PediTools Sources and Methods

PediTools sources and methods

For each PediTools growth calculator: the publications it is based on, the ages (or lengths) it covers, and how its Z-scores and percentiles are calculated.

Jump to: How to cite · Sources for each calculator · How values are calculated

How to cite

If you use these calculators in research or publications, please cite PediTools, and the publications of the growth charts you used (listed for each calculator below):

Chou JH, Roumiantsev S, Singh R. PediTools Electronic Growth Chart Calculators: Applications in Clinical Care, Research, and Quality Improvement. J Med Internet Res. 2020;22(1):e16204. doi:10.2196/16204. PMID: 32012066

Sources for each calculator

Fenton 2025

Publications

Fenton TR, Elmrayed S, Alshaikh BN. Fenton Third-Generation Growth Charts of Preterm Infants Without Abnormal Fetal Growth: A Systematic Review and Meta-Analysis. Paediatr Perinat Epidemiol. 2025;39(6):543-555. doi:10.1111/ppe.70035. PMID: 40534585

Measures

Measure	Range	Unit	Z-score and percentile
Weight	22 4/7 to 50 0/7 weeks	g	LMS; WHO restricted LMS beyond ±3 SD
Head circumference	22 4/7 to 50 0/7 weeks	cm	LMS
Length	23 4/7 to 50 0/7 weeks	cm	LMS

LMS parameters

Checked row by row against the authors' LMS table (not published) (2026-10-13).

Methods

Z-scores beyond ±3 SD: WHO's restricted LMS methodFenton TR, Elmrayed S, Alshaikh BN. 2025 Fenton Growth Chart Clinical Calculator, version 1.1 (Excel workbook). Unpublished, provided by the authors; 2025.
Z-scores beyond ±3 SD: WHO's restricted LMS methodWHO Multicentre Growth Reference Study Group. WHO Child Growth Standards: Length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age: Methods and development. World Health Organization; 2006. ISBN 924154693X

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Fenton 2013

Publications

Fenton TR, Kim JH. A systematic review and meta-analysis to revise the Fenton growth chart for preterm infants. BMC Pediatr. 2013;13:59. doi:10.1186/1471-2431-13-59. PMID: 23601190

Measures

Measure	Range	Unit	Z-score and percentile
Weight	22 4/7 to 50 0/7 weeks	g	LMS
Head circumference	23 4/7 to 50 0/7 weeks	cm	LMS
Length	23 4/7 to 50 0/7 weeks	cm	LMS

LMS parameters

Checked row by row against the authors' LMS table (not published) (2026-10-13).

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Olsen 2010

Publications

Olsen IE, Groveman SA, Lawson ML, Clark RH, Zemel BS. New intrauterine growth curves based on United States data. Pediatrics. 2010;125(2):e214-24. doi:10.1542/peds.2009-0913. PMID: 20100760

Measures

Measure	Range	Unit	Z-score and percentile
Weight	23 0/7 to 41 6/7 weeks	g	LMS
Head circumference	23 0/7 to 41 6/7 weeks	cm	LMS
Length	23 0/7 to 41 6/7 weeks	cm	LMS

LMS parameters

Checked row by row against Olsen 2010, Table 3 (2026-10-12).

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Olsen 2015 BMI

Publications

Olsen IE, Lawson ML, Ferguson AN, et al. BMI curves for preterm infants. Pediatrics. 2015;135(3):e572-81. doi:10.1542/peds.2014-2777. PMID: 25687149

Measures

Measure	Range	Unit	Z-score and percentile
BMI	24 0/7 to 41 6/7 weeks	g/cm2*10	LMS

LMS parameters

Checked row by row against Olsen 2015, Tables 1–2 (2026-10-12).

