Calculate annualized height growth velocity, Z-score, and approximate percentile from two measurements or a known rate using age- and sex-specific reference values.

Required: two heights, elapsed time, reference mean, and reference SD.

Reference mean and SD must use the selected velocity unit.

Use the mean from the same published clinical reference as the SD.

Educational estimate only—not a diagnosis. Percentile is a normal-distribution approximation from the entered mean and SD, not a CDC height-for-age percentile. Reference choice, age, sex, pubertal timing, measurement technique, and interval all affect interpretation; review concerns with a pediatric clinician.

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 you want an approximate percentile, you can convert the Z-score using the standard normal cumulative distribution function:

Percentile ≈ (Z) × 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 child’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 ≈ Φ(Z) × 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 : 

Use the following variables as an example problem to test your knowledge.

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