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Calculator: Height-for-age percentiles and Z-scores, females 2 to 20 years (CDC)


 Calculator: Height-for-age percentiles and Z-scores, females 2 to 20 years (CDC)

 
Input
 
Age  
Height  

 
Results
 
Important: Inputs must be complete to perform calculation.

 
 
Z-score  
Percentile  
 
Decimal precision  

 

 

 Height-for-age percentile interpretation

 
Percentile <5: Short stature
Percentile ≥5 and <95: Normal stature
Percentile ≥95: Tall stature

 
 

 
Notes
  • This calculator is based on the United States Centers for Disease Control and Prevention (CDC) growth reference.
  • This calculator uses measured standing height for females 2 to 20 years of age.
  • In some cases, including consideration of pharmacotherapy, more stringent definitions of short or tall stature are used, with thresholds of <3rd percentile or <1st percentile for short stature and >97th or >99th percentile for tall stature.
  • 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 height-for-age percentiles for this sex and age group in UpToDate.
  • Z-scores may be used to do 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 = ((Height/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).

 

 LMS table: Height-for-age percentiles, females 2 to 20 years, CDC growth reference (United States)

 
Age [months] Power [L] Median [M] Variation [S]
24 1.0724 84.9756 0.0408
24.5 1.0513 85.3973 0.0409
25.5 1.0420 86.2903 0.0411
26.5 1.0126 87.1571 0.0413
27.5 0.9705 87.9960 0.0415
28.5 0.9211 88.8055 0.0416
29.5 0.8682 89.5848 0.0417
30.5 0.8145 90.3334 0.0418
31.5 0.7620 91.0515 0.0418
32.5 0.7117 91.7396 0.0418
33.5 0.6643 92.3985 0.0419
34.5 0.6203 93.0295 0.0419
35.5 0.5796 93.6338 0.0420
36.5 0.5420 94.2134 0.0420
37.5 0.5114 94.7964 0.0421
38.5 0.4828 95.3739 0.0422
39.5 0.4555 95.9469 0.0423
40.5 0.4292 96.5164 0.0424
41.5 0.4034 97.0834 0.0425
42.5 0.3779 97.6485 0.0426
43.5 0.3526 98.2125 0.0427
44.5 0.3273 98.7759 0.0428
45.5 0.3020 99.3394 0.0429
46.5 0.2766 99.9033 0.0431
47.5 0.2512 100.4681 0.0432
48.5 0.2257 101.0339 0.0433
49.5 0.2003 101.6012 0.0434
50.5 0.1749 102.1700 0.0435
51.5 0.1497 102.7406 0.0436
52.5 0.1247 103.3130 0.0436
53.5 0.1000 103.8873 0.0437
54.5 0.0757 104.4635 0.0438
55.5 0.0518 105.0415 0.0439
56.5 0.0285 105.6213 0.0440
57.5 0.0059 106.2029 0.0441
58.5 -0.0161 106.7861 0.0441
59.5 -0.0374 107.3707 0.0442
60.5 -0.0577 107.9566 0.0443
61.5 -0.0772 108.5436 0.0443
62.5 -0.0957 109.1316 0.0444
63.5 -0.1132 109.7202 0.0445
64.5 -0.1297 110.3092 0.0445
65.5 -0.1450 110.8984 0.0446
66.5 -0.1592 111.4876 0.0447