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INTERGROWTH-21st newborn size

Publications

Measures

Measure	Range	Unit	Z-score and percentile
Weight	Gestational age at birth 24 0/7 to 42 6/7 weeks	kg	Normal (log scale) below 33 0/7 weeks; skew t (ST3) from 33 0/7 weeks
Head circumference	Gestational age at birth 24 0/7 to 42 6/7 weeks	cm	Normal below 33 0/7 weeks; skew t (ST3) from 33 0/7 weeks
Length	Gestational age at birth 24 0/7 to 42 6/7 weeks	cm	Normal below 33 0/7 weeks; skew t (ST3) from 33 0/7 weeks
Weight-to-length ratio	Gestational age at birth 24 0/7 to 42 6/7 weeks	kg/m	Normal, separate equations below and from 33 0/7 weeks

Parameters

Checked against the INTERGROWTH-21st newborn spreadsheets (ST3 rows from 231 days: every value identical, also to gigs 0.5.2), gigs 0.5.2 and growthstandards (very preterm equations), INTERGROWTH-21st's weight-to-length ratio calculator, and the official centile and z-score tables (tests/tools/verify_intergrowth_sources.R, 2026-10-17).

Methods

Ohuma EO, Altman DG, International Fetal and Newborn Growth Consortium for the 21st Century (INTERGROWTH-21st Project). Statistical methodology for constructing gestational age-related charts using cross-sectional and longitudinal data: The INTERGROWTH-21st project as a case study. Stat Med. 2019;38(19):3507-3526. doi:10.1002/sim.8018. PMID: 30488491
Rigby RA, Stasinopoulos DM, Heller GZ, De Bastiani F. Distributions for Modeling Location, Scale, and Shape: Using GAMLSS in R. Chapman & Hall/CRC; 2019. ISBN 9780367278847
Below 33+0 weeks: INTERGROWTH-21st's very preterm size at birth references; from 33+0 weeks: the newborn size standards (Villar 2014). The two meet at 33+0 weeks but do not join exactly, so the same measurement can change centile between 32+6 and 33+0 weeks, most for head circumference (about 0.4 SD for boys and 0.3 SD for girls)Villar J, Giuliani F, Fenton TR, et al. INTERGROWTH-21st very preterm size at birth reference charts. Lancet. 2016;387(10021):844-5. doi:10.1016/S0140-6736(16)00384-6. PMID: 26898853

More information

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INTERGROWTH-21st postnatal growth (preterm)

Publications

Villar J, Giuliani F, Bhutta ZA, et al. Postnatal growth standards for preterm infants: the Preterm Postnatal Follow-up Study of the INTERGROWTH-21st Project. Lancet Glob Health. 2015;3(11):e681-91. doi:10.1016/S2214-109X(15)00163-1. PMID: 26475015

Measures

Measure	Range	Unit	Z-score and percentile
Weight	27 0/7 to 64 0/7 weeks	kg	Normal (log scale)
Head circumference	27 0/7 to 64 0/7 weeks	cm	Normal
Length	27 0/7 to 64 0/7 weeks	cm	Normal (log scale)
Weight-for-length	Length 35 to 65 cm	kg	Normal

Parameters

Checked against gigs 0.5.2 and growthstandards (every equation), Villar 2015's supplementary appendix (by hand), and the official z-score tables (tests/tools/verify_intergrowth_sources.R, 2026-10-17).

Checked against gigs 0.5.2 (every equation) (tests/tools/verify_intergrowth_sources.R, 2026-10-17).

Methods

Ohuma EO, Altman DG, International Fetal and Newborn Growth Consortium for the 21st Century (INTERGROWTH-21st Project). Statistical methodology for constructing gestational age-related charts using cross-sectional and longitudinal data: The INTERGROWTH-21st project as a case study. Stat Med. 2019;38(19):3507-3526. doi:10.1002/sim.8018. PMID: 30488491
The standards are for monitoring postnatal growth of preterm infants, especially after 32 weeks' postmenstrual age: of the 201 infants, 28 were born at 33 weeks or earlier (12 at 27 to 32 weeks), so the authors describe them as robust for infants born at 33 to 36 completed weeksVillar J, Giuliani F, Bhutta ZA, et al. Postnatal growth standards for preterm infants: the Preterm Postnatal Follow-up Study of the INTERGROWTH-21st Project. Lancet Glob Health. 2015;3(11):e681-91. doi:10.1016/S2214-109X(15)00163-1. PMID: 26475015
Weight-for-length: the equations are not in Villar 2015; they were supplied to gigs by Dr Eric Ohuma (the package's documentation), and are checked against gigs' tablesParker SR, Vesel L, Ohuma EO. gigs: A package for standardising fetal, neonatal, and child growth assessment. J Open Source Softw. 2025;10(106):7655. doi:10.21105/joss.07655.

