How the percentile is calculated
The CDC 2000 Growth Charts describe how height (stature) and weight are distributed among US children at every age from 2 to 20. Instead of publishing every percentile, the CDC publishes three numbers for each sex and each half month of age: L (a skewness term), M (the median) and S (the spread). This calculator uses those official LMS values.
Step 1, find the reference at the exact age. The CDC rows are listed at 24, 24.5, 25.5, 26.5 months and so on. For an 8-year-old (96 months), the calculator blends the 95.5 and 96.5 month rows in proportion to the age, so a child a few weeks older gets a slightly taller median.
Step 2, convert the measurement to a z-score. z = ((X / M)^L − 1) / (L × S), where X is the height in centimeters or the weight in kilograms. A z-score of 0 means exactly the median; −1.64 and +1.64 mark the 5th and 95th percentiles.
Step 3, turn z into a percentile with the standard normal distribution. A girl who is 127 cm tall at 8 years 0 months has a z-score just under 0, which is about the 46th percentile: roughly 46 of every 100 girls her age in the reference population are shorter. Inches and pounds are converted to metric first, so both unit systems give identical answers.