{
  "id": "psychrometric",
  "version": "4d1a8aaa69a3",
  "status": "published",
  "name": "Psychrometric Calculator",
  "question": "What is the psychrometric state?",
  "summary": "Psychrometric calculator: humidity ratio, relative humidity, dew point, wet bulb, enthalpy, specific volume and density of moist air from the dry bulb and the relative humidity, wet bulb or dew point.",
  "category": "physics",
  "subcategory": "weather",
  "url": "https://www.acalculator.org/physics/psychrometric-calculator",
  "markdown": "https://www.acalculator.org/physics/psychrometric-calculator.md",
  "kind": "function",
  "method": "p_sat(t) by Buck (1996); p_w = RH × p_sat(t), p_sat(dew point), or from the wet bulb t*: W = ((2501 − 2.326 t*) W_s* − 1.006 (t − t*)) ÷ (2501 + 1.86 t − 4.186 t*); W = 0.62198 p_w ÷ (p − p_w); h = 1.006 t + W (2501 + 1.86 t); v = 287.058 T ÷ (p − p_w).",
  "assumptions": [
    "Moist air is a mix of ideal gases; enthalpy is zero for dry air and liquid water at 0 °C.",
    "Below 0 °C the saturation pressure is over ice (the dew point is a frost point); the wet-bulb balance uses 4.186 t* for the added water at any temperature."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "t": {
        "title": "Dry-bulb temperature",
        "description": "The air temperature from an ordinary thermometer.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 233.14999999999998,
        "maximum": 333.15
      },
      "by": {
        "title": "Humidity from",
        "description": "Which humidity value you know: relative humidity, wet-bulb temperature or dew point.",
        "type": "string",
        "enum": [
          "rh",
          "wet",
          "dew"
        ]
      },
      "rh": {
        "title": "Relative humidity",
        "description": "The relative humidity, from 0.1% to 100%.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0.1,
        "maximum": 100
      },
      "twb": {
        "title": "Wet-bulb temperature",
        "description": "The wet-bulb temperature; it cannot be above the dry bulb.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 233.14999999999998,
        "maximum": 333.15
      },
      "tdp": {
        "title": "Dew point",
        "description": "The dew point; it cannot be above the dry bulb.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 233.14999999999998,
        "maximum": 333.15
      },
      "p": {
        "title": "Air pressure",
        "description": "The actual air pressure; 101.325 kPa (14.696 psi) at sea level.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "pressure",
        "minimum": 50000,
        "maximum": 110000
      }
    }
  },
  "outputs": {
    "w": {
      "label": "Humidity ratio (g/kg)",
      "description": "Grams of water vapour per kilogram of dry air: 1,000 × 0.62198 p_w ÷ (p − p_w).",
      "format": "number"
    },
    "grains": {
      "label": "Humidity ratio (gr/lb)",
      "description": "Grains of water vapour per pound of dry air (7,000 grains to the pound).",
      "format": "number"
    },
    "rh": {
      "label": "Relative humidity (%)",
      "description": "p_w ÷ p_sat at the dry bulb.",
      "format": "number"
    },
    "dewPoint": {
      "label": "Dew point",
      "description": "The temperature at which the air becomes saturated when cooled (a frost point below 0 °C).",
      "format": "quantity",
      "unit": "F"
    },
    "wetBulb": {
      "label": "Wet bulb",
      "description": "The adiabatic saturation temperature.",
      "format": "quantity",
      "unit": "F"
    },
    "enthalpy": {
      "label": "Enthalpy (kJ/kg dry air)",
      "description": "1.006 t + W (2501 + 1.86 t), from 0 °C dry air and liquid water.",
      "format": "number"
    },
    "volume": {
      "label": "Specific volume (m³/kg dry air)",
      "description": "R_d × T ÷ (p − p_w): the volume holding 1 kg of dry air.",
      "format": "number"
    },
    "volumeFt": {
      "label": "Specific volume (ft³/lb dry air)",
      "description": "The specific volume in cubic feet per pound of dry air.",
      "format": "number"
    },
    "density": {
      "label": "Density (kg/m³)",
      "description": "(1 + W) ÷ v: the mass of moist air per cubic metre.",
      "format": "number"
    },
    "vapour": {
      "label": "Vapour pressure (kPa)",
      "description": "The partial pressure of water vapour p_w.",
      "format": "number"
    },
    "saturationP": {
      "label": "Saturation pressure (kPa)",
      "description": "The Buck saturation vapour pressure at the dry bulb.",
      "format": "number"
    },
    "saturationDeg": {
      "label": "Degree of saturation (%)",
      "description": "W ÷ W_s, with W_s the humidity ratio of saturated air at the dry bulb.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "t": "25 °C",
      "by": "rh",
      "rh": 50,
      "twb": "18 °C",
      "tdp": "14 °C",
      "p": "101.325 kPa"
    },
    "outputs": {
      "w": 9.879429812501137,
      "grains": 69.15600868750795,
      "rh": 50,
      "dewPoint": 287.0129637408803,
      "wetBulb": 291.039404126369,
      "enthalpy": 50.317847447346644,
      "volume": 0.8580881553151618,
      "volumeFt": 13.745253687544938,
      "density": 1.176894732268608,
      "vapour": 1.5842657061377174,
      "saturationP": 3.168531412275435,
      "saturationDeg": 49.20580807964074
    },
    "text": "The humidity ratio is 9.88 g/kg, with a dew point of 13.9 °C, a wet bulb of 17.9 °C and an enthalpy of 50.32 kJ/kg."