More information

INTERGROWTH-21st. INTERGROWTH-21st: International standards for fetal growth and newborn size (tools and resources). https://intergrowth21.com

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CDC 0–36 months

Publications

Kuczmarski RJ, Ogden CL, Guo SS, et al. 2000 CDC Growth Charts for the United States: methods and development. Vital Health Stat 11. 2002;(246):1-190. PMID: 12043359

Measures

Measure	Range	Unit	Z-score and percentile
Weight	0 to 36 months	kg	LMS
Length	0 to 36 months	cm	LMS
Head circumference	0 to 36 months	cm	LMS
Weight-for-length	Length 45 to 103.5 cm	kg	LMS

LMS parameters

Centers for Disease Control and Prevention. CDC growth charts: data files (LMS parameters and percentiles). https://www.cdc.gov/growthcharts/cdc-data-files.htm

Checked row by row against CDC's data files (2026-10-12).

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WHO 0–24 months

Publications

Measures

Measure	Range	Unit	Z-score and percentile
Weight	0 to 24 months	kg	LMS; WHO restricted LMS beyond ±3 SD
Length	0 to 24 months	cm	LMS
Head circumference	0 to 24 months	cm	LMS
Weight-for-length	Length 45 to 110 cm	kg	LMS; WHO restricted LMS beyond ±3 SD

LMS parameters

Checked row by row against WHO's monthly tables; CDC's copy is identical (2026-10-12).

Checked row by row against WHO's expanded tables in 0.1 cm steps (2026-10-12).

Methods

Z-scores beyond ±3 SD: WHO's restricted LMS methodWHO Multicentre Growth Reference Study Group. WHO Child Growth Standards: Length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age: Methods and development. World Health Organization; 2006. ISBN 924154693X

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WHO 0–5 years (daily)

Publications

Measures

Measure	Range	Unit	Z-score and percentile
Weight	0 to 5 years (0 to 1856 days)	kg	LMS; WHO restricted LMS beyond ±3 SD
Length/height	0 to 5 years (0 to 1856 days)	cm	LMS
Head circumference	0 to 5 years (0 to 1856 days)	cm	LMS
Weight-for-length	Length 45 to 110 cm	kg	LMS; WHO restricted LMS beyond ±3 SD
Weight-for-height	Height 65 to 120 cm	kg	LMS; WHO restricted LMS beyond ±3 SD
BMI	0 to 5 years (0 to 1856 days)	kg/m²	LMS; WHO restricted LMS beyond ±3 SD

LMS parameters

World Health Organization. WHO Child Growth Standards: standards and tables by indicator. https://www.who.int/tools/child-growth-standards/standards

Checked row by row against WHO's expanded (daily) tables (2026-10-12).

Checked row by row against WHO's expanded tables in 0.1 cm steps (2026-10-12).

