On this page
Your child's numbers, step by step
Every percentile calculator does this behind the scenes. Here is the same math, using your child's numbers and the CDC reference data.
What L, M and S mean
The CDC summarized growth data for thousands of US children as three numbers for every month of age, separately for boys and girls:1
- M is the median BMI: half of children that age have a lower BMI.
- S describes the spread, roughly how much BMI varies around the median.
- L corrects for skew. BMI isn't symmetrical: there's a longer tail on the high side. L reshapes the data so a normal distribution fits.1
Values are listed at the middle of each month (24.5, 25.5 months and so on).2 For ages in between, interpolate between the two nearest rows.
The z-score formula
z = ((BMI ÷ M)^L − 1) ÷ (L × S)
Worked example for a boy aged 100.5 months (8 years 4 months) with a BMI of 16.22. The CDC values are L = −3.1149, M = 15.899 and S = 0.1054:2
- BMI ÷ M = 16.22 ÷ 15.899 = 1.0200
- 1.0200 raised to the power −3.1149 = 0.9402
- 0.9402 − 1 = −0.0598
- L × S = −3.1149 × 0.1054 = −0.3283
- z = −0.0598 ÷ −0.3283 = 0.18
From z-score to percentile
The percentile is the share of the normal distribution below the z-score. In Excel or Google Sheets: =NORM.S.DIST(0.18,TRUE), which gives 0.57, the 57th percentile.
| Percentile | z-score |
|---|---|
| 5th | −1.645 |
| 50th | 0 |
| 85th | 1.036 |
| 95th | 1.645 |
A percentile is a comparison, not a body measurement:
| What a BMI percentile shows | What it doesn't show |
|---|---|
| How a child's BMI compares with others of the same age and sex | How much of their weight is fat, muscle or bone |
| Where they sit against the CDC's 2000 reference data | How they compare with children measured today |
| Whether they're tracking along the same curve over time | A diagnosis or a full picture of their health |
| A precise position up to about the 97th percentile | Reliable differences far above the 95th percentile |
Above the 95th percentile
At the top of the chart, percentiles squeeze together, and the LMS method becomes less reliable above about the 97th percentile.3 The CDC instead expresses very high BMIs as a percent of the 95th percentile: 120% or more is severe obesity (class 2), and 140% or more is class 3.3 The calculator above shows this figure automatically.
Frequently asked questions
Where do I get the L, M and S values?
From the CDC's growth chart data files. This site uses the same table, and the calculator shows the values it used for your child's age.
Can I calculate a BMI percentile in Excel?
Yes. Put L, M and S in cells, calculate z with the formula above, and use =NORM.S.DIST(z,TRUE) for the percentile. BMI formulas in Excel.
Why not just compare BMI to a chart?
You can read an approximate percentile from a printed CDC growth chart. The LMS calculation gives the exact value. BMI for kids.
Sources
This page is for education and is not medical advice. Talk with a healthcare professional about your weight and health.
