{
  "id": "density-altitude",
  "version": "810d5503b6aa",
  "status": "published",
  "name": "Density Altitude Calculator",
  "question": "What is the density altitude?",
  "summary": "Density altitude calculator for pilots: density altitude from field elevation, altimeter setting, temperature and dew point, with the pressure altitude, the ISA temperature and the 118.8 ft per °C rule of thumb.",
  "category": "physics",
  "subcategory": "weather",
  "url": "https://www.acalculator.org/physics/density-altitude-calculator",
  "markdown": "https://www.acalculator.org/physics/density-altitude-calculator.md",
  "kind": "function",
  "method": "PA = elevation + 145,366.45 × (1 − (A ÷ 1,013.25)^0.190284) ft; P = 1,013.25 × (1 − PA ÷ 145,366.45)^(1 ÷ 0.190284) hPa; e = 6.11 × 10^(7.5Td ÷ (237.7 + Td)) hPa; Tv = T ÷ (1 − (e ÷ P) × 0.378) K; DA = 145,442.16 × (1 − (17.326 × P_inHg ÷ (1.8 × Tv))^0.235) ft.",
  "assumptions": [
    "The standard atmosphere: 1,013.25 hPa and 15 °C at sea level, cooling 1.9812 °C per 1,000 ft.",
    "Leave the dew point empty for dry air; humidity raises density altitude, often by a few hundred feet on a warm, humid day."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "elev": {
        "title": "Field elevation",
        "description": "The elevation of the airport or place, above mean sea level.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": -457.20000000000005,
        "maximum": 6096
      },
      "alt": {
        "title": "Altimeter setting",
        "description": "The altimeter setting (QNH) from ATIS, METAR or the tower.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "pressure",
        "minimum": 90000,
        "maximum": 110000
      },
      "t": {
        "title": "Outside air temperature",
        "description": "The air temperature at the field.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 213.14999999999998,
        "maximum": 333.15
      },
      "td": {
        "title": "Dew point",
        "description": "The dew point at the field, for the humidity. Leave empty for dry air.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 213.14999999999998,
        "maximum": 333.15
      }
    }
  },
  "outputs": {
    "da": {
      "label": "Density altitude",
      "description": "The height in the standard atmosphere with the same air density.",
      "format": "quantity",
      "unit": "ft"
    },
    "pa": {
      "label": "Pressure altitude",
      "description": "Field elevation + the altimeter correction (NWS formula).",
      "format": "quantity",
      "unit": "ft"
    },
    "rule": {
      "label": "Rule of thumb",
      "description": "Pressure altitude + 118.8 ft × (temperature − ISA temperature in °C), for dry air.",
      "format": "quantity",
      "unit": "ft"
    },
    "isa": {
      "label": "ISA temperature (°C)",
      "description": "The standard-atmosphere temperature at the pressure altitude: 15 − 1.9812 per 1,000 ft.",
      "format": "number"
    },
    "stationHpa": {
      "label": "Station pressure (hPa)",
      "description": "The actual pressure at the field in hectopascals.",
      "format": "number"
    },
    "stationInHg": {
      "label": "Station pressure (inHg)",
      "description": "The actual pressure at the field in inches of mercury.",
      "format": "number"
    },
    "vapourHpa": {
      "label": "Vapour pressure (hPa)",
      "description": "The water vapour pressure from the dew point (0 for dry air).",
      "format": "number"
    },
    "virtualC": {
      "label": "Virtual temperature (°C)",
      "description": "The temperature dry air would need to have the same density as this moist air.",
      "format": "number"
    },
    "ratio": {
      "label": "Density ratio (%)",
      "description": "17.326 × P ÷ Tv: the air density as a percentage of standard sea-level density.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "elev": "5000 ft",
      "alt": "29.92 inHg",
      "t": "30 °C"
    },
    "outputs": {
      "da": 2383.991102958771,
      "pa": 1524.3537962996788,
      "rule": 2426.289305557675,
      "isa": 5.091700324052088,
      "stationHpa": 842.9708867388681,
      "stationInHg": 24.892916208636443,
      "vapourHpa": 0,
      "virtualC": 30,
      "ratio": 79.0394682190399
    },
    "text": "The density altitude is 7,821 ft (pressure altitude 5,001 ft)."
