{
  "id": "rate-of-natural-increase",
  "version": "b9742cff100b",
  "status": "published",
  "name": "Rate of Natural Increase Calculator",
  "question": "What is the rate of natural increase?",
  "summary": "Computes the rate of natural increase (RNI): births minus deaths as a percent of the population, from counts or from the crude birth and death rates per 1,000.",
  "category": "statistics",
  "subcategory": "descriptive",
  "url": "https://www.acalculator.org/statistics/rate-of-natural-increase-calculator",
  "markdown": "https://www.acalculator.org/statistics/rate-of-natural-increase-calculator.md",
  "kind": "function",
  "method": "RNI (%) = (births − deaths) ÷ population × 100. From rates per 1,000: RNI (%) = (crude birth rate − crude death rate) ÷ 10. Crude birth rate = births ÷ population × 1,000; crude death rate = deaths ÷ population × 1,000.",
  "assumptions": [
    "Births and deaths are for one year, and the population is the one the rates are based on, usually at midyear.",
    "Migration is left out: natural increase counts only births and deaths.",
    "Arithmetic is exact on the typed decimals; the RNI shows to 3 decimals and the rates to 2, halves up."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "I know the",
        "description": "Numbers of births, deaths and people, or the crude birth and death rates per 1,000.",
        "type": "string",
        "enum": [
          "counts",
          "rates"
        ]
      },
      "births": {
        "title": "Live births in the year",
        "description": "The number of live births in the population during the year.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000
      },
      "deaths": {
        "title": "Deaths in the year",
        "description": "The number of deaths in the population during the year.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000
      },
      "pop": {
        "title": "Population",
        "description": "The population the rate is based on, usually at the middle of the year.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "br": {
        "title": "Crude birth rate (per 1,000)",
        "description": "Live births per 1,000 people in the year.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000
      },
      "dr": {
        "title": "Crude death rate (per 1,000)",
        "description": "Deaths per 1,000 people in the year.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000
      }
    }
  },
  "outputs": {
    "rni": {
      "label": "Rate of natural increase",
      "description": "(Births − deaths) ÷ population × 100, or (birth rate − death rate) ÷ 10.",
      "format": "percent"
    },
    "perThousand": {
      "label": "Natural increase per 1,000 people",
      "description": "Birth rate − death rate.",
      "format": "number"
    },
    "increase": {
      "label": "Natural increase (births − deaths)",
      "description": "Negative when deaths outnumber births (natural decrease).",
      "format": "number"
    },
    "birthRate": {
      "label": "Crude birth rate (per 1,000)",
      "description": "Births ÷ population × 1,000.",
      "format": "number"
    },
    "deathRate": {
      "label": "Crude death rate (per 1,000)",
      "description": "Deaths ÷ population × 1,000.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": "counts",
      "births": 12000,
      "deaths": 8000,
      "pop": 1000000,
      "br": 17,
      "dr": 8
    },
    "outputs": {
      "rni": 0.4,
      "perThousand": 4,
      "increase": 4000,
      "birthRate": 12,
      "deathRate": 8
    },
    "text": "The rate of natural increase is 0.4%, or 4 per 1,000 people in the year."
  },
  "examples": [
    {
      "given": {
        "from": "counts",
        "births": 12000,
        "deaths": 8000,
        "pop": 1000000
      },
      "expect": {
        "rni": 0.4,
        "perThousand": 4,
        "increase": 4000,
        "birthRate": 12,
        "deathRate": 8
      },
      "source": "Population Reference Bureau, Glossary of Demographic Terms (rate of natural increase: the rate at which a population is increasing or decreasing in a year due to a surplus or deficit of births over deaths, as a percentage of the base population; birth rate and death rate: live births and deaths per 1,000 population in a year). https://www.prb.org/resources/glossary/; hand calculation in content.mdx: (12,000 − 8,000) ÷ 1,000,000 × 100 = 0.4%"
    },
    {
      "given": {
        "from": "counts",
        "births": 9500,
        "deaths": 11200,
        "pop": 850000
      },
      "expect": {
        "rni": -0.2,
        "perThousand": -2,
        "increase": -1700,
        "birthRate": 11.176470588235293,
        "deathRate": 13.176470588235293
      },
      "source": "Population Reference Bureau, Glossary of Demographic Terms (rate of natural increase: the rate at which a population is increasing or decreasing in a year due to a surplus or deficit of births over deaths, as a percentage of the base population; birth rate and death rate: live births and deaths per 1,000 population in a year). https://www.prb.org/resources/glossary/; hand calculation in content.mdx: (9,500 − 11,200) ÷ 850,000 × 100 = −0.2%"
    },
    {
      "given": {
        "from": "rates",
        "br": 17,
        "dr": 8
      },
      "expect": {
        "rni": 0.9,
        "perThousand": 9
      },
      "source": "Population Reference Bureau, Glossary of Demographic Terms (rate of natural increase: the rate at which a population is increasing or decreasing in a year due to a surplus or deficit of births over deaths, as a percentage of the base population; birth rate and death rate: live births and deaths per 1,000 population in a year). https://www.prb.org/resources/glossary/; hand calculation in content.mdx: (17 − 8) ÷ 10 = 0.9%"
    },
    {
      "given": {
        "from": "rates",
        "br": 9.2,
        "dr": 10.6
      },
      "expect": {
        "rni": -0.14,
        "perThousand": -1.4
      },
      "source": "Population Reference Bureau, Glossary of Demographic Terms (rate of natural increase: the rate at which a population is increasing or decreasing in a year due to a surplus or deficit of births over deaths, as a percentage of the base population; birth rate and death rate: live births and deaths per 1,000 population in a year). https://www.prb.org/resources/glossary/; hand calculation in content.mdx: (9.2 − 10.6) ÷ 10 = −0.14%"
    },
    {
      "given": {
        "from": "counts",
        "births": 25481,
        "deaths": 21736,
        "pop": 2345678
      },
      "expect": {
        "rni": 0.1596553320617749,
        "birthRate": 10.862957319802632,
        "deathRate": 9.266403999184885
      },
      "source": "Population Reference Bureau, Glossary of Demographic Terms (rate of natural increase: the rate at which a population is increasing or decreasing in a year due to a surplus or deficit of births over deaths, as a percentage of the base population; birth rate and death rate: live births and deaths per 1,000 population in a year). https://www.prb.org/resources/glossary/; hand calculation in content.mdx: 3,745 ÷ 2,345,678 × 100 = 0.1597% (Python Fraction)"
    }
  ],
  "sources": [
    "Population Reference Bureau, Glossary of Demographic Terms: rate of natural increase (or decrease), the rate at which a population is increasing (or decreasing) in a given year due to a surplus (or deficit) of births over deaths, expressed as a percentage of the base population; birth rate (crude birth rate), the number of live births per 1,000 population in a given year; death rate (crude death rate), the number of deaths per 1,000 population in a given year; growth rate, which adds net migration. https://www.prb.org/resources/glossary/ (retrieved 2026-10-19)"
  ],
  "related": [
    "growth-rate",
    "exponential-growth",
    "percentage-change",
    "incidence-rate"
  ],
  "changelog": []
}