Methods

Z-scores beyond ±3 SD: WHO's restricted LMS methodWHO Multicentre Growth Reference Study Group. WHO Child Growth Standards: Length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age: Methods and development. World Health Organization; 2006. ISBN 924154693X
Lying length vs standing height: lying length is used before 24 months and standing height from 24 months; a child measured in the other position is adjusted by 0.7 cm (added to a standing height before 24 months, subtracted from a lying length from 24 months), also for BMI and weight-for-length/height. Standing before 9 months is not expected: such a value is used as lying length, not adjustedWHO Multicentre Growth Reference Study Group. WHO Child Growth Standards: Length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age: Methods and development. World Health Organization; 2006. ISBN 924154693X
The same rule and the switch at 24 months (730.5 days) as WHO's Anthro softwareSchumacher D, Borghi E, Polonsky J, Gatica Dominguez G. anthro: Computation of the WHO Child Growth Standards. R package version 1.1.0. https://cran.r-project.org/package=anthro

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WHO Canada 0–24 months

Publications

Measures

Measure	Range	Unit	Z-score and percentile
Weight	0 to 24 months	kg	LMS; WHO restricted LMS beyond ±3 SD
Length	0 to 24 months	cm	LMS
Head circumference	0 to 24 months	cm	LMS
Weight-for-length	Length 45 to 110 cm	kg	LMS; WHO restricted LMS beyond ±3 SD

LMS parameters

Canadian Pediatric Endocrine Group. WHO Growth Charts for Canada: LMS and percentile data files (WHOGrowthChartData2014.zip, distribution 3, Sets 1 and 2). https://cpeg-gcep.net/sites/default/files/upload/bookfiles/WHOGrowthChartData2014.zip

Checked row by row against CPEG's LMS files (WHOGrowthChartData2014.zip, distribution 3); the rows from WHO's tables also against WHO's own files (2026-10-15).

Methods

Z-scores beyond ±3 SD: WHO's restricted LMS methodWHO Multicentre Growth Reference Study Group. WHO Child Growth Standards: Length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age: Methods and development. World Health Organization; 2006. ISBN 924154693X
Percentiles beyond ±3 SD: the 0.1st and 99.9th percentile curves of the Canadian charts (CPEG's data files) are plain LMS, while weight and weight-for-length Z-scores beyond ±3 use WHO's restricted LMS method. The two place these percentiles at most 0.11% of the weight apart, so a value right on one of the printed curves (Z ±3.09) can get a percentile slightly different from 0.1 or 99.9Canadian Pediatric Endocrine Group. WHO Growth Charts for Canada: LMS and percentile data files (WHOGrowthChartData2014.zip, distribution 3, Sets 1 and 2). https://cpeg-gcep.net/sites/default/files/upload/bookfiles/WHOGrowthChartData2014.zip

More information

Dietitians of Canada, Canadian Paediatric Society. A Health Professional's Guide for using the WHO Growth Charts for Canada (Redesigned 2014). Dietitians of Canada; 2014.

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CDC 2–20 years

Publications

Kuczmarski RJ, Ogden CL, Guo SS, et al. 2000 CDC Growth Charts for the United States: methods and development. Vital Health Stat 11. 2002;(246):1-190. PMID: 12043359

Measures

Measure	Range	Unit	Z-score and percentile
Weight	2 to 20 years (24 to 240 months)	kg	LMS
Stature	2 to 20 years (24 to 240 months)	cm	LMS
Weight-for-stature	Height 77 to 121.5 cm	kg	LMS
BMI	2 to 20 years (24 to 240.5 months)	kg/m²	LMS; CDC extended method at or above the 95th percentile

LMS parameters

Centers for Disease Control and Prevention. CDC growth charts: data files (LMS parameters and percentiles). https://www.cdc.gov/growthcharts/cdc-data-files.htm

Checked row by row against CDC's data files (2026-10-12).

Methods

BMI at or above the 95th percentile: CDC extended BMI-for-age methodWei R, Ogden CL, Parsons VL, Freedman DS, Hales CM. A method for calculating BMI z-scores and percentiles above the 95th percentile of the CDC growth charts. Ann Hum Biol. 2020;47(6):514-521. doi:10.1080/03014460.2020.1808065. PMID: 32901504
BMI categories, including severe obesity classes 2 and 3Hampl SE, Hassink SG, Skinner AC, et al. Clinical Practice Guideline for the Evaluation and Treatment of Children and Adolescents With Obesity. Pediatrics. 2023;151(2):e2022060640. doi:10.1542/peds.2022-060640. PMID: 36622115

