{
  "id": "homa-ir",
  "version": "8e924341d24c",
  "status": "published",
  "name": "HOMA-IR Calculator",
  "question": "What is my HOMA-IR?",
  "summary": "Calculates insulin resistance (HOMA-IR) and beta-cell function (HOMA-%B) from fasting glucose and fasting insulin with the Matthews 1985 formulas, in US or SI units.",
  "category": "health",
  "subcategory": "clinical",
  "url": "https://www.acalculator.org/health/homa-ir-calculator",
  "markdown": "https://www.acalculator.org/health/homa-ir-calculator.md",
  "kind": "function",
  "method": "HOMA-IR = glucose (mmol/L) × insulin (µU/mL) ÷ 22.5 = glucose (mg/dL) × insulin (µU/mL) ÷ 405; HOMA-%B = 20 × insulin (µU/mL) ÷ (glucose (mmol/L) − 3.5).",
  "assumptions": [
    "Both values are fasting, from the same blood sample.",
    "Glucose mg/dL ÷ 18 = mmol/L (the factor behind the 405 constant); insulin pmol/L ÷ 6 = µU/mL.",
    "HOMA-%B is shown only when glucose is over 3.5 mmol/L (63 mg/dL).",
    "There is no single normal cut-off: it depends on the insulin assay and the population."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "units": {
        "title": "Units",
        "description": "US units (glucose mg/dL, insulin µU/mL) or SI units (glucose mmol/L, insulin pmol/L).",
        "type": "string",
        "enum": [
          "us",
          "si"
        ]
      },
      "glucose": {
        "title": "Fasting glucose (mg/dL)",
        "description": "Fasting plasma glucose, in mg/dL.",
        "type": "number",
        "minimum": 20,
        "maximum": 600
      },
      "insulin": {
        "title": "Fasting insulin (µU/mL)",
        "description": "Fasting insulin, in microunits per milliliter (the same number as mU/L).",
        "type": "number",
        "minimum": 0.5,
        "maximum": 300
      },
      "glucoseSi": {
        "title": "Fasting glucose (mmol/L)",
        "description": "Fasting plasma glucose, in mmol/L.",
        "type": "number",
        "minimum": 1.1,
        "maximum": 33.3
      },
      "insulinSi": {
        "title": "Fasting insulin (pmol/L)",
        "description": "Fasting insulin, in picomoles per liter.",
        "type": "number",
        "minimum": 3,
        "maximum": 1800
      }
    }
  },
  "outputs": {
    "homaIr": {
      "label": "HOMA-IR",
      "description": "Insulin resistance: glucose (mmol/L) × insulin (µU/mL) ÷ 22.5. 1.0 is the reference of the model.",
      "format": "number"
    },
    "homaB": {
      "label": "HOMA-%B",
      "description": "Beta-cell function: 20 × insulin ÷ (glucose − 3.5), in percent of the reference. Only for glucose over 3.5 mmol/L.",
      "format": "percent"
    },
    "glucoseOther": {
      "label": "Glucose in the other unit",
      "description": "The glucose converted with 18 mg/dL per mmol/L.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "units": "us",
      "glucose": 90,
      "insulin": 10,
      "glucoseSi": 5,
      "insulinSi": 60
    },
    "outputs": {
      "homaIr": 2.2222222222222223,
      "homaB": 133.33333333333334,
      "glucoseOther": "5.0 mmol/L"
    },
    "text": "Your HOMA-IR is 2.22."
  },
  "examples": [
    {
      "given": {
        "units": "si",
        "glucoseSi": 4.5,
        "insulinSi": 30
      },
      "expect": {
        "homaIr": 1,
        "homaB": 100
      },
      "source": "Matthews et al., Diabetologia 1985: 4.5 × 5 ÷ 22.5 = 1 and 20 × 5 ÷ (4.5 − 3.5) = 100% (hand calculation in content.mdx)"
    },
    {
      "given": {
        "units": "us",
        "glucose": 90,
        "insulin": 10
      },
      "expect": {
        "homaIr": 2.2222222222222223,
        "homaB": 133.33333333333334,
        "glucoseOther": "5.0 mmol/L"
      },
      "source": "Matthews 1985: 90 × 10 ÷ 405 = 2.22; 90 ÷ 18 = 5 mmol/L, 20 × 10 ÷ 1.5 = 133.3% (hand calculation in content.mdx)"
    },
    {
      "given": {
        "units": "us",
        "glucose": 126,
        "insulin": 25
      },
      "expect": {
        "homaIr": 7.777777777777778,
        "homaB": 142.85714285714286
      },
      "source": "126 × 25 ÷ 405 = 7.78; 126 ÷ 18 = 7 mmol/L, 20 × 25 ÷ 3.5 = 142.9% (hand calculation in content.mdx)"
    },
    {
      "given": {
        "units": "si",
        "glucoseSi": 3.2,
        "insulinSi": 12
      },
      "expect": {
        "homaIr": 0.28444444444444444,
        "glucoseOther": "58 mg/dL"
      },
      "source": "3.2 × (12 ÷ 6) ÷ 22.5 = 0.284; the %B formula needs glucose over 3.5 mmol/L (hand calculation)"
    }
  ],
  "sources": [
    "Matthews DR, Hosker JP, Rudenski AS, Naylor BA, Treacher DF, Turner RC. Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man. Diabetologia. 1985;28(7):412-419. https://doi.org/10.1007/BF00280883",
    "Knopp JL, Holder-Pearson L, Chase JG. Insulin units and conversion factors: a story of truth, boots, and faster half-truths. J Diabetes Sci Technol. 2019;13(3):597-600. https://doi.org/10.1177/1932296818805074",
    "Wallace TM, Levy JC, Matthews DR. Use and abuse of HOMA modeling. Diabetes Care. 2004;27(6):1487-1495. https://doi.org/10.2337/diacare.27.6.1487"
  ],
  "related": [],
  "changelog": [
    {
      "date": "2026-09-29",
      "note": "Published after this site's editorial review against the cited sources (no clinician review); the page notice says so."
    }
  ]
}