67.5 -0.1722 112.0764 0.0447
68.5 -0.1840 112.6646 0.0448
69.5 -0.1947 113.2519 0.0448
70.5 -0.2040 113.8380 0.0449
71.5 -0.2122 114.4226 0.0449
72.5 -0.2191 115.0055 0.0450
73.5 -0.2247 115.5863 0.0450
74.5 -0.2291 116.1648 0.0451
75.5 -0.2323 116.7406 0.0451
76.5 -0.2343 117.3136 0.0451
77.5 -0.2351 117.8833 0.0452
78.5 -0.2348 118.4496 0.0452
79.5 -0.2333 119.0123 0.0453
80.5 -0.2307 119.5710 0.0453
81.5 -0.2271 120.1254 0.0453
82.5 -0.2224 120.6755 0.0454
83.5 -0.2168 121.2210 0.0454
84.5 -0.2102 121.7617 0.0455
85.5 -0.2028 122.2974 0.0455
86.5 -0.1945 122.8279 0.0455
87.5 -0.1855 123.3531 0.0456
88.5 -0.1757 123.8728 0.0456
89.5 -0.1653 124.3870 0.0457
90.5 -0.1544 124.8956 0.0457
91.5 -0.1428 125.3985 0.0457
92.5 -0.1308 125.8956 0.0458
93.5 -0.1184 126.3869 0.0458
94.5 -0.1056 126.8724 0.0459
95.5 -0.0926 127.3522 0.0459
96.5 -0.0793 127.8263 0.0460
97.5 -0.0658 128.2947 0.0460
98.5 -0.0522 128.7576 0.0461
99.5 -0.0385 129.2152 0.0461
100.5 -0.0247 129.6675 0.0462
101.5 -0.0110 130.1148 0.0463
102.5 0.0027 130.5574 0.0463
103.5 0.0164 130.9954 0.0464
104.5 0.0301 131.4293 0.0465
105.5 0.0436 131.8593 0.0466
106.5 0.0571 132.2859 0.0467
107.5 0.0706 132.7094 0.0468
108.5 0.0841 133.1304 0.0469
109.5 0.0977 133.5493 0.0470
110.5 0.1115 133.9667 0.0471
111.5 0.1254 134.3832 0.0472
112.5 0.1397 134.7995 0.0474
113.5 0.1544 135.2163 0.0475
114.5 0.1698 135.6342 0.0477
115.5 0.1859 136.0540 0.0478
116.5 0.2030 136.4766 0.0480
117.5 0.2212 136.9027 0.0482
118.5 0.2408 137.3333 0.0483
119.5 0.2619 137.7691 0.0485
120.5 0.2847 138.2112 0.0487
121.5 0.3096 138.6602 0.0489
122.5 0.3366 139.1172 0.0491
123.5 0.3659 139.5829 0.0493
124.5 0.3977 140.0581 0.0495
125.5 0.4321 140.5435 0.0496
126.5 0.4692 141.0397 0.0498
127.5 0.5089 141.5472 0.0500
128.5 0.5514 142.0664 0.0501
129.5 0.5963 142.5974 0.0503
130.5 0.6436 143.1404 0.0504
131.5 0.6931 143.6950 0.0505
132.5 0.7443 144.2609 0.0505
133.5 0.7969 144.8376 0.0506
134.5 0.8505 145.4240 0.0506
135.5 0.9044 146.0192 0.0505
136.5 0.9581 146.6217 0.0505
137.5 1.0111 147.2300 0.0504
138.5 1.0625 147.8424 0.0502
139.5 1.1117 148.4569 0.0500
140.5 1.1581 149.0714 0.0498
141.5 1.2011 149.6839 0.0496
142.5 1.2399 150.2920 0.0493
143.5 1.2740 150.8936 0.0489
144.5 1.3030 151.4866 0.0486
145.5 1.3266 152.0687 0.0482
146.5 1.3444 152.6381 0.0478
147.5 1.3564 153.1930 0.0474
148.5 1.3626 153.7317 0.0470
149.5 1.3631 154.2529 0.0466
150.5 1.3582 154.7555 0.0462
151.5 1.3482 155.2385 0.0458
152.5 1.3338 155.7012 0.0454
153.5 1.3154 156.1432 0.0450
154.5 1.2937 156.5643 0.0446
155.5 1.2693 156.9644 0.0442
156.5 1.2430 157.3437 0.0439
