This formula for BMI is the same for adults and children. However, the value is interpreted differently in children. In kids and teenagers, BMI is age and sex-specific.
This is because body fat and weight standards change with age and sex due to different body structures and hormone fluctuations.
As an example, an 8-year-old girl with a BMI of 22 would fall into the greater than 95th percentile and would be considered obese. However, a 15-year-old girl with a BMI of 22 would fall between the 50th and 75th percentile and would be considered to be a healthy weight.
These BMI charts are available on the CDC website.