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WHO 5–19 years

Publications

de Onis M, Onyango AW, Borghi E, Siyam A, Nishida C, Siekmann J. Development of a WHO growth reference for school-aged children and adolescents. Bull World Health Organ. 2007;85(9):660-7. doi:10.2471/BLT.07.043497. PMID: 18026621

Measures

Measure	Range	Unit	Z-score and percentile
Weight	5 years to 10 years 1 month (60 to 121 months)	kg	LMS; WHO restricted LMS beyond ±3 SD
Height	5 years to 19 years 1 month (60 to 229 months)	cm	LMS
BMI	5 years to 19 years 1 month (60 to 229 months)	kg/m²	LMS; WHO restricted LMS beyond ±3 SD

LMS parameters

Checked row by row against WHO's expanded tables (61-228 months; weight 61-120) and WHO's anthroplus R package 1.1.0 (every row, including 60 and 229 months, weight 121); BMI also against WHO's worked examples (2026-10-13).

Methods

Z-scores beyond ±3 SD: WHO's restricted LMS methodWorld Health Organization. Computation of centiles and z-scores for height-for-age, weight-for-age and BMI-for-age. https://cdn.who.int/media/docs/default-source/child-growth/growth-reference-5-19-years/computation.pdf?sfvrsn=c2ff6a95_4

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WHO Canada 2–19 years

Publications

Measures

Measure	Range	Unit	Z-score and percentile
Weight	2 years to 19 years 1 month (24 to 229 months)	kg	LMS; WHO restricted LMS beyond ±3 SD
Height	2 years to 19 years 1 month (24 to 229 months)	cm	LMS
BMI	2 years to 19 years 1 month (24 to 229 months)	kg/m²	LMS; WHO restricted LMS beyond ±3 SD

LMS parameters

Canadian Pediatric Endocrine Group. WHO Growth Charts for Canada: LMS and percentile data files (WHOGrowthChartData2014.zip, distribution 3, Sets 1 and 2). https://cpeg-gcep.net/sites/default/files/upload/bookfiles/WHOGrowthChartData2014.zip

Checked row by row against CPEG's LMS files (WHOGrowthChartData2014.zip, distribution 3); the rows from WHO's tables also against WHO's own files (2026-10-15).

Methods

Z-scores beyond ±3 SD: WHO's restricted LMS methodWHO Multicentre Growth Reference Study Group. WHO Child Growth Standards: Length/height-for-age, weight-for-age, weight-for-length, weight-for-height and body mass index-for-age: Methods and development. World Health Organization; 2006. ISBN 924154693X
Z-scores beyond ±3 SD: WHO's restricted LMS methodWorld Health Organization. Computation of centiles and z-scores for height-for-age, weight-for-age and BMI-for-age. https://cdn.who.int/media/docs/default-source/child-growth/growth-reference-5-19-years/computation.pdf?sfvrsn=c2ff6a95_4
Weight-for-age from 10 years: the Canadian Pediatric Endocrine Group's re-analysis. Its curves do not join WHO's smoothly, so the percentiles step between 120 and 121 months (e.g. girls' 97th percentile 45.7 → 49.3 kg), and the same weight can get a noticeably different Z-score and percentile from 121 months. This is in the published Canadian charts, not a calculation errorRodd C, Metzger DL, Sharma A. Extending World Health Organization weight-for-age reference curves to older children. BMC Pediatr. 2014;14:32. doi:10.1186/1471-2431-14-32. PMID: 24490896
Percentiles beyond ±3 SD: the 0.1st and 99.9th percentile curves of the Canadian charts (CPEG's data files) are plain LMS, while weight and BMI Z-scores beyond ±3 use WHO's restricted LMS method. The two place these percentiles at most 0.9% of the weight or BMI apart (e.g. 0.3 kg/m² at a BMI of 32), so a value right on one of the printed curves (Z ±3.09) can get a percentile slightly different from 0.1 or 99.9Canadian Pediatric Endocrine Group. WHO Growth Charts for Canada: LMS and percentile data files (WHOGrowthChartData2014.zip, distribution 3, Sets 1 and 2). https://cpeg-gcep.net/sites/default/files/upload/bookfiles/WHOGrowthChartData2014.zip

