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


 Calculator: Height-for-age percentiles and Z-scores, males 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 males 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, males 2 to 20 years, CDC growth reference (United States)

 
Age [months] Power [L] Median [M] Variation [S]
24 0.9415 86.4522 0.0403
24.5 1.0072 86.8616 0.0404
25.5 0.8373 87.6525 0.0406
26.5 0.6815 88.4233 0.0407
27.5 0.5388 89.1755 0.0408
28.5 0.4077 89.9104 0.0409
29.5 0.2868 90.6291 0.0410
30.5 0.1745 91.3324 0.0410
31.5 0.0694 92.0213 0.0409
32.5 -0.0297 92.6964 0.0409
33.5 -0.1243 93.3585 0.0408
34.5 -0.2153 94.0082 0.0408
35.5 -0.3039 94.6464 0.0407
36.5 -0.3909 95.2736 0.0405
37.5 -0.2548 95.9147 0.0406
38.5 -0.1257 96.5473 0.0406
39.5 -0.0032 97.1719 0.0407
40.5 0.1129 97.7890 0.0407
41.5 0.2228 98.3990 0.0408
42.5 0.3265 99.0025 0.0408
43.5 0.4244 99.6000 0.0409
44.5 0.5164 100.1918 0.0410
45.5 0.6026 100.7783 0.0411
46.5 0.6832 101.3600 0.0412
47.5 0.7582 101.9373 0.0413
48.5 0.8276 102.5105 0.0413
49.5 0.8917 103.0799 0.0414
50.5 0.9504 103.6459 0.0415
51.5 1.0038 104.2087 0.0416
52.5 1.0521 104.7687 0.0417
53.5 1.0954 105.3262 0.0418
54.5 1.1337 105.8813 0.0420
55.5 1.1671 106.4343 0.0421
56.5 1.1958 106.9855 0.0422
57.5 1.2200 107.5350 0.0423
58.5 1.2397 108.0830 0.0424
59.5 1.2551 108.6296 0.0425
60.5 1.2664 109.1751 0.0426
61.5 1.2736 109.7196 0.0427
62.5 1.2770 110.2631 0.0428
63.5 1.2767 110.8058 0.0429
64.5 1.2729 111.3477 0.0430
65.5 1.2657 111.8890 0.0431
66.5 1.2554 112.4296 0.0432
67.5 1.2421 112.9696 0.0433
68.5 1.2260 113.5090 0.0434
69.5 1.2073 114.0479 0.0434
70.5 1.1861 114.5861 0.0435
71.5 1.1628 115.1238 0.0436
72.5 1.1374 115.6609 0.0437
73.5 1.1103 116.1973 0.0437
74.5 1.0815 116.7329 0.0438
75.5 1.0514 117.2678 0.0439
76.5 1.0201 117.8018 0.0439
77.5 0.9878 118.3348 0.0440
78.5 0.9549 118.8668 0.0441
79.5 0.9213 119.3977 0.0441
80.5 0.8875 119.9272 0.0442
81.5 0.8536 120.4554 0.0442
82.5 0.8198 120.9821 0.0443
83.5 0.7862 121.5072 0.0443
84.5 0.7532 122.0305 0.0444
85.5 0.7209 122.5520 0.0445
86.5 0.6895 123.0714 0.0445
87.5 0.6591 123.5886 0.0446
88.5 0.6300 124.1035 0.0446
89.5 0.6022 124.6160 0.0447
90.5 0.5759 125.1259 0.0447
91.5 0.5512 125.6331 0.0448
92.5 0.5283 126.1374 0.0449
93.5 0.5071 126.6388 0.0449
94.5 0.4879 127.1370 0.0450
95.5 0.4706 127.6320 0.0451
96.5 0.4553 128.1237 0.0451
97.5 0.4419 128.6119 0.0452
98.5 0.4306 129.0966 0.0453
99.5 0.4213 129.5777 0.0454
100.5 0.4139 130.0550 0.0454
101.5 0.4084 130.5286 0.0455
102.5 0.4048 130.9983 0.0456
103.5 0.4029 131.4641 0.0457
104.5 0.4026 131.9260 0.0458
105.5 0.4039 132.3840 0.0459
106.5 0.4066 132.8381 0.0460
107.5 0.4106 133.2882 0.0461
108.5 0.4157 133.7345 0.0462
109.5 0.4218 134.1769 0.0463
110.5 0.4287 134.6155 0.0464
111.5 0.4362 135.0504 0.0465
112.5 0.4442 135.4818 0.0467
113.5 0.4526 135.9097 0.0468
114.5 0.4610 136.3343 0.0469
115.5 0.4695 136.7557 0.0470
116.5 0.4777 137.1742 0.0471
117.5 0.4856 137.5899 0.0473
118.5 0.4929 138.0032 0.0474
119.5 0.4997 138.4143 0.0475
120.5 0.5056 138.8234 0.0476
121.5 0.5106 139.2310 0.0477
122.5 0.5145 139.6373 0.0478
123.5 0.5174 140.0427 0.0480
124.5 0.5190 140.4477 0.0481
125.5 0.5195 140.8527 0.0482
126.5 0.5186 141.2582 0.0483
127.5 0.5164 141.6646 0.0484
128.5 0.5130 142.0725 0.0485
129.5 0.5084 142.4824 0.0486
