{
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  "question": "Using the Magnus formula, what is the dew point at 25 degrees C and 60% relative humidity?",
  "answer": "16.69 degrees C",
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      "label": "Improved Magnus form approximation of saturation vapor pressure",
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  "source": {
    "kind": "doi",
    "value": "Alduchov, O.A. and Eskridge, R.E. (1996). Improved Magnus form approximation of saturation vapor pressure. Journal of Applied Meteorology, 35(4), 601-609.",
    "retrieved_utc": "2026-09-30T19:54:00Z"
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  "method": {
    "name": "Dew point (Magnus formula)",
    "version": "1",
    "source_url_or_file": "methods/dew-point-magnus.cjs",
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  "method_deck": {
    "inputs": [
      {
        "name": "temp_c",
        "type": "number",
        "unit": "degrees C",
        "required": true,
        "description": "Air temperature."
      },
      {
        "name": "relative_humidity_percent",
        "type": "number",
        "unit": "%",
        "required": true,
        "description": "Relative humidity.",
        "min": 1,
        "max": 100
      }
    ],
    "outputs": [
      {
        "name": "dew_point_c",
        "unit": "degrees C",
        "description": "Dew point temperature."
      }
    ],
    "steps": [
      "Magnus formula with the Alduchov-Eskridge coefficients: alpha = ln(RH/100) + (b*T)/(c+T), where T is temperature in C, RH is relative humidity in percent, b=17.62, c=243.12.",
      "Dew point Td = (c * alpha) / (b - alpha), in degrees C.",
      "Round to 2 decimals.",
      "Valid roughly for T between -45 C and 60 C and RH between 1% and 100%."
    ],
    "constants": [
      {
        "name": "magnus_b",
        "value": 17.62,
        "unit": "dimensionless",
        "source": 0
      },
      {
        "name": "magnus_c",
        "value": 243.12,
        "unit": "degrees C",
        "source": 0
      }
    ],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "temp_c": 25,
          "relative_humidity_percent": 60
        },
        "expected": {
          "answer": "16.69 degrees C"
        },
        "check": "By hand: alpha = ln(0.6) + (17.62*25)/(243.12+25) = -0.51083 + 1.64299 = 1.13216; Td = (243.12*1.13216)/(17.62-1.13216) = 275.25/16.4878 = 16.69. Cross-checked against the common rule-of-thumb Td ~ T - (100-RH)/5 = 25 - 8 = 17, which is close."
      },
      {
        "name": "test vector: cooler and drier",
        "inputs": {
          "temp_c": 20,
          "relative_humidity_percent": 50
        },
        "expected": {
          "answer": "9.26 degrees C"
        },
        "check": "By hand: alpha = ln(0.5) + (17.62*20)/(243.12+20) = -0.69315 + 1.33933 = 0.64619; Td = (243.12*0.64619)/(17.62-0.64619) = 157.10/16.9738 = 9.26. Cross-checked against the rule-of-thumb Td ~ T - (100-RH)/5 = 20 - 10 = 10, which is close."
      }
    ],
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        "added_utc": "2026-09-30T22:39:30.722Z",
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