More information

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Down syndrome (Zemel) 0–36 months

Publications

Zemel BS, Pipan M, Stallings VA, et al. Growth Charts for Children With Down Syndrome in the United States. Pediatrics. 2015;136(5):e1204-11. doi:10.1542/peds.2015-1652. PMID: 26504127

Measures

Measure	Range	Unit	Z-score and percentile
Weight	0 to 36 months	kg	LMS
Length	1 to 36 months	cm	LMS
Head circumference	1 to 36 months	cm	LMS
Weight-for-length	Length 49 to 93 cm; 52 to 90 cm (boys; girls)	kg	LMS

LMS parameters

Checked row by row against Zemel 2015, Supplemental Tables 4–19 (2026-10-12).

More information

Centers for Disease Control and Prevention. Growth charts for children with Down syndrome. https://www.cdc.gov/birth-defects/hcp/down-syndrome-growth-charts/

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Down syndrome (Zemel) 2–20 years

Publications

Zemel BS, Pipan M, Stallings VA, et al. Growth Charts for Children With Down Syndrome in the United States. Pediatrics. 2015;136(5):e1204-11. doi:10.1542/peds.2015-1652. PMID: 26504127

Measures

Measure	Range	Unit	Z-score and percentile
Weight	2 to 20 years	kg	LMS
Height	2 to 20 years	cm	LMS
Head circumference	2 to 20 years	cm	LMS
BMI	2 to 20 years	kg/m²	LMS

LMS parameters

Checked row by row against Zemel 2015, Supplemental Tables 4–19 (2026-10-12).

More information

Centers for Disease Control and Prevention. Growth charts for children with Down syndrome. https://www.cdc.gov/birth-defects/hcp/down-syndrome-growth-charts/

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Cerebral palsy (Brooks) 2–20 years

Publications

Brooks J, Day S, Shavelle R, Strauss D. Low weight, morbidity, and mortality in children with cerebral palsy: new clinical growth charts. Pediatrics. 2011;128(2):e299-307. doi:10.1542/peds.2010-2801. PMID: 21768315

Measures

Measure	Range	Unit	Z-score and percentile
Weight	2 to 20 years	kg	LMS
Height	2 to 20 years	cm	LMS
BMI	2 to 20 years	kg/m²	LMS

One table for each GMFCS level: GMFCS I; GMFCS II; GMFCS III; GMFCS IV; GMFCS V, no feeding tube; GMFCS V, feeding tube.

LMS parameters

Wright CM, Reynolds L, Ingram E, Cole TJ, Brooks J. Validation of US cerebral palsy growth charts using a UK cohort. Dev Med Child Neurol. 2017;59(9):933-938. doi:10.1111/dmcn.13495. PMID: 28656704

Checked row by row against the authors' LMS table (not published) (2026-10-13).

More information

Life Expectancy Project. Cerebral Palsy Growth Charts. https://lifeexpectancy.org/articles/NewGrowthCharts.shtml

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Arm circumference (Abdel-Rahman) 2 months–18 years

Publications

Abdel-Rahman SM, Bi C, Thaete K. Construction of Lambda, Mu, Sigma Values for Determining Mid-Upper Arm Circumference z Scores in U.S. Children Aged 2 Months Through 18 Years. Nutr Clin Pract. 2017;32(1):68-76. doi:10.1177/0884533616676597. PMID: 27856693

Measures

Measure	Range	Unit	Z-score and percentile
Mid-upper arm circumference	2 to 222 months	cm	LMS

LMS parameters

Checked row by row against Abdel-Rahman 2017, Table 1 (2026-10-12).

