### Description

The distribution of head circumference for young girls age 0-3 years can be used to evaluate the physical development of a child.

month

5th%

10th%

25th%

50th%

75th%

90th%

95th%

0

32.1

32.9

33.5

34.3

34.8

35.5

35.9

1

34.2

34.8

35.6

36.4

37.1

37.8

38.3

3

37.3

37.8

38.7

39.5

40.4

41.2

41.7

6

40.3

40.9

41.6

42.4

43.3

44.1

44.6

9

42.3

42.8

43.5

44.3

45.1

46

46.4

12

43.5

44.1

44.8

45.6

46.4

47.2

47.6

18

45

45.6

46.3

47.1

47.9

48.6

49.1

24

46.1

46.5

47.3

48.1

48.8

49.6

50.1

30

47

47.3

48

48.8

49.4

50.3

50.8

36

47.6

47.9

48.5

49.3

50

50.8

51.4

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

5th% for head circumference in centimeters =

= ((0.0000012 * ((months)^5)) - (0.000148 * ((months)^4)) + (0.0069556 * ((months)^3)) - (0.163182 * ((months)^2)) + (2.1303285 * (months)) + 32.158424)

10th% for head circumference in centimeters =

= ((0.0000009 * ((months)^5)) - (0.000112 * ((months)^4)) + (0.0055756 * ((months)^3)) - (0.141338 * ((months)^2)) + (1.9989488 * (months)) + 32.919519)

25th% for head circumference in centimeters =

= ((0.0000015 * ((months)^5)) - (0.000173 * ((months)^4)) + (0.007584 * ((months)^3)) - (0.168351 * ((months)^2)) + (2.1255298 * (months)) + 33.56967)

50th% for head circumference in centimeters =

= ((0.0000015 * ((months)^5)) - (0.000173 * ((months)^4)) + (0.007584 * ((months)^3)) - (0.168351 * ((months)^2)) + (2.1255298 * (months)) + 34.36967)

75th% for head circumference in centimeters =

= ((0.0000022 * ((months)^5)) - (0.000238 * ((months)^4)) + (0.0097861 * ((months)^3)) - (0.200918 * ((months)^2)) + (2.319393 * (months)) + 34.892429)

90th% for head circumference in centimeters =

= ((0.000002 * ((months)^5)) - (0.000225 * ((months)^4)) + (0.0095797 * ((months)^3)) - (0.202581 * ((months)^2)) + (2.3600106 * (months)) + 35.57647)

95th% for head circumference in centimeters =

= ((0.0000025 * ((months)^5)) - (0.000263 * ((months)^4)) + (0.0107852 * ((months)^3)) - (0.217873 * ((months)^2)) + (2.4261526 * (months)) + 35.996165)

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

age in years

coefficient

0

8.9285714

-572.0879

9168.5865

0.08

7.6595745

-520.3319

8841.4340

0.25

7.2460114

-536.2795

9927.2723

0.5

8.0084129

-640.704

12818.7820

0.75

7.6161563

-636.9205

13319.0420

1

8.0084129

-691.9579

14951.0410

1.5

8.0084129

-715.9831

16006.9970

2

7.0665829

-643.3103

14643.8330

2.5

6.1605449

-565.2556

12963.4800

3

5.5454984

-510.7165

11750.1020

51 to 95%ile

age in years

coefficient

0

-17.150840

1231.30750

-22005.50

0.08

-9.934896

765.78808

-14661.32

0.25

-5.769429

489.00749

-10264.09

0.5

-5.769429

522.47018

-11730.74

0.75

-7.072285

662.56164

-15422.00

1

-7.066583

680.96734

-16308.07

1.5

-7.616156

755.31283

-18629.57

2

-9.516090

956.71999

-23951.51

2.5

-11.462920

1163.41390

-29425.64

3

-9.564570

984.36147

-25232.23