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	0.03790
1	1	53.6872	0.03640
2	1	57.0673	0.03568
3	1	59.8029	0.03520
4	1	62.0899	0.03486
5	1	64.0301	0.03463
6	1	65.7311	0.03448
7	1	67.2873	0.03441
8	1	68.7498	0.03440
9	1	70.1435	0.03444
10	1	71.4818	0.03452
11	1	72.7710	0.03464
12	1	74.0150	0.03479
13	1	75.2176	0.03496
14	1	76.3817	0.03514
15	1	77.5099	0.03534
16	1	78.6055	0.03555
17	1	79.6710	0.03576
18	1	80.7079	0.03598
19	1	81.7182	0.03620
20	1	82.7036	0.03643
21	1	83.6654	0.03666
22	1	84.6040	0.03688
23	1	85.5202	0.03711
24	1	86.4153	0.03734

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	0.03795
1	1	54.7244	0.03557
2	1	58.4249	0.03424
3	1	61.4292	0.03328
4	1	63.8860	0.03257
5	1	65.9026	0.03204
6	1	67.6236	0.03165
7	1	69.1645	0.03139
8	1	70.5994	0.03124
9	1	71.9687	0.03117
10	1	73.2812	0.03118
11	1	74.5388	0.03125
12	1	75.7488	0.03137
13	1	76.9186	0.03154
14	1	78.0497	0.03174
15	1	79.1458	0.03197
16	1	80.2113	0.03222
17	1	81.2487	0.03250
18	1	82.2587	0.03279
19	1	83.2418	0.03310
20	1	84.1996	0.03342
21	1	85.1348	0.03376
22	1	86.0477	0.03410
23	1	86.9410	0.03445
24	1	87.8161	0.03479

