{
  "id": "incidence-rate",
  "version": "abc0ab55fd32",
  "status": "published",
  "name": "Incidence Rate Calculator",
  "question": "What is the incidence rate?",
  "summary": "Computes the incidence rate (new cases ÷ person-time at risk) or the incidence proportion (new cases ÷ population at risk), per 100 to per 1,000,000.",
  "category": "statistics",
  "subcategory": "probability",
  "url": "https://www.acalculator.org/statistics/incidence-rate-calculator",
  "markdown": "https://www.acalculator.org/statistics/incidence-rate-calculator.md",
  "kind": "function",
  "method": "Incidence rate = new cases ÷ person-time at risk × 10ⁿ; incidence proportion = new cases ÷ population at risk at the start × 10ⁿ.",
  "assumptions": [
    "Person-time counts only the time each person was at risk (free of the disease and followed up).",
    "The person-time unit only names the result; the page does not convert between years, months and days."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "m": {
        "title": "Measure",
        "description": "Incidence rate uses person-time; incidence proportion (risk, attack rate) uses the people at risk at the start.",
        "type": "string",
        "enum": [
          "rate",
          "proportion"
        ]
      },
      "cases": {
        "title": "New cases",
        "description": "The number of new cases of the disease or injury during the period.",
        "type": "integer",
        "minimum": 0,
        "maximum": 1000000000000
      },
      "pt": {
        "title": "Person-time at risk",
        "description": "The time each person was observed while at risk, added up for everyone, in the unit below.",
        "type": "number",
        "minimum": 0.000001,
        "maximum": 10000000000000
      },
      "u": {
        "title": "Person-time unit",
        "description": "The unit the person-time is counted in; it names the result.",
        "type": "string",
        "enum": [
          "years",
          "months",
          "days"
        ]
      },
      "pop": {
        "title": "People at risk at the start",
        "description": "The size of the population at risk at the start of the period.",
        "type": "integer",
        "minimum": 1,
        "maximum": 1000000000000
      },
      "per": {
        "title": "Show per",
        "description": "The multiplier 10ⁿ, chosen so the result is easy to read.",
        "type": "string",
        "enum": [
          "1",
          "100",
          "1000",
          "10000",
          "100000",
          "1000000"
        ]
      }
    }
  },
  "outputs": {
    "incidence": {
      "label": "Incidence",
      "description": "New cases ÷ the denominator, times the multiplier you chose.",
      "format": "number"
    },
    "raw": {
      "label": "Without the multiplier",
      "description": "New cases ÷ the denominator, per person-time unit or per person.",
      "format": "number"
    },
    "text": {
      "label": "Unit",
      "description": "What the incidence counts: new cases per the multiplier and denominator.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "m": "rate",
      "cases": 16,
      "pt": 6400,
      "u": "years",
      "pop": 2100,
      "per": "1000"
    },
    "outputs": {
      "incidence": 2.5,
      "raw": 0.0025,
      "text": "new cases per 1,000 person-years"
    },
    "text": "The incidence is 2.5 new cases per 1,000 person-years."
  },
  "examples": [
    {
      "given": {
        "m": "rate",
        "cases": 16,
        "pt": 6400,
        "per": "1000"
      },
      "expect": {
        "incidence": 2.5,
        "raw": 0.0025,
        "text": "new cases per 1,000 person-years"
      },
      "source": "CDC, Principles of Epidemiology, Lesson 3, section 2, incidence rate example (16 ÷ 6,400 = 2.5 per 1,000 person-years); https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html"
    },
    {
      "given": {
        "m": "proportion",
        "cases": 16,
        "pop": 2100,
        "per": "1000"
      },
      "expect": {
        "incidence": 7.619047619047619
      },
      "source": "CDC, Principles of Epidemiology, Lesson 3, section 2 (incidence proportion 16 ÷ 2,100 = 7.6 per 1,000); https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html"
    },
    {
      "given": {
        "m": "proportion",
        "cases": 100,
        "pop": 189,
        "per": "100"
      },
      "expect": {
        "incidence": 52.91005291005291
      },
      "source": "CDC, Principles of Epidemiology, Lesson 3, section 2 (100 ÷ 189 × 100 = 52.9%); https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html"
    },
    {
      "given": {
        "m": "rate",
        "cases": 72,
        "pt": 1862,
        "per": "1000"
      },
      "expect": {
        "incidence": 38.66809881847476
      },
      "source": "CDC, Principles of Epidemiology, Lesson 3, section 2 (72 deaths in 1,862 person-years, printed as 38.6 per 1,000 person-years; 72 ÷ 1,862 × 1,000 = 38.668); https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html"
    },
    {
      "given": {
        "m": "rate",
        "cases": 44232,
        "pt": 290809777,
        "per": "100000"
      },
      "expect": {
        "incidence": 15.209942546051332
      },
      "source": "CDC, Principles of Epidemiology, Lesson 3, section 2 (44,232 ÷ 290,809,777 × 100,000 = 15.21 per 100,000); https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html"
    }
  ],
  "sources": [
    "Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice, 3rd ed., Lesson 3, Section 2: Morbidity Frequency Measures (incidence proportion, incidence rate, person-time), retrieved 2026-10-18. https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html"
  ],
  "related": [
    "odds-ratio",
    "nnt",
    "sensitivity-specificity",
    "percentage"
  ],
  "changelog": []
}