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Calculator: Head circumference-for-age percentiles and Z-scores, 0 to 36 months (CDC)

Calculator: Head circumference-for-age percentiles and Z-scores, 0 to 36 months (CDC)

 
Input
 
Sex Female

 Male
Age  
Head circumference  

 
Results
 
Important: Inputs must be complete to perform calculation.

 
 
Z-score    
Percentile    
 
Decimal precision  
 

 

 
Head circumference-for-age percentile interpretation

 
Percentile <3: Microcephaly
Percentile ≥3 and <97: Normal head circumference
Percentile ≥97: Macrocephaly

 
 

 
Notes
  • This calculator is based on the United States Centers for Disease Control and Prevention (CDC) growth reference.
  • Microcephaly is a Head circumference greater than 2 standard deviations below the mean.
  • Macrocephaly is a Head circumference greater than 2 standard deviations above the mean.
  • At the extremes (>97th percentile or <3rd percentile), small differences in percentiles represent clinically important differences. At these extremes, the Z-score is a more precise reflection of how far the measurement deviates from the mean and is a useful tool for tracking changes.
  • For all LMS tables, the row in the table corresponding to the patient-specific value is found in the first column of the table; values to be used for L (the Box-Cox power), M (the median), and S (the generalized coefficient of variation) in the equation for Z-score are retrieved.
  • The accuracy of the calculation can be assessed by viewing the graph of head circumference-for-age percentiles for this sex and age group in UpToDate.
  • Z-scores may be used to perform a table lookup for the corresponding percentile in the Normal table percentiles for Z-score table (below). Numbers along the left side (Y-axis) of the table represent the first number and first decimal place of the Z-score, while the numbers along the top (X-axis) of the table represent the second decimal position of the Z-score.

 
Equations used
 
Z-score = ((Head_Circumference/M)L - 1) / (L * S)
Percentile = ZtoPercentile(Z-score)

 

 
Examples
 
Z-scorePercentile equivalent
- 3.0
0.3
- 2.0
2.5
+ 2.0
97.5
+ 3.0
99.7

 
References
  1. Centers for Disease Control and Prevention, National Center for Health Statistics. Clinical growth charts. https://www.cdc.gov/growthcharts/clinical_charts.htm (Accessed on June 26, 2023).

 
Appendix

 
LMS table: Head circumference-for-age percentiles, females 0 to 36 months, CDC growth reference (United States)
 
Age [months] Power [L] Median [M] Variation [S]
0 -1.2987 34.7116 0.0469
0.5 -1.4403 36.0345 0.0430
1.5 -1.5810 37.9767 0.0381
2.5 -1.5931 39.3801 0.0351
3.5 -1.5215 40.4677 0.0331
4.5 -1.3946 41.3484 0.0317
5.5 -1.2317 42.0834 0.0307
6.5 -1.0466 42.7103 0.0300
7.5 -0.8489 43.2543 0.0294
8.5 -0.6458 43.7325 0.0290
9.5 -0.4422 44.1574 0.0287
10.5 -0.2416 44.5384 0.0285
11.5 -0.0467 44.8824 0.0284
12.5 0.1410 45.1951 0.0283
13.5 0.3204 45.4808 0.0283
14.5 0.4908 45.7431 0.0283
15.5 0.6519 45.9849 0.0283
16.5 0.8037 46.2086 0.0284
17.5 0.9463 46.4162 0.0285
18.5 1.0798 46.6095 0.0286
19.5 1.2046 46.7899 0.0287
20.5 1.3211 46.9586 0.0288
21.5 1.4296 47.1168 0.0290
22.5 1.5306 47.2654 0.0291
23.5 1.6245 47.4052 0.0293
24.5 1.7117 47.5369 0.0295
25.5 1.7926 47.6612 0.0297
26.5 1.8676 47.7787 0.0299
27.5 1.9370 47.8898 0.0301
28.5 2.0014 47.9951 0.0303
29.5 2.0609 48.0949 0.0305
30.5 2.1159 48.1896 0.0307
31.5 2.1667 48.2796 0.0309
32.5 2.2136 48.3651 0.0311
33.5 2.2569 48.4465 0.0314
34.5 2.2968 48.5240 0.0316
35.5 2.3336 48.5978 0.0318
36 2.3508 48.6334 0.0319

 
LMS table: Head circumference-for-age percentiles, males 0 to 36 months, CDC growth reference (United States)
 
Age [months] Power [L] Median [M] Variation [S]
0 4.4278 35.8137 0.0522
0.5 4.3109 37.1936 0.0473
1.5 3.8696 39.2074 0.0409
2.5 3.3056 40.6523 0.0370
3.5 2.7206 41.7652 0.0344
4.5 2.1680 42.6612 0.0325
5.5 1.6755 43.4049 0.0311
6.5 1.2552 44.0361 0.0300
7.5 0.9105 44.5810 0.0292
8.5 0.6395 45.0576 0.0287
9.5 0.4370 45.4791 0.0282
10.5 0.2963 45.8551 0.0279
11.5 0.2101 46.1930 0.0277
12.5 0.1711 46.4985 0.0276
13.5 0.1724 46.7764 0.0275
14.5 0.2074 47.0302 0.0275
15.5 0.2702 47.2630 0.0276
16.5 0.3558 47.4772 0.0277
17.5 0.4594 47.6750 0.0278
18.5 0.5772 47.8582 0.0279
19.5 0.7058 48.0282 0.0281
20.5 0.8423 48.1864 0.0283
21.5 0.9843 48.3338 0.0285
22.5 1.1296 48.4714 0.0287
23.5 1.2767 48.6001 0.0290
24.5 1.4241 48.7206 0.0292
25.5 1.5706 48.8337 0.0295
26.5 1.7154 48.9398 0.0298
27.5 1.8577 49.0395 0.0301
28.5 1.9968 49.1332 0.0303
29.5 2.1324 49.2215 0.0306
30.5 2.2641 49.3046 0.0309
31.5 2.3917 49.3829 0.0312
32.5 2.5149 49.4568 0.0316
33.5 2.6337 49.5264 0.0319
34.5 2.7479 49.5922 0.0322
35.5 2.8577 49.6542 0.0325
36 2.9109 49.6839 0.0327