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Arm circumference (Mramba) 5–19 years

Publications

Mramba L, Ngari M, Mwangome M, et al. A growth reference for mid upper arm circumference for age among school age children and adolescents, and validation for mortality: growth curve construction and longitudinal cohort study. BMJ. 2017;358:j3423. doi:10.1136/bmj.j3423. PMID: 28774873

Measures

Measure	Range	Unit	Z-score and percentile
Mid-upper arm circumference	5 to 19 years (60 to 228 months)	cm	LMS

LMS parameters

Checked row by row against the authors' R package MUACz; the BMJ web appendix agrees (2026-10-12).

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WHO arm circumference and skinfolds 3–60 months

Publications

WHO Multicentre Growth Reference Study Group. WHO Child Growth Standards: Head circumference-for-age, arm circumference-for-age, triceps skinfold-for-age and subscapular skinfold-for-age: Methods and development. World Health Organization; 2007. ISBN 9789241547185

Measures

Measure	Range	Unit	Z-score and percentile
Mid-upper arm circumference	3 to 60 months	cm	LMS; WHO restricted LMS beyond ±3 SD
Triceps skinfold	3 to 60 months	mm	LMS; WHO restricted LMS beyond ±3 SD
Subscapular skinfold	3 to 60 months	mm	LMS; WHO restricted LMS beyond ±3 SD

LMS parameters

World Health Organization. WHO Child Growth Standards: standards and tables by indicator. https://www.who.int/tools/child-growth-standards/standards

Checked row by row against WHO's monthly tables (subscapular: WHO's z-score tables) (2026-10-12).

Methods

Z-scores beyond ±3 SD: WHO's restricted LMS methodWHO Multicentre Growth Reference Study Group. WHO Child Growth Standards: Head circumference-for-age, arm circumference-for-age, triceps skinfold-for-age and subscapular skinfold-for-age: Methods and development. World Health Organization; 2007. ISBN 9789241547185

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Skinfolds (Addo) 1.5–20 years

Publications

Addo OY, Himes JH. Reference curves for triceps and subscapular skinfold thicknesses in US children and adolescents. Am J Clin Nutr. 2010;91(3):635-42. doi:10.3945/ajcn.2009.28385. PMID: 20053877

Measures

Measure	Range	Unit	Z-score and percentile
Triceps skinfold	1.5 to 20 years	mm	LMS
Subscapular skinfold	1.5 to 20 years	mm	LMS

LMS parameters

Checked row by row against Addo & Himes 2010, Tables 2–5 (2026-10-12).

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Fenton 2003 (legacy)

Publications

Fenton TR. A new growth chart for preterm babies: Babson and Benda's chart updated with recent data and a new format. BMC Pediatr. 2003;3:13. doi:10.1186/1471-2431-3-13. PMID: 14678563

Measures

Measure	Range	Unit	Z-score and percentile
Weight	22 0/7 to 50 6/7 weeks	kg	LMS
Head circumference	22 0/7 to 50 6/7 weeks	cm	LMS
Length	22 0/7 to 50 6/7 weeks	cm	LMS

LMS parameters

Fenton TR, Sauve RS. Using the LMS method to calculate z-scores for the Fenton preterm infant growth chart. Eur J Clin Nutr. 2007;61(12):1380-5. doi:10.1038/sj.ejcn.1602667. PMID: 17299469

Checked row by row against Fenton & Sauve 2007, Tables 1–3 (2026-10-12).

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How values are calculated

L, M and S are interpolated linearly between the rows of the chart's table. Nothing is calculated outside a chart's range. Where the rows are the middle of age bands (e.g. 22 3/7 weeks for the week from 22 0/7), the range reaches half a band beyond the first and last rows.

Some charts' authors prescribe a different method at the extremes, used only for those charts: WHO's restricted LMS method beyond ±3 SD (WHO charts), and CDC's extended BMI-for-age method at or above the 95th percentile.

The INTERGROWTH-21st charts are not LMS: each is a distribution with its own parameters, by day of gestation or as equations, described below.

