Head Circumference for Boys 0-3

Data: head circumference in centimeters.

Polynomial equations approximating this data were calculated in JMP, as follows:

5th% for head circumference in centimeters =

= ((-8.4 * 10^(-8) * ((months)^6)) + (0.0000106 * ((months)^5)) - (0.000546 * ((months)^4)) + (0.0149958 * ((months)^3)) - (0.243795 * ((months)^2)) + (2.5218565 * (months)) + 32.610369)

10th% for head circumference in centimeters =

= ((-9 * 10^(-8) * ((months)^6)) + (0.0000113 * ((months)^5)) - (0.000575 * ((months)^4)) + (0.0156669 * ((months)^3)) - (0.25234 * ((months)^2)) + (2.570534 * (months)) + 33.032701)

25th% for head circumference in centimeters =

= ((-9.2 * 10^(-8) * ((months)^6)) + (0.0000111 * ((months)^5)) - (0.000547 * ((months)^4)) + (0.0146785 * ((months)^3)) - (0.239547 * ((months)^2)) + (2.5080993 * (months)) + 33.915289)

50th% for head circumference in centimeters =

= ((-9.4 * 10^(-8) * ((months)^6)) + (0.0000114 * ((months)^5)) - (0.000568 * ((months)^4)) + (0.0152087 * ((months)^3)) - (0.245625 * ((months)^2)) + (2.537425 * (months)) + 34.835751)

75th% for head circumference in centimeters =

= ((-1.6 * 10^(-7) * ((months)^6)) + (0.0000186 * ((months)^5)) - (0.00087 * ((months)^4)) + (0.0212998 * ((months)^3)) - (0.303215 * ((months)^2)) + (2.7456556 * (months)) + 35.622878)

90th% for head circumference in centimeters =

= ((0.0000019 * ((months)^5)) - (0.000217 * ((months)^4)) + (0.0094392 * ((months)^3)) - (0.20525 * ((months)^2)) + (2.4391856 * (months)) + 36.684292)

Note: This equation is fifth order, while the others in the series are sixth order. The sixth order equation for the 90th percentile data gave less accurate results, while the fifth order was appropriate. The sixth order equation is: (((-1) * (10^(-7)) * ((months)^6)) + (0.0000126 * ((months)^5)) - (0.000625 * ((months)^4)) + (0.0165703 * ((months)^3)) - (0.260665 * ((months)^2)) + (2.5934976 * (months)) + 36.62589).

95th% for head circumference in centimeters =

= ((-1.2 * 10^(-7) * ((months)^6)) + (0.000014 * ((months)^5)) - (0.000674 * ((months)^4)) + (0.0173798 * ((months)^3)) - (0.267385 * ((months)^2)) + (2.6135233 * (months)) + 37.218546)

Distribution of Head Circumference by Month

If the same data is analyzed for each month, then the percentile represented by a given head circumference can be derived. Initially third and fourth order polynomial equations were tried, but were found to be inaccurate. Using 2 second order polynomials for above and below the 50th percentile gave equations adequate for most clinical situations.

5 to 50%ile

51 to 95%ile