LMS table: Normal table percentiles for Z-score

Z	0	1	2	3	4	5	6	7	8	9
-3.0	0.13%	0.13%	0.13%	0.12%	0.12%	0.11%	0.11%	0.11%	0.10%	0.10%
-2.9	0.19%	0.18%	0.18%	0.17%	0.16%	0.16%	0.15%	0.15%	0.14%	0.14%
-2.8	0.26%	0.25%	0.24%	0.23%	0.23%	0.22%	0.21%	0.21%	0.20%	0.19%
-2.7	0.35%	0.34%	0.33%	0.32%	0.31%	0.30%	0.29%	0.28%	0.27%	0.26%
-2.6	0.47%	0.45%	0.44%	0.43%	0.41%	0.40%	0.39%	0.38%	0.37%	0.36%
-2.5	0.62%	0.60%	0.59%	0.57%	0.55%	0.54%	0.52%	0.51%	0.49%	0.48%
-2.4	0.82%	0.80%	0.78%	0.75%	0.73%	0.71%	0.70%	0.68%	0.66%	0.64%
-2.3	1.07%	1.04%	1.02%	0.99%	0.96%	0.94%	0.91%	0.89%	0.87%	0.84%
-2.2	1.39%	1.36%	1.32%	1.29%	1.26%	1.22%	1.19%	1.16%	1.13%	1.10%
-2.1	1.79%	1.74%	1.70%	1.66%	1.62%	1.58%	1.54%	1.50%	1.46%	1.43%
-2.0	2.28%	2.22%	2.17%	2.12%	2.07%	2.02%	1.97%	1.92%	1.88%	1.83%
-1.9	2.87%	2.81%	2.74%	2.68%	2.62%	2.56%	2.50%	2.44%	2.39%	2.33%
-1.8	3.59%	3.52%	3.44%	3.36%	3.29%	3.22%	3.14%	3.07%	3.01%	2.94%
-1.7	4.46%	4.36%	4.27%	4.18%	4.09%	4.01%	3.92%	3.84%	3.75%	3.67%
-1.6	5.48%	5.37%	5.26%	5.16%	5.05%	4.95%	4.85%	4.75%	4.65%	4.55%
-1.5	6.68%	6.55%	6.43%	6.30%	6.18%	6.06%	5.94%	5.82%	5.71%	5.59%
-1.4	8.08%	7.93%	7.78%	7.64%	7.49%	7.35%	7.22%	7.08%	6.94%	6.81%
-1.3	9.68%	9.51%	9.34%	9.18%	9.01%	8.85%	8.69%	8.53%	8.38%	8.23%
-1.2	11.51%	11.31%	11.12%	10.94%	10.75%	10.57%	10.38%	10.20%	10.03%	9.85%
-1.1	13.57%	13.35%	13.14%	12.92%	12.71%	12.51%	12.30%	12.10%	11.90%	11.70%
-1.0	15.87%	15.63%	15.39%	15.15%	14.92%	14.69%	14.46%	14.23%	14.01%	13.79%
-0.9	18.41%	18.14%	17.88%	17.62%	17.36%	17.11%	16.85%	16.60%	16.35%	16.11%
-0.8	21.19%	20.90%	20.61%	20.33%	20.05%	19.77%	19.49%	19.22%	18.94%	18.67%
-0.7	24.20%	23.89%	23.58%	23.27%	22.97%	22.66%	22.36%	22.07%	21.77%	21.48%
-0.6	27.43%	27.09%	26.76%	26.44%	26.11%	25.79%	25.46%	25.14%	24.83%	24.51%
-0.5	30.85%	30.50%	30.15%	29.81%	29.46%	29.12%	28.77%	28.43%	28.10%	27.76%
-0.4	34.46%	34.09%	33.72%	33.36%	33.00%	32.64%	32.28%	31.92%	31.56%	31.21%
-0.3	38.21%	37.83%	37.45%	37.07%	36.69%	36.32%	35.94%	35.57%	35.20%	34.83%
-0.2	42.07%	41.68%	41.29%	40.91%	40.52%	40.13%	39.74%	39.36%	38.97%	38.59%
-0.1	46.02%	45.62%	45.22%	44.83%	44.43%	44.04%	43.64%	43.25%	42.86%	42.47%
-0.0	50.00%	49.60%	49.20%	48.80%	48.40%	48.01%	47.61%	47.21%	46.81%	46.41%
0.0	50.00%	50.40%	50.80%	51.20%	51.60%	51.99%	52.39%	52.79%	53.19%	53.59%
0.1	53.98%	54.38%	54.78%	55.17%	55.57%	55.96%	56.36%	56.75%	57.14%	57.54%
0.2	57.93%	58.32%	58.71%	59.10%	59.48%	59.87%	60.26%	60.64%	61.03%	61.41%
0.3	61.79%	62.17%	62.55%	62.93%	63.31%	63.68%	64.06%	64.43%	64.80%	65.17%
0.4	65.54%	65.91%	66.28%	66.64%	67.00%	67.36%	67.72%	68.08%	68.44%	68.79%
0.5	69.15%	69.50%	69.85%	70.19%	70.54%	70.88%	71.23%	71.57%	71.90%	72.24%
0.6	72.58%	72.91%	73.24%	73.57%	73.89%	74.22%	74.54%	74.86%	75.18%	75.49%
0.7	75.80%	76.12%	76.42%	76.73%	77.04%	77.34%	77.64%	77.94%	78.23%	78.52%
0.8	78.81%	79.10%	79.39%	79.67%	79.96%	80.23%	80.51%	80.79%	81.06%	81.33%
0.9	81.59%	81.86%	82.12%	82.38%	82.64%	82.89%	83.15%	83.40%	83.65%	83.89%
1.0	84.13%	84.38%	84.61%	84.85%	85.08%	85.31%	85.54%	85.77%	85.99%	86.21%
1.1	86.43%	86.65%	86.86%	87.08%	87.29%	87.49%	87.70%	87.90%	88.10%	88.30%
1.2	88.49%	88.69%	88.88%	89.07%	89.25%	89.44%	89.62%	89.80%	89.97%	90.15%
1.3	90.32%	90.49%	90.66%	90.82%	90.99%	91.15%	91.31%	91.47%	91.62%	91.77%
1.4	91.92%	92.07%	92.22%	92.36%	92.51%	92.65%	92.79%	92.92%	93.06%	93.19%
1.5	93.32%	93.45%	93.57%	93.70%	93.82%	93.94%	94.06%	94.18%	94.30%	94.41%
1.6	94.52%	94.63%	94.74%	94.85%	94.95%	95.05%	95.15%	95.25%	95.35%	95.45%
1.7	95.54%	95.64%	95.73%	95.82%	95.91%	95.99%	96.08%	96.16%	96.25%	96.33%
1.8	96.41%	96.49%	96.56%	96.64%	96.71%	96.78%	96.86%	96.93%	97.00%	97.06%
1.9	97.13%	97.19%	97.26%	97.32%	97.38%	97.44%	97.50%	97.56%	97.62%	97.67%
2.0	97.73%	97.78%	97.83%	97.88%	97.93%	97.98%	98.03%	98.08%	98.12%	98.17%
2.1	98.21%	98.26%	98.30%	98.34%	98.38%	98.42%	98.46%	98.50%	98.54%	98.57%
2.2	98.61%	98.65%	98.68%	98.71%	98.75%	98.78%	98.81%	98.84%	98.87%	98.90%
2.3	98.93%	98.96%	98.98%	99.01%	99.04%	99.06%	99.09%	99.11%	99.13%	99.16%
2.4	99.18%	99.20%	99.22%	99.25%	99.27%	99.29%	99.31%	99.32%	99.34%	99.36%
2.5	99.38%	99.40%	99.41%	99.43%	99.45%	99.46%	99.48%	99.49%	99.51%	99.52%
2.6	99.53%	99.55%	99.56%	99.57%	99.59%	99.60%	99.61%	99.62%	99.63%	99.64%
2.7	99.65%	99.66%	99.67%	99.68%	99.69%	99.70%	99.71%	99.72%	99.73%	99.74%
2.8	99.74%	99.75%	99.76%	99.77%	99.77%	99.78%	99.79%	99.80%	99.80%	99.81%
2.9	99.81%	99.82%	99.83%	99.83%	99.84%	99.84%	99.85%	99.85%	99.86%	99.86%
3.0	99.87%	99.87%	99.87%	99.88%	99.88%	99.89%	99.89%	99.89%	99.90%	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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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. Click here for full notice and disclaimer.

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