Calculator: Length-for-age percentiles and Z-scores, 0 to 24 months (WHO)

Input

Sex	Female
	Male
Age
Length

Results

Important: Inputs must be complete to perform calculation.


Z-score
Percentile

Decimal precision

Notes

This calculator is based on the World Health Organization (WHO) growth standard.
This calculator uses measured recumbent length for infants and toddlers from birth through 24 months of age.
It is not valid for standing height.
At the extremes (>97^th percentile or <3^rd 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 length-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 = ((Length/M)^L - 1) / (L * S)

Percentile = ZtoPercentile(Z-score)

References

World Health Organization. The WHO Child Growth Standards. https://www.who.int/childgrowth/standards/en/ (Accessed on June 26, 2023).

LMS table: Length-for-age percentiles, females 0 to 24 months, WHO growth standard

Age [months]	Power [L]	Median [M]	Variation [S]
0	1	49.1477	0.0379
1	1	53.6872	0.0364
2	1	57.0673	0.0357
3	1	59.8029	0.0352
4	1	62.0899	0.0349
5	1	64.0301	0.0346
6	1	65.7311	0.0345
7	1	67.2873	0.0344
8	1	68.7498	0.0344
9	1	70.1435	0.0344
10	1	71.4818	0.0345
11	1	72.7710	0.0346
12	1	74.0150	0.0348
13	1	75.2176	0.0350
14	1	76.3817	0.0351
15	1	77.5099	0.0353
16	1	78.6055	0.0355
17	1	79.6710	0.0358
18	1	80.7079	0.0360
19	1	81.7182	0.0362
20	1	82.7036	0.0364
21	1	83.6654	0.0367
22	1	84.6040	0.0369
23	1	85.5202	0.0371
24	1	86.4153	0.0373

LMS table: Length-for-age percentiles, males 0 to 24 months, WHO growth standard

Age [months]	Power [L]	Median [M]	Variation [S]
0	1	49.8842	0.0379
1	1	54.7244	0.0356
2	1	58.4249	0.0342
3	1	61.4292	0.0333
4	1	63.8860	0.0326
5	1	65.9026	0.0320
6	1	67.6236	0.0316
7	1	69.1645	0.0314
8	1	70.5994	0.0312
9	1	71.9687	0.0312
10	1	73.2812	0.0312
11	1	74.5388	0.0312
12	1	75.7488	0.0314
13	1	76.9186	0.0315
14	1	78.0497	0.0317
15	1	79.1458	0.0320
16	1	80.2113	0.0322
17	1	81.2487	0.0325
18	1	82.2587	0.0328
19	1	83.2418	0.0331
20	1	84.1996	0.0334
21	1	85.1348	0.0338
22	1	86.0477	0.0341
23	1	86.9410	0.0345
24	1	87.8161	0.0348

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.

All information contained in and produced by the EBMcalc system is provided for educational purposes only. This information should not be used for the diagnosis or treatment of any health problem or disease. THIS INFORMATION IS NOT INTENDED TO REPLACE CLINICAL JUDGMENT OR GUIDE INDIVIDUAL PATIENT CARE IN ANY MANNER.

Topic 15631 Version 14.0

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Calculator: Length-for-age percentiles and Z-scores, 0 to 24 months (WHO)