{
  "id": "dew-point",
  "version": "0a266617fbe9",
  "status": "published",
  "name": "Dew Point Calculator",
  "question": "What is the dew point?",
  "summary": "Computes the dew point from air temperature and relative humidity with the Magnus formula, or the relative humidity or air temperature from the other two.",
  "category": "physics",
  "subcategory": "weather",
  "url": "https://www.acalculator.org/physics/dew-point-calculator",
  "markdown": "https://www.acalculator.org/physics/dew-point-calculator.md",
  "kind": "formulas",
  "method": "Td = b·γ ÷ (a − γ), where γ = ln(RH ÷ 100) + a·T ÷ (b + T), a = 17.625 and b = 243.04 °C, with T and Td in °C (Magnus formula, Alduchov and Eskridge 1996).",
  "assumptions": [
    "Saturation is over liquid water, also below 0 °C. Over ice, the frost point is a little higher than this dew point.",
    "The Magnus coefficients a = 17.625 and b = 243.04 °C fit the saturation vapor pressure from −40 °C to 50 °C, so the air temperature and the dew point must both be in that range.",
    "Relative humidity is between 0% (not included) and 100%."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "t": {
        "title": "Air temperature",
        "description": "The dry-bulb air temperature.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 233.14999999999998,
        "maximum": 323.15
      },
      "rh": {
        "title": "Relative humidity",
        "description": "The relative humidity over water, in percent.",
        "type": "number",
        "x-unit": "percent",
        "exclusiveMinimum": 0,
        "maximum": 100
      },
      "td": {
        "title": "Dew point",
        "description": "The temperature to which the air must cool, at the same pressure, to become saturated.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 233.14999999999998,
        "maximum": 323.15
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "t",
      "rh",
      "td"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "temp": {
      "label": "Air temperature",
      "description": "The dry-bulb air temperature.",
      "format": "quantity",
      "unit": "F"
    },
    "rh": {
      "label": "Relative humidity",
      "description": "The relative humidity over water, in percent.",
      "format": "percent"
    },
    "dewPoint": {
      "label": "Dew point",
      "description": "The temperature to which the air must cool, at the same pressure, to become saturated.",
      "format": "quantity",
      "unit": "F"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "t": 293.15,
      "rh": 50
    },
    "outputs": {
      "dewPoint": 282.4111066305342
    },
    "text": "At 68 °F and 50% relative humidity, the dew point is 48.7 °F."
  },
  "examples": [
    {
      "given": {
        "t": 293.15,
        "rh": 50
      },
      "expect": {
        "td": 282.4111066305342
      },
      "source": "hand calculation in content.mdx: γ = ln 0.5 + 17.625 × 20 ÷ 263.04 = 0.64695; Td = 243.04 × 0.64695 ÷ (17.625 − 0.64695) = 9.26 °C (Alduchov and Eskridge 1996 coefficients)"
    },
    {
      "given": {
        "t": 303.15,
        "rh": 70
      },
      "expect": {
        "td": 297.08046783483707
      },
      "source": "hand calculation in content.mdx: γ = ln 0.7 + 17.625 × 30 ÷ 273.04 = 1.57985; Td = 243.04 × 1.57985 ÷ (17.625 − 1.57985) = 23.93 °C"
    },
    {
      "given": {
        "t": 298.15,
        "td": 298.15
      },
      "expect": {
        "rh": 100
      },
      "source": "definition of the dew point (WMO No. 8): at T = Td the air is saturated, RH = 100%",
      "tolerance": 1e-12
    },
    {
      "given": {
        "rh": 40,
        "td": 278.15
      },
      "expect": {
        "t": 292.047808525763
      },
      "source": "hand calculation in content.mdx: s = 17.625 × 5 ÷ 248.04 − ln 0.4 = 1.27158; T = 243.04 × 1.27158 ÷ (17.625 − 1.27158) = 18.90 °C"
    }
  ],
  "sources": [
    "Alduchov, O. A., and R. E. Eskridge (1996). Improved Magnus form approximation of saturation vapor pressure. Journal of Applied Meteorology 35(4), 601–609. https://doi.org/10.1175/1520-0450(1996)035<0601:IMFAOS>2.0.CO;2",
    "World Meteorological Organization, Guide to Instruments and Methods of Observation (WMO-No. 8), Volume I, Chapter 4, Measurement of humidity: definitions of dew point and relative humidity. https://library.wmo.int/idurl/4/68695",
    "National Weather Service, The Dew Point vs Humidity: comfort guide for summer dew points. https://www.weather.gov/arx/why_dewpoint_vs_humidity",
    "NIST Special Publication 811 (2008), section 4.2.1.1: T/K = t/°C + 273.15, and Appendix B.8: t/°C = (t/°F − 32) ÷ 1.8. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "density",
    "speed"
  ],
  "changelog": []
}