{
  "id": "wet-bulb",
  "version": "3c3a0634eef4",
  "status": "published",
  "name": "Wet Bulb Calculator",
  "question": "What is the wet bulb temperature?",
  "summary": "Estimates the wet-bulb temperature from the air temperature and relative humidity at sea-level pressure, with the Stull (2011) formula.",
  "category": "physics",
  "subcategory": "weather",
  "url": "https://www.acalculator.org/physics/wet-bulb-calculator",
  "markdown": "https://www.acalculator.org/physics/wet-bulb-calculator.md",
  "kind": "function",
  "method": "Tw = T·atan[0.151977·(RH + 8.313659)^½] + atan(T + RH) − atan(RH − 1.676331) + 0.00391838·RH^(3/2)·atan(0.023101·RH) − 4.686035, with T and Tw in °C, RH in percent and atan in radians (Stull 2011).",
  "assumptions": [
    "Air pressure is standard sea-level pressure, 101.325 kPa. At high altitude the true wet-bulb temperature is a little lower.",
    "The formula is an empirical fit for relative humidity from 5% to 99% and air temperature from −20 °C to 50 °C; Stull gives its error as −1 °C to +0.65 °C, with a mean absolute error under 0.3 °C.",
    "Where the formula gives a wet-bulb temperature above the air temperature: below 0 °C (cold, dry air, which Stull leaves out) the page gives no answer; at 0 °C or above (only near 99% humidity above 43 °C, by at most 0.04 °C) it shows the air temperature."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "t": {
        "title": "Air temperature",
        "description": "The dry-bulb air temperature, from −20 °C to 50 °C (−4 °F to 122 °F).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 253.149999999,
        "maximum": 323.15000000099997
      },
      "rh": {
        "title": "Relative humidity",
        "description": "The relative humidity, from 5% to 99%.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 5,
        "maximum": 99
      }
    }
  },
  "outputs": {
    "wetBulb": {
      "label": "Wet-bulb temperature",
      "description": "The temperature a wet thermometer reads as water evaporates from it, at sea-level pressure.",
      "format": "quantity",
      "unit": "F"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "t": 293.15,
      "rh": 50
    },
    "outputs": {
      "wetBulb": 286.84934196898814
    },
    "text": "At 68 °F and 50% relative humidity, the wet-bulb temperature is 56.7 °F."
  },
  "examples": [
    {
      "given": {
        "t": 293.15,
        "rh": 50
      },
      "expect": {
        "wetBulb": 286.84934196898814
      },
      "source": "Stull, R., 2011: Wet-Bulb Temperature from Relative Humidity and Air Temperature. J. Appl. Meteor. Climatol., 50, 2267–2269, https://doi.org/10.1175/JAMC-D-11-0143.1 (example: 20 °C and 50% give 13.7 °C); NCAR Command Language, wetbulb_stull (13.69934 °C), https://www.ncl.ucar.edu/Document/Functions/Contributed/wetbulb_stull.shtml"
    },
    {
      "given": {
        "t": 308.15,
        "rh": 75
      },
      "expect": {
        "wetBulb": 304.250776617508
      },
      "source": "hand calculation in content.mdx from Stull, R., 2011: Wet-Bulb Temperature from Relative Humidity and Air Temperature. J. Appl. Meteor. Climatol., 50, 2267–2269, https://doi.org/10.1175/JAMC-D-11-0143.1; Python 3 with math.atan"
    },
    {
      "given": {
        "t": 303.15,
        "rh": 20
      },
      "expect": {
        "wetBulb": 289.05048267974274
      },
      "source": "hand calculation in content.mdx from Stull, R., 2011: Wet-Bulb Temperature from Relative Humidity and Air Temperature. J. Appl. Meteor. Climatol., 50, 2267–2269, https://doi.org/10.1175/JAMC-D-11-0143.1; Python 3 with math.atan"
    },
    {
      "given": {
        "t": 318.15,
        "rh": 99
      },
      "expect": {
        "wetBulb": 318.15
      },
      "source": "hand calculation in content.mdx: Stull gives 45.0100 °C > 45 °C, capped at the air temperature; Stull, R., 2011: Wet-Bulb Temperature from Relative Humidity and Air Temperature. J. Appl. Meteor. Climatol., 50, 2267–2269, https://doi.org/10.1175/JAMC-D-11-0143.1",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "Stull, R., 2011: Wet-Bulb Temperature from Relative Humidity and Air Temperature. Journal of Applied Meteorology and Climatology, 50, 2267–2269 (equation 1; valid for RH 5% to 99% and T −20 °C to 50 °C, except cold and dry air). https://doi.org/10.1175/JAMC-D-11-0143.1 (retrieved 2026-10-02)",
    "NCAR Command Language, wetbulb_stull: the Stull (2011) method, its range, and the example 20 °C, 50% → 13.69934 °C. https://www.ncl.ucar.edu/Document/Functions/Contributed/wetbulb_stull.shtml (retrieved 2026-10-02)"
  ],
  "related": [
    "dew-point",
    "heat-index",
    "wind-chill"
  ],
  "changelog": []
}