{
  "id": "population-density",
  "version": "81a8686c8edf",
  "status": "published",
  "name": "Population Density Calculator",
  "question": "What is the population density?",
  "summary": "Divides a population by its land area to give the population density in people per square mile and per square kilometer, from an area in any common unit.",
  "category": "everyday-life",
  "url": "https://www.acalculator.org/everyday-life/population-density-calculator",
  "markdown": "https://www.acalculator.org/everyday-life/population-density-calculator.md",
  "kind": "function",
  "method": "Density = population ÷ land area. Area is converted exactly: 1 sq mi = 2.589988110336 km², 1 acre = 0.0040468564224 km², 1 hectare = 0.01 km².",
  "assumptions": [
    "The area is land area, as the Census Bureau uses; include water only if you mean to.",
    "You type both numbers; the page looks up no data."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "pop": {
        "title": "Population",
        "description": "The number of people living in the place.",
        "type": "integer",
        "minimum": 0,
        "maximum": 100000000000
      },
      "area": {
        "title": "Land area",
        "description": "The land area of the place, in the unit below. Water is usually left out.",
        "type": "number",
        "minimum": 0.000001,
        "maximum": 1000000000000
      },
      "u": {
        "title": "Area unit",
        "description": "The unit the land area is typed in.",
        "type": "string",
        "enum": [
          "km2",
          "mi2",
          "ha",
          "acre",
          "m2"
        ]
      }
    }
  },
  "outputs": {
    "perMi2": {
      "label": "People per square mile",
      "description": "Population ÷ land area in square miles.",
      "format": "number"
    },
    "perKm2": {
      "label": "People per square kilometer",
      "description": "Population ÷ land area in square kilometers.",
      "format": "number"
    },
    "perAcre": {
      "label": "People per acre",
      "description": "Population ÷ land area in acres.",
      "format": "number"
    },
    "areaKm2": {
      "label": "Land area in square kilometers",
      "description": "The typed area converted to square kilometers.",
      "format": "number"
    },
    "areaMi2": {
      "label": "Land area in square miles",
      "description": "The typed area converted to square miles.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "pop": 331449281,
      "area": 3533038.28,
      "u": "mi2"
    },
    "outputs": {
      "perMi2": 93.8142343026071,
      "perKm2": 36.22187836624337,
      "perAcre": 0.1465847410978236,
      "areaKm2": 9150527.138561951,
      "areaMi2": 3533038.28
    },
    "text": "The population density is 93.81 people per square mile (36.22 per square kilometer)."
  },
  "examples": [
    {
      "given": {
        "pop": 331449281,
        "area": 3533038.28,
        "u": "mi2"
      },
      "expect": {
        "perMi2": 93.8142343026071,
        "perKm2": 36.221878366243374
      },
      "source": "US Census Bureau QuickFacts, United States: population April 1, 2020 331,449,281; land area 2020 3,533,038.28 sq mi; population per square mile 2020 93.8; https://www.census.gov/quickfacts/note/POP060220",
      "tolerance": 1e-12
    },
    {
      "given": {
        "pop": 1000000,
        "area": 250,
        "u": "km2"
      },
      "expect": {
        "perKm2": 4000,
        "perMi2": 10359.952441344,
        "areaMi2": 96.52553963561147
      },
      "source": "hand calculation in content.mdx: 1,000,000 ÷ 250 = 4,000 per km²; × 2.589988110336 = 10,359.95 per sq mi; https://www.census.gov/quickfacts/note/POP060220",
      "tolerance": 1e-12
    },
    {
      "given": {
        "pop": 500,
        "area": 200,
        "u": "acre"
      },
      "expect": {
        "perAcre": 2.5,
        "perMi2": 1600
      },
      "source": "hand calculation in content.mdx: 500 ÷ 200 = 2.5 per acre; 640 acres per square mile, so 2.5 × 640 = 1,600; https://www.census.gov/quickfacts/note/POP060220"
    }
  ],
  "sources": [
    "US Census Bureau. QuickFacts note: Land Area and Persons Per Square Mile (density is the population divided by the land area in square miles or square kilometers), retrieved 2026-10-18. https://www.census.gov/quickfacts/note/POP060220",
    "US Census Bureau. QuickFacts, United States (population April 1, 2020; land area in square miles, 2020; population per square mile, 2020), retrieved 2026-10-18. https://www.census.gov/quickfacts/fact/table/US/POP060220",
    "NIST. Special Publication 811, Guide for the Use of the International System of Units, Appendix B.8 (foot, mile, square mile, hectare), retrieved 2026-10-18. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8"
  ],
  "related": [
    "area",
    "percentage",
    "growth-rate",
    "square-footage"
  ],
  "changelog": []
}