 
LMS table: Normal table percentiles for Z-score
 
Z 1 3 5 7 9
-3.0 0.13% 0.12% 0.11% 0.11% 0.10%
-2.9 0.18% 0.17% 0.16% 0.15% 0.14%
-2.8 0.25% 0.23% 0.22% 0.21% 0.19%
-2.7 0.34% 0.32% 0.30% 0.28% 0.26%
-2.6 0.45% 0.43% 0.40% 0.38% 0.36%
-2.5 0.60% 0.57% 0.54% 0.51% 0.48%
-2.4 0.80% 0.75% 0.71% 0.68% 0.64%
-2.3 1.04% 0.99% 0.94% 0.89% 0.84%
-2.2 1.36% 1.29% 1.22% 1.16% 1.10%
-2.1 1.74% 1.66% 1.58% 1.50% 1.43%
-2.0 2.22% 2.12% 2.02% 1.92% 1.83%
-1.9 2.81% 2.68% 2.56% 2.44% 2.33%
-1.8 3.52% 3.36% 3.22% 3.07% 2.94%
-1.7 4.36% 4.18% 4.01% 3.84% 3.67%
-1.6 5.37% 5.16% 4.95% 4.75% 4.55%
-1.5 6.55% 6.30% 6.06% 5.82% 5.59%
-1.4 7.93% 7.64% 7.35% 7.08% 6.81%
-1.3 9.51% 9.18% 8.85% 8.53% 8.23%
-1.2 11.31% 10.94% 10.57% 10.20% 9.85%
-1.1 13.35% 12.92% 12.51% 12.10% 11.70%
-1.0 15.63% 15.15% 14.69% 14.23% 13.79%
-0.9 18.14% 17.62% 17.11% 16.60% 16.11%
-0.8 20.90% 20.33% 19.77% 19.22% 18.67%
-0.7 23.89% 23.27% 22.66% 22.07% 21.48%
-0.6 27.09% 26.44% 25.79% 25.14% 24.51%
-0.5 30.50% 29.81% 29.12% 28.43% 27.76%
-0.4 34.09% 33.36% 32.64% 31.92% 31.21%
-0.3 37.83% 37.07% 36.32% 35.57% 34.83%
-0.2 41.68% 40.91% 40.13% 39.36% 38.59%
-0.1 45.62% 44.83% 44.04% 43.25% 42.47%
-0.0 49.60% 48.80% 48.01% 47.21% 46.41%
0.0 50.40% 51.20% 51.99% 52.79% 53.59%
0.1 54.38% 55.17% 55.96% 56.75% 57.54%
0.2 58.32% 59.10% 59.87% 60.64% 61.41%
0.3 62.17% 62.93% 63.68% 64.43% 65.17%
0.4 65.91% 66.64% 67.36% 68.08% 68.79%
0.5 69.50% 70.19% 70.88% 71.57% 72.24%
0.6 72.91% 73.57% 74.22% 74.86% 75.49%
0.7 76.12% 76.73% 77.34% 77.94% 78.52%
0.8 79.10% 79.67% 80.23% 80.79% 81.33%
0.9 81.86% 82.38% 82.89% 83.40% 83.89%
1.0 84.38% 84.85% 85.31% 85.77% 86.21%
1.1 86.65% 87.08% 87.49% 87.90% 88.30%
1.2 88.69% 89.07% 89.44% 89.80% 90.15%
1.3 90.49% 90.82% 91.15% 91.47% 91.77%
1.4 92.07% 92.36% 92.65% 92.92% 93.19%
1.5 93.45% 93.70% 93.94% 94.18% 94.41%
1.6 94.63% 94.85% 95.05% 95.25% 95.45%
1.7 95.64% 95.82% 95.99% 96.16% 96.33%
1.8 96.49% 96.64% 96.78% 96.93% 97.06%
1.9 97.19% 97.32% 97.44% 97.56% 97.67%
2.0 97.78% 97.88% 97.98% 98.08% 98.17%
2.1 98.26% 98.34% 98.42% 98.50% 98.57%
2.2 98.65% 98.71% 98.78% 98.84% 98.90%
2.3 98.96% 99.01% 99.06% 99.11% 99.16%
2.4 99.20% 99.25% 99.29% 99.32% 99.36%
2.5 99.40% 99.43% 99.46% 99.49% 99.52%
2.6 99.55% 99.57% 99.60% 99.62% 99.64%
2.7 99.66% 99.68% 99.70% 99.72% 99.74%
2.8 99.75% 99.77% 99.78% 99.80% 99.81%
2.9 99.82% 99.83% 99.84% 99.85% 99.86%
3.0 99.87% 99.88% 99.89% 99.89% 99.90%

 
Only digits 0 to 9 and a single decimal point (".") are acceptable as numeric inputs. Attempted input of other characters into a numeric field may lead to an incorrect result.

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Topic 13417 Version 22.0

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