  },
  "examples": [
    {
      "given": {
        "elev": 0,
        "alt": 101325,
        "t": 288.15
      },
      "expect": {
        "pa": 0,
        "isa": 15,
        "da": 5.109212246358173
      },
      "source": "Wikipedia, Density altitude (DA = 145,442.16 × (1 − [17.326 × P ÷ T]^0.235), P in inHg, T in °R; DA ≈ PA + 118.8 × (OAT − ISA)), https://en.wikipedia.org/wiki/Density_altitude (retrieved 2026-10-05); Wikipedia, Pressure altitude (145,366.45 × [1 − (p ÷ 1,013.25)^0.190284] ft), https://en.wikipedia.org/wiki/Pressure_altitude (retrieved 2026-10-05); hand calculation in content.mdx: P = 29.921 inHg, T = 518.67 °R, 17.326 × 29.921 ÷ 518.67 = 0.99951, DA = 145,442.16 × (1 − 0.99951^0.235) = 16.76 ft (the 17.326 constant is rounded, so DA is not exactly 0)",
      "tolerance": 1e-9
    },
    {
      "given": {
        "elev": 1524,
        "alt": 101320.74811900273,
        "t": 303.15
      },
      "expect": {
        "da": 2383.991102958771,
        "rule": 2426.289305557675,
        "stationHpa": 842.9708867388681
      },
      "source": "Wikipedia, Density altitude (DA = 145,442.16 × (1 − [17.326 × P ÷ T]^0.235), P in inHg, T in °R; DA ≈ PA + 118.8 × (OAT − ISA)), https://en.wikipedia.org/wiki/Density_altitude (retrieved 2026-10-05); hand calculation in content.mdx: PA = 5,001.16 ft, P = 842.97 hPa = 24.8929 inHg, T = 545.67 °R, 17.326 × 24.8929 ÷ 545.67 = 0.790395, DA = 7,821.5 ft; rule of thumb 5,001.16 + 118.8 × (30 − 5.0917) = 7,960.3 ft",
      "tolerance": 1e-9
    },
    {
      "given": {
        "elev": 1524,
        "alt": 101320.74811900273,
        "t": 303.15,
        "td": 293.15
      },
      "expect": {
        "vapourHpa": 23.340673695870713,
        "da": 2487.578041719115
      },
      "source": "MetPod, Density Altitude (DA) Calculation, NOAA formulas e = 6.11 × 10^(7.5Td ÷ (237.7 + Td)) and Tv = T ÷ (1 − (e ÷ p)(1 − 0.622)), https://www.metpod.co.uk/calculators/density-alt/ (retrieved 2026-10-05); Wikipedia, Density altitude (DA = 145,442.16 × (1 − [17.326 × P ÷ T]^0.235), P in inHg, T in °R; DA ≈ PA + 118.8 × (OAT − ISA)), https://en.wikipedia.org/wiki/Density_altitude (retrieved 2026-10-05); hand calculation in content.mdx: e = 6.11 × 10^(150 ÷ 257.7) = 23.341 hPa; Tv = 303.15 ÷ (1 − 23.341 ÷ 842.97 × 0.378) = 306.356 K; 17.326 × 24.8929 ÷ (1.8 × 306.356) = 0.782122; DA = 8,161.3 ft",
      "tolerance": 1e-9
    }
  ],
  "sources": [
    "Wikipedia, Density altitude: DA = 145,442.16 × (1 − [17.326 × P ÷ T]^0.235) and DA ≈ PA + 118.8 × (OAT − ISA), retrieved 2026-10-05. https://en.wikipedia.org/wiki/Density_altitude",
    "Wikipedia, Pressure altitude: h = 145,366.45 × [1 − (p ÷ 1,013.25)^0.190284] ft, retrieved 2026-10-05. https://en.wikipedia.org/wiki/Pressure_altitude",
    "MetPod, Density Altitude (DA) Calculation: the NOAA vapour pressure and virtual temperature formulas, retrieved 2026-10-05. https://www.metpod.co.uk/calculators/density-alt/",
    "National Weather Service, Density Altitude Calculator, retrieved 2026-10-05. https://www.weather.gov/epz/wxcalc_densityaltitude"
  ],
  "related": [
    "pressure-altitude",
    "air-density",
    "e6b"
  ],
  "changelog": []
}