130.5 0.5025 142.8949 0.0487
131.5 0.4957 143.3107 0.0488
132.5 0.4879 143.7304 0.0489
133.5 0.4794 144.1545 0.0490
134.5 0.4704 144.5838 0.0491
135.5 0.4611 145.0190 0.0492
136.5 0.4519 145.4607 0.0493
137.5 0.4429 145.9097 0.0494
138.5 0.4346 146.3665 0.0495
139.5 0.4273 146.8320 0.0496
140.5 0.4215 147.3066 0.0497
141.5 0.4175 147.7911 0.0497
142.5 0.4158 148.2859 0.0498
143.5 0.4168 148.7917 0.0499
144.5 0.4209 149.3088 0.0499
145.5 0.4286 149.8376 0.0500
146.5 0.4402 150.3784 0.0501
147.5 0.4561 150.9313 0.0501
148.5 0.4765 151.4964 0.0502
149.5 0.5018 152.0735 0.0502
150.5 0.5320 152.6624 0.0503
151.5 0.5672 153.2627 0.0503
152.5 0.6075 153.8738 0.0503
153.5 0.6527 154.4951 0.0503
154.5 0.7028 155.1255 0.0504
155.5 0.7574 155.7642 0.0504
156.5 0.8162 156.4099 0.0503
157.5 0.8789 157.0612 0.0503
158.5 0.9451 157.7168 0.0503
159.5 1.0140 158.3751 0.0502
160.5 1.0854 159.0344 0.0501
161.5 1.1585 159.6931 0.0500
162.5 1.2328 160.3493 0.0499
163.5 1.3076 161.0015 0.0498
164.5 1.3825 161.6478 0.0497
165.5 1.4567 162.2865 0.0495
166.5 1.5298 162.9161 0.0493
167.5 1.6012 163.5350 0.0491
168.5 1.6704 164.1418 0.0489
169.5 1.7370 164.7352 0.0487
170.5 1.8005 165.3140 0.0485
171.5 1.8605 165.8771 0.0483
172.5 1.9168 166.4236 0.0480
173.5 1.9689 166.9528 0.0478
174.5 2.0168 167.4641 0.0475
175.5 2.0601 167.9571 0.0472
176.5 2.0988 168.4313 0.0470
177.5 2.1326 168.8867 0.0467
178.5 2.1617 169.3231 0.0464
179.5 2.1858 169.7405 0.0462
180.5 2.2052 170.1393 0.0459
181.5 2.2197 170.5195 0.0456
182.5 2.2296 170.8815 0.0454
183.5 2.2349 171.2257 0.0451
184.5 2.2358 171.5525 0.0448
185.5 2.2326 171.8626 0.0446
186.5 2.2253 172.1563 0.0444
187.5 2.2144 172.4343 0.0441
188.5 2.1999 172.6972 0.0439
189.5 2.1823 172.9456 0.0437
190.5 2.1617 173.1801 0.0435
191.5 2.1385 173.4014 0.0433
192.5 2.1130 173.6101 0.0431
193.5 2.0855 173.8067 0.0429
194.5 2.0562 173.9920 0.0427
195.5 2.0255 174.1665 0.0426
196.5 1.9936 174.3308 0.0424
197.5 1.9608 174.4854 0.0423
198.5 1.9273 174.6310 0.0421
199.5 1.8934 174.7680 0.0420
200.5 1.8593 174.8969 0.0418
201.5 1.8252 175.0182 0.0417
202.5 1.7913 175.1323 0.0416
203.5 1.7578 175.2398 0.0415
204.5 1.7247 175.3410 0.0414
205.5 1.6923 175.4362 0.0413
206.5 1.6607 175.5259 0.0412
207.5 1.6298 175.6104 0.0411
208.5 1.6000 175.6901 0.0411
209.5 1.5711 175.7652 0.0410
210.5 1.5433 175.8360 0.0409
211.5 1.5165 175.9028 0.0409
212.5 1.4909 175.9658 0.0408
213.5 1.4665 176.0254 0.0408
214.5 1.4431 176.0816 0.0407
215.5 1.4210 176.1348 0.0407
216.5 1.4000 176.1850 0.0406
217.5 1.3801 176.2326 0.0406
218.5 1.3614 176.2776 0.0406
219.5 1.3438 176.3202 0.0405
220.5 1.3272 176.3606 0.0405
221.5 1.3117 176.3989 0.0405
222.5 1.2971 176.4352 0.0405
223.5 1.2836 176.4697 0.0405
224.5 1.2710 176.5024 0.0404
225.5 1.2593 176.5335 0.0404
226.5 1.2484 176.5630 0.0404
227.5 1.2384 176.5911 0.0404
228.5 1.2292 176.6179 0.0404
229.5 1.2207 176.6433 0.0404
230.5 1.2129 176.6676 0.0404
231.5 1.2057 176.6907 0.0404
232.5 1.1993 176.7127 0.0404
233.5 1.1934 176.7337 0.0404
234.5 1.1880 176.7538 0.0404
235.5 1.1832 176.7730 0.0404
236.5 1.1789 176.7913 0.0404
237.5 1.1751 176.8088 0.0404
238.5 1.1716 176.8255 0.0404
239.5 1.1686 176.8415 0.0404
240 1.1673 176.8492 0.0404

 

 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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