{
  "id": "baby-percentile",
  "version": "839f87cd972f",
  "status": "published",
  "name": "Baby Percentile Calculator",
  "question": "What is my baby’s percentile?",
  "summary": "Finds a baby’s weight, length and head circumference percentiles and z-scores from birth to 24 months on the WHO child growth standards.",
  "category": "health",
  "subcategory": "body",
  "url": "https://www.acalculator.org/health/baby-percentile-calculator",
  "markdown": "https://www.acalculator.org/health/baby-percentile-calculator.md",
  "kind": "function",
  "method": "z = ((x ÷ M)^L − 1) ÷ (L × S) for each measurement x; percentile = Φ(z) × 100, with L, M and S for the sex and age from the WHO tables, read on a straight line between whole months.",
  "assumptions": [
    "The WHO 2006 growth standards describe healthy breastfed babies; the CDC advises them for all US children under 2.",
    "Age in months is 12 × years + months, or the days from birth to the measurement ÷ 30.4375.",
    "Each percentile is rounded half up to one decimal place and shown between 0.1 and 99.9. The chart bands mark the 2.3rd and 97.7th percentiles, the screening cut-offs the CDC advises with the WHO charts.",
    "A percentile compares a baby with a reference group. It 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": 2
      },
      "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 baby’s weight.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "minimum": 0.5,
        "maximum": 250
      },
      "length": {
        "title": "Length",
        "description": "The baby’s length, measured lying down.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.1,
        "maximum": 2.5
      },
      "head": {
        "title": "Head circumference",
        "description": "Around the head, above the eyebrows and ears.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0.1,
        "maximum": 2.5
      }
    }
  },
  "outputs": {
    "weightPct": {
      "label": "Weight percentile",
      "description": "The share of babies of the same sex and age with a smaller weight, rounded to one decimal place and shown between 0.1 and 99.9.",
      "format": "number"
    },
    "weightZ": {
      "label": "Weight z-score",
      "description": "How many standard deviations the weight is from the WHO median for the age.",
      "format": "number"
    },
    "lengthPct": {
      "label": "Length percentile",
      "description": "The share of babies of the same sex and age with a smaller length, rounded to one decimal place and shown between 0.1 and 99.9.",
      "format": "number"
    },
    "lengthZ": {
      "label": "Length z-score",
      "description": "How many standard deviations the length is from the WHO median for the age.",
      "format": "number"
    },
    "headPct": {
      "label": "Head percentile",
      "description": "The share of babies of the same sex and age with a smaller head, rounded to one decimal place and shown between 0.1 and 99.9.",
      "format": "number"
    },
    "headZ": {
      "label": "Head z-score",
      "description": "How many standard deviations the head is from the WHO median for the age.",
      "format": "number"
    },
    "age": {
      "label": "Age",
      "description": "The baby’s age in years and months.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "sex": "male",
      "from": "age",
      "years": 0,
      "months": 6,
      "born": "2026-03-30",
      "on": "2026-09-30",
      "weight": 7.71107029,
      "length": 0.6730999999999999,
      "head": 0.43179999999999996
    },
    "outputs": {
      "weightPct": 39.8,
      "weightZ": -0.25962160579482163,
      "lengthPct": 44.2,
      "lengthZ": -0.1465224097475492,
      "headPct": 45.1,
      "headZ": -0.12337961823859286,
      "age": "6 months"
    },
    "text": "At 6 months, the weight is at percentile 39.8 on the WHO growth standard."
  },
  "examples": [
    {
      "given": {
        "sex": "male",
        "from": "age",
        "years": 0,
        "months": 6,
        "weight": 7.934,
        "length": 0.6488071,
        "head": 0.4533835
      },
      "expect": {
        "weightPct": 50,
        "weightZ": 0,
        "lengthPct": 10,
        "lengthZ": -1.2815524632412154,
        "headPct": 95,
        "headZ": 1.6448567630712236
      },
      "source": "WHO boys month 6 (CDC copies of the WHO tables): weight 50th percentile 7.934 kg, length 10th 64.88071 cm, head circumference 95th 45.33835 cm; Python 3 cross-check in docs/progress/WP-54.md"
    },
    {
      "given": {
        "sex": "female",
        "from": "dates",
        "born": "2025-12-01",
        "on": "2026-09-01",
        "weight": 8,
        "length": 0.7,
        "head": 0.43
      },
      "expect": {
        "weightPct": 41,
        "weightZ": -0.22876764927082147,
        "lengthPct": 47.6,
        "lengthZ": -0.060536933933018795,
        "headPct": 26.7,
        "headZ": -0.6208774221509571,
        "age": "9 months"
      },
      "source": "WHO girls, 274 days = 9.002 months, between the month 9 and month 10 rows; hand calculation in content.mdx"
    },
    {
      "given": {
        "sex": "male",
        "from": "age",
        "years": 1,
        "months": 6,
        "weight": 9
      },
      "expect": {
        "weightPct": 4,
        "weightZ": -1.7507259770177208
      },
      "source": "WHO boys weight-for-age, month 18: L 0.0211, M 10.9385, S 0.11119; hand calculation in content.mdx"
    }
  ],
  "sources": [
    "Centers for Disease Control and Prevention. WHO growth charts data files: weight-for-age, length-for-age and head circumference-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",
    "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. Geneva: World Health Organization, 2007. https://www.who.int/publications/i/item/9789241547185",
    "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"
  ],
  "related": [
    "weight-percentile",
    "height-percentile",
    "growth-chart"
  ],
  "changelog": []
}