LMS method

Z-scores come from each chart's published LMS parameters (L: skewness, M: median, S: coefficient of variation). For a measurement X:

Z = \frac{{(\frac{X}{M})}^{L} - 1}{L S}

for L \neq 0

Z = \frac{\ln (\frac{X}{M})}{S}

for L = 0

The percentile is that of Z on the normal distribution. Conversely, the measurement at a given Z (used for the median, Z = 0, and for expected growth at the same Z at a later age) is:

X = M {(1 + L S Z)}^{\frac{1}{L}}

for L \neq 0

X = M e^{S Z}

for L = 0

WHO restricted LMS method ("SD23")

For the charts whose authors prescribe it (each calculator's section says which): within ±3 SD, the Z-score is the LMS Z-score. Beyond, with ${SD}_{k}$ the measurement at Z = k (the LMS formula above), Z-scores and measurements follow a straight line spaced by the distance between the 2 SD and 3 SD values:

Z = 3 + \frac{X - {SD}_{3}}{{SD}_{3} - {SD}_{2}}

for X > {SD}_{3}

Z = - 3 + \frac{X - {SD}_{- 3}}{{SD}_{- 2} - {SD}_{- 3}}

for X < {SD}_{- 3}

and conversely:

X = {SD}_{3} + (Z - 3) ({SD}_{3} - {SD}_{2})

for Z > 3

X = {SD}_{- 3} + (Z + 3) ({SD}_{- 2} - {SD}_{- 3})

for Z < - 3

CDC extended BMI-for-age method

For CDC 2000 BMI-for-age at or above the 95th percentile (CDC 2–20 years). With $P_{95}$ the BMI at the 95th percentile (the LMS formula above at Z = 1.645) and $σ$ by age a in years:

σ = 0.3728 + 0.5196 a - 0.0091 a^{2}

for boys

σ = 0.8334 + 0.3712 a - 0.0011 a^{2}

for girls

the percentile and Z-score are:

percentile = 90 + 10 Φ (\frac{BMI - P_{95}}{σ})

for BMI \geq P_{95}

Z = Φ^{- 1} (\frac{percentile}{100})

where $Φ$ is the standard normal distribution function.

Skew t distribution (ST3): INTERGROWTH-21st newborn size from 33+0 weeks

For each sex and day of gestation, INTERGROWTH-21st gives four parameters: $μ$ (location), $σ$ (scale), $ν$ (skewness) and $τ$ (degrees of freedom). The distribution is a Student t with $τ$ degrees of freedom, scaled by $\frac{σ}{ν}$ below $μ$ and by $σ ν$ above it (the ST3 distribution of the gamlss.dist R package). With $T_{τ}$ the Student t distribution function, a measurement y is at:

F (y) = \frac{2 T_{τ} (\frac{ν (y - μ)}{σ})}{1 + ν^{2}}

for y < μ

F (y) = \frac{1 + 2 ν^{2} (T_{τ} (\frac{y - μ}{σ ν}) - \frac{1}{2})}{1 + ν^{2}}

for y \geq μ

Z = Φ^{- 1} (F (y))

The percentile is 100 $F (y)$ . The measurement at a given Z (the median, Z = 0) is the inverse. $μ$ is not the median unless $ν = 1$ .

Normal distribution with equations for the mean and SD

INTERGROWTH-21st's very preterm newborn size (below 33+0 weeks), weight-to-length ratio, postnatal growth and weight-for-length: the mean $μ (x)$ and standard deviation $σ (x)$ are equations in gestational age, postmenstrual age or length x, published by INTERGROWTH-21st (each calculator's section names the scale used):

Z = \frac{\ln y - μ (x)}{σ}

for the log scale (weight; postnatal length)

Z = \frac{y - μ (x)}{σ}

for the other measures

The percentile is that of Z on the normal distribution. Conversely, the measurement at a given Z:

y = e^{μ (x) + Z σ (x)}

for the log scale

y = μ (x) + Z σ (x)

for the other measures