{
  "id": "growth-chart",
  "version": "5ad26a0e2354",
  "status": "published",
  "name": "Growth Chart Calculator",
  "question": "Where’s my child on the growth chart?",
  "summary": "Finds a child’s weight and height percentiles from birth to 20, on the WHO standards under 2 and the CDC growth charts from 2.",
  "category": "health",
  "subcategory": "body",
  "url": "https://www.acalculator.org/health/growth-chart-calculator",
  "markdown": "https://www.acalculator.org/health/growth-chart-calculator.md",
  "kind": "function",
  "method": "z = ((x ÷ M)^L − 1) ÷ (L × S); percentile = Φ(z) × 100, with WHO tables under 24 months and CDC from 24.",
  "assumptions": [
    "WHO 2006 standards under 24 months (length lying down); CDC 2000 charts from 24 months to 20 years (height standing).",
    "L, M and S are read on a straight line between table ages; percentiles are rounded half up to 0.1.",
    "A percentile is not a diagnosis; a doctor looks at growth over time."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "sex": {
        "title": "Sex",
        "description": "The child’s sex. Boys and girls have separate growth charts.",
        "type": "string",
        "enum": [
          "male",
          "female"
        ]
      },
      "from": {
        "title": "Based on",
        "description": "Enter the age in years and months, or the birth date and the date of the measurement.",
        "type": "string",
        "enum": [
          "age",
          "dates"
        ]
      },
      "years": {
        "title": "Years",
        "description": "The age in whole years.",
        "type": "integer",
        "minimum": 0,
        "maximum": 20
      },
      "months": {
        "title": "Months",
        "description": "Months past the whole years, 0 to under 12. Decimals are allowed: 2 weeks is about 0.5.",
        "type": "number",
        "minimum": 0,
        "exclusiveMaximum": 12
      },
      "born": {
        "title": "Birth date",
        "description": "The child’s date of birth.",
        "type": "string",
        "format": "date"
      },
      "on": {
        "title": "Measured on",
        "description": "The date of the measurement. Today, unless you change it.",
        "type": "string",
        "format": "date"
      },
      "weight": {
        "title": "Weight",
        "description": "The child’s weight.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "minimum": 0.5,
        "maximum": 250
      },
      "height": {
        "title": "Height",
        "description": "Height without shoes; under 2, length lying down.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.1,
        "maximum": 2.5
      }
    }
  },
  "outputs": {
    "weightPct": {
      "label": "Weight percentile",
      "description": "The share of children of the same sex and age with a lower weight (0.1 to 99.9).",
      "format": "number"
    },
    "weightZ": {
      "label": "Weight z-score",
      "description": "Standard deviations of the weight from the median for the age.",
      "format": "number"
    },
    "heightPct": {
      "label": "Height percentile",
      "description": "The share of children of the same sex and age with a lower height (0.1 to 99.9).",
      "format": "number"
    },
    "heightZ": {
      "label": "Height z-score",
      "description": "Standard deviations of the height from the median for the age.",
      "format": "number"
    },
    "bmi": {
      "label": "BMI",
      "description": "Weight ÷ height², when both are entered.",
      "format": "number"
    },
    "age": {
      "label": "Age",
      "description": "The age in years and months.",
      "format": "text"
    },
    "chart": {
      "label": "Growth charts",
      "description": "The charts used for this age.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "sex": "male",
      "from": "age",
      "years": 4,
      "months": 0,
      "born": "2022-09-30",
      "on": "2026-09-30",
      "weight": 15.875732950000002,
      "height": 1.0287
    },
    "outputs": {
      "weightPct": 42.6,
      "weightZ": -0.18704171048103266,
      "heightPct": 56.1,
      "heightZ": 0.15294820596703812,
      "bmi": 15,
      "age": "4 years",
      "chart": "CDC growth charts (2 to 20 years)"
    },
    "text": "At 4 years, weight is at percentile 42.6 and height at percentile 56.1 on the CDC growth charts (2 to 20 years)."
  },
  "examples": [
    {
      "given": {
        "sex": "female",
        "from": "age",
        "years": 5,
        "months": 0.5,
        "weight": 19.95048336,
        "height": 1.079566031
      },
      "expect": {
        "weightPct": 75,
        "weightZ": 0.6744897512479507,
        "heightPct": 50,
        "heightZ": 0,
        "bmi": 17.1
      },
      "source": "CDC wtage.csv P75 and statage.csv P50, girls, 60.5 months"
    },
    {
      "given": {
        "sex": "male",
        "from": "age",
        "years": 1,
        "months": 3,
        "weight": 11,
        "height": 0.8
      },
      "expect": {
        "weightPct": 72.2,
        "weightZ": 0.5886246213217036,
        "heightPct": 63.2,
        "heightZ": 0.33758959886619716,
        "bmi": 17.2,
        "chart": "WHO growth standards (birth to 24 months)"
      },
      "source": "WHO boys, month 15; hand calculation in content.mdx"
    },
    {
      "given": {
        "sex": "male",
        "from": "age",
        "years": 16,
        "months": 0,
        "weight": 60,
        "height": 1.75
      },
      "expect": {
        "weightPct": 46.5,
        "heightPct": 57.9,
        "bmi": 19.6
      },
      "source": "CDC boys, 192 months; hand calculation in content.mdx"
    },
    {
      "given": {
        "sex": "male",
        "from": "age",
        "years": 3,
        "months": 0,
        "weight": 14
      },
      "expect": {
        "weightPct": 41.7,
        "weightZ": -0.21032431790324033
      },
      "source": "CDC wtage.csv, boys, 36 months (between the 35.5 and 36.5 rows); hand calculation in content.mdx"
    }
  ],
  "sources": [
    "Centers for Disease Control and Prevention, National Center for Health Statistics. CDC growth charts data files: weight-for-age and stature-for-age, 2 to 20 years (wtage.csv, statage.csv), with the LMS instructions. https://www.cdc.gov/growthcharts/cdc-data-files.htm",
    "Centers for Disease Control and Prevention. WHO growth charts data files: weight-for-age and length-for-age, birth to 24 months (CDC copies of the WHO tables). https://www.cdc.gov/growthcharts/who-data-files.htm",
    "WHO 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. Geneva: World Health Organization, 2006. https://www.who.int/publications/i/item/924154693X",
    "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. https://www.cdc.gov/nchs/data/series/sr_11/sr11_246.pdf",
    "Grummer-Strawn LM, Reinold C, Krebs NF. Use of World Health Organization and CDC growth charts for children aged 0-59 months in the United States. MMWR Recomm Rep. 2010;59(RR-9):1-15. https://www.cdc.gov/mmwr/preview/mmwrhtml/rr5909a1.htm",
    "Marsaglia G. Evaluating the normal distribution. J Stat Softw. 2004;11(4):1-11 (the series used for Φ). https://doi.org/10.18637/jss.v011.i04"
  ],
  "related": [
    "weight-percentile",
    "height-percentile",
    "bmi-kids",
    "baby-percentile"
  ],
  "changelog": []
}