediction of how old a child will be when he or she reaches peak height velocity (​PHV​) is based on the differential growth and timing of leg length and sitting height. The legs grow before the torso does, meaning that there is initially little sitting height growth. This is followed by an increase in sitting height growth.

Given the child's age, the date of the standing and sitting height measurements, and weight at the time of the measurements, it is possible to calculate an estimate of age at peak height velocity (​APHV​). An online tool for this is found in the Resources, as is a normal childhood growth chart.

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