157.5 1.2153 157.7025 0.0435
158.5 1.1870 158.0411 0.0432
159.5 1.1585 158.3603 0.0429
160.5 1.1304 158.6606 0.0426
161.5 1.1031 158.9427 0.0424
162.5 1.0770 159.2075 0.0421
163.5 1.0523 159.4557 0.0419
164.5 1.0294 159.6882 0.0417
165.5 1.0083 159.9058 0.0415
166.5 0.9891 160.1094 0.0413
167.5 0.9718 160.2997 0.0412
168.5 0.9566 160.4777 0.0410
169.5 0.9432 160.6441 0.0409
170.5 0.9318 160.7995 0.0408
171.5 0.9221 160.9449 0.0407
172.5 0.9140 161.0808 0.0406
173.5 0.9075 161.2079 0.0405
174.5 0.9025 161.3268 0.0404
175.5 0.8987 161.4381 0.0403
176.5 0.8961 161.5423 0.0403
177.5 0.8947 161.6399 0.0402
178.5 0.8941 161.7315 0.0402
179.5 0.8945 161.8174 0.0401
180.5 0.8956 161.8980 0.0401
181.5 0.8973 161.9738 0.0400
182.5 0.8997 162.0450 0.0400
183.5 0.9025 162.1120 0.0400
184.5 0.9058 162.1752 0.0400
185.5 0.9094 162.2347 0.0399
186.5 0.9134 162.2908 0.0399
187.5 0.9176 162.3439 0.0399
188.5 0.9220 162.3940 0.0399
189.5 0.9266 162.4414 0.0399
190.5 0.9314 162.4862 0.0398
191.5 0.9362 162.5287 0.0398
192.5 0.9411 162.5690 0.0398
193.5 0.9461 162.6072 0.0398
194.5 0.9511 162.6435 0.0398
195.5 0.9561 162.6781 0.0398
196.5 0.9611 162.7109 0.0398
197.5 0.9661 162.7421 0.0398
198.5 0.9710 162.7719 0.0398
199.5 0.9759 162.8002 0.0398
200.5 0.9808 162.8273 0.0398
201.5 0.9856 162.8531 0.0397
202.5 0.9903 162.8778 0.0397
203.5 0.9949 162.9013 0.0397
204.5 0.9995 162.9238 0.0397
205.5 1.0040 162.9454 0.0397
206.5 1.0084 162.9660 0.0397
207.5 1.0127 162.9858 0.0397
208.5 1.0169 163.0047 0.0397
209.5 1.0211 163.0228 0.0397
210.5 1.0251 163.0402 0.0397
211.5 1.0291 163.0569 0.0397
212.5 1.0330 163.0729 0.0397
213.5 1.0368 163.0882 0.0397
214.5 1.0405 163.1030 0.0397
215.5 1.0441 163.1172 0.0397
216.5 1.0476 163.1308 0.0397
217.5 1.0510 163.1439 0.0397
218.5 1.0543 163.1565 0.0397
219.5 1.0576 163.1686 0.0397
220.5 1.0608 163.1802 0.0397
221.5 1.0639 163.1914 0.0397
222.5 1.0669 163.2022 0.0397
223.5 1.0698 163.2126 0.0397
224.5 1.0727 163.2226 0.0397
225.5 1.0754 163.2322 0.0397
226.5 1.0781 163.2415 0.0397
227.5 1.0808 163.2504 0.0397
228.5 1.0833 163.2590 0.0397
229.5 1.0858 163.2673 0.0397
230.5 1.0882 163.2753 0.0397
231.5 1.0906 163.2830 0.0397
232.5 1.0929 163.2904 0.0396
233.5 1.0951 163.2976 0.0396
234.5 1.0972 163.3045 0.0396
235.5 1.0993 163.3111 0.0396
236.5 1.1014 163.3175 0.0396
237.5 1.1033 163.3237 0.0396
238.5 1.1053 163.3297 0.0396
239.5 1.1071 163.3354 0.0396
240 1.1080 163.3383 0.0396

 

 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.

Information on this page may not appear correctly if printed.

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Topic 13416 Version 17.0