  },
  "examples": [
    {
      "given": {
        "t": 298.15,
        "by": "rh",
        "rh": 50,
        "p": 101325
      },
      "expect": {
        "w": 9.879429812501137,
        "enthalpy": 50.317847447346644,
        "twb": 291.039404126369
      },
      "source": "Wikipedia, Arden Buck equation (Buck 1996: 6.1121 exp((18.678 − T/234.5)(T/(257.14 + T))) hPa over water, 6.1115 exp((23.036 − T/333.7)(T/(279.82 + T))) hPa over ice), https://en.wikipedia.org/wiki/Arden_Buck_equation (retrieved 2026-10-05); Engineering ToolBox, Humidity Ratio of Air (x = 0.62198 p_w ÷ (p_a − p_w)), https://www.engineeringtoolbox.com/humidity-ratio-air-d_686.html (retrieved 2026-10-05); Engineering ToolBox, Enthalpy of Moist Air (h = 1.006 t + x (1.86 t + 2501) kJ/kg), https://www.engineeringtoolbox.com/enthalpy-moist-air-d_683.html (retrieved 2026-10-05); hand calculation in content.mdx: p_sat = 3,168.53 Pa, p_w = 1,584.27 Pa, W = 0.62198 × 1,584.27 ÷ 99,740.73 = 0.0098794; h = 25.15 + 0.0098794 × 2,547.5 = 50.318 kJ/kg; wet bulb 17.889 °C by bisection",
      "tolerance": 1e-9
    },
    {
      "given": {
        "t": 293.15,
        "by": "dew",
        "tdp": 283.15,
        "p": 101325
      },
      "expect": {
        "rh": 52.509907921591726,
        "tdp": 283.15,
        "w": 7.629633269920221
      },
      "source": "Wikipedia, Arden Buck equation (Buck 1996: 6.1121 exp((18.678 − T/234.5)(T/(257.14 + T))) hPa over water, 6.1115 exp((23.036 − T/333.7)(T/(279.82 + T))) hPa over ice), https://en.wikipedia.org/wiki/Arden_Buck_equation (retrieved 2026-10-05); Engineering ToolBox, Humidity Ratio of Air (x = 0.62198 p_w ÷ (p_a − p_w)), https://www.engineeringtoolbox.com/humidity-ratio-air-d_686.html (retrieved 2026-10-05); hand calculation in content.mdx: p_w = p_sat(10 °C) = 1,227.86 Pa, p_sat(20 °C) = 2,338.34 Pa, RH = 52.51%; W = 0.62198 × 1,227.86 ÷ 100,097.14 = 0.0076296",
      "tolerance": 1e-9
    },
    {
      "given": {
        "t": 303.15,
        "by": "wet",
        "twb": 303.15,
        "p": 101325
      },
      "expect": {
        "rh": 100,
        "tdp": 303.15
      },
      "source": "Wikipedia, Arden Buck equation (Buck 1996: 6.1121 exp((18.678 − T/234.5)(T/(257.14 + T))) hPa over water, 6.1115 exp((23.036 − T/333.7)(T/(279.82 + T))) hPa over ice), https://en.wikipedia.org/wiki/Arden_Buck_equation (retrieved 2026-10-05); hand calculation in content.mdx: with t* = t the wet-bulb balance gives W = W_s, so RH = 100% and the dew point is 30 °C",
      "tolerance": 1e-9
    }
  ],
  "sources": [
    "Wikipedia, Arden Buck equation: Buck (1996) saturation vapour pressure over water and over ice, retrieved 2026-10-05. https://en.wikipedia.org/wiki/Arden_Buck_equation",
    "Engineering ToolBox, Humidity Ratio of Air: x = 0.62198 p_w ÷ (p_a − p_w), retrieved 2026-10-05. https://www.engineeringtoolbox.com/humidity-ratio-air-d_686.html",
    "Engineering ToolBox, Enthalpy of Moist Air: h = 1.006 t + x (1.86 t + 2501) kJ/kg, retrieved 2026-10-05. https://www.engineeringtoolbox.com/enthalpy-moist-air-d_683.html",
    "Wikipedia, Density of air: the gas constant of dry air R_d = 287.058 J/(kg·K), retrieved 2026-10-05. https://en.wikipedia.org/wiki/Density_of_air"
  ],
  "related": [
    "dew-point",
    "wet-bulb",
    "air-density"
  ],
  "changelog": []
}