Calculate growth velocity (height velocity) in cm or inches per year from two height measurements, plus an optional Z-score and reference percentile.

Annualizes the height change. Add a reference mean and SD to compare it using a normal-distribution assumption.

Reference mean and SD for a percentile
Mean and SD from the same reference for age, sex and interval. Leave both blank for velocity only.

Related Calculators

Growth Velocity Z-score Formula

The following formula is used to calculate the growth velocity Z-score (standard deviation score) for a given current growth velocity, mean growth velocity, and standard deviation of growth velocity.

Z = (V - M) / SD

If the untransformed reference velocities can be modeled by a normal distribution, convert this Z-score using the standard normal cumulative distribution function. This approximation is not a substitute for interval-specific clinical charts or their LMS transformations:

Percentile โ‰ˆ Phi(Z) ร— 100

Variables:

  • Z is the growth velocity Z-score (standard deviation score/SDS)
  • V is the current growth velocity
  • M is the mean growth velocity for age and sex
  • SD is the standard deviation of growth velocity for age and sex
  • Percentile is the approximate percentile corresponding to Z (normal approximation)

To calculate the growth velocity Z-score, subtract the mean growth velocity from the current growth velocity. Then, divide the result by the standard deviation of growth velocity for age and sex. To estimate a percentile, convert the Z-score using a normal CDF (or use published reference percentiles when available).

What is Growth Velocity Z-score?

Growth velocity Z-score (also called a standard deviation score, SDS) is a standardized measure used to compare an individual’s growth rate to a reference population. It describes how far a childโ€™s growth velocity is above or below the mean growth velocity for their age and sex, measured in standard deviations. A Z-score can be converted to an approximate percentile (assuming a normal distribution), but clinical tools may also use published reference percentiles.

How to Calculate Growth Velocity Z-score (and Approximate Percentile)?

The following steps outline how to calculate the Growth Velocity Z-score and estimate a percentile.

  1. First, determine the current growth velocity (V).
  2. Next, determine the mean growth velocity for age and sex (M).
  3. Next, determine the standard deviation of growth velocity for age and sex (SD).
  4. Calculate the Z-score using the formula Z = (V – M) / SD.
  5. If needed, estimate an approximate percentile using Percentile โ‰ˆ ฮฆ(Z) ร— 100 (normal approximation), or compare with published reference percentiles.
  6. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

These hypothetical values illustrate the arithmetic; they are not reference values for a particular child. They give Z = 1 and an approximate normal-model percentile of 84.13%.

Current Growth Velocity (V) = 5 cm/year

Mean Growth Velocity for Age and Sex (M) = 4 cm/year

Standard Deviation of Growth Velocity for Age and Sex (SD) = 1 cm/year