{
  "id": "heat-index",
  "version": "c759a4a2a53c",
  "status": "published",
  "name": "Heat Index Calculator",
  "question": "What is the heat index?",
  "summary": "Computes the heat index (how hot it feels) from the air temperature and relative humidity with the US National Weather Service algorithm, in °F and °C, with the NWS caution level.",
  "category": "physics",
  "subcategory": "weather",
  "url": "https://www.acalculator.org/physics/heat-index-calculator",
  "markdown": "https://www.acalculator.org/physics/heat-index-calculator.md",
  "kind": "function",
  "method": "HI = 0.5 × (T + 61 + (T − 68) × 1.2 + RH × 0.094); if (HI + T) ÷ 2 ≥ 80 °F, HI = −42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²·RH + 0.00085282T·RH² − 0.00000199T²·RH², with the NWS adjustments (T in °F, RH in %).",
  "assumptions": [
    "The temperature is measured in the shade; full sun can add up to 15 °F to the heat index (NWS).",
    "The formulas are the NWS algorithm; the regression was fitted to Steadman’s apparent temperature tables and is not meant for extreme temperatures or humidity.",
    "Temperatures from 40 °F to 130 °F (4.44… °C to 54.44… °C: the box takes 4.45 °C but not 4.4 °C) and humidity from 0% to 100%."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "t": {
        "title": "Air temperature",
        "description": "The air temperature in the shade.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 277.5944444444445,
        "maximum": 327.5944444444445
      },
      "rh": {
        "title": "Relative humidity",
        "description": "The relative humidity, in percent.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 100
      }
    }
  },
  "outputs": {
    "heatIndexF": {
      "label": "Heat index (°F)",
      "description": "How hot it feels, in °F, by the NWS algorithm.",
      "format": "number"
    },
    "heatIndexC": {
      "label": "Heat index (°C)",
      "description": "The same heat index in °C: (°F − 32) × 5 ÷ 9.",
      "format": "number"
    },
    "formula": {
      "label": "Formula used",
      "description": "Steadman’s simple formula, or the Rothfusz regression with any NWS adjustment.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "t": 310.9277777777778,
      "rh": 40
    },
    "outputs": {
      "heatIndexF": 109.2555618,
      "heatIndexC": 42.91975655555556,
      "formula": "Rothfusz regression"
    },
    "text": "At 100 °F and 40% relative humidity, the heat index is 109.3 °F (42.9 °C)."
  },
  "examples": [
    {
      "given": {
        "t": 310.9277777777778,
        "rh": 40
      },
      "expect": {
        "heatIndexF": 109.2555618,
        "heatIndexC": 42.91975655555556,
        "formula": "Rothfusz regression"
      },
      "source": "NWS Weather Prediction Center, The Heat Index Equation (Rothfusz 1990 regression); NWS heat index chart: 109 °F at 100 °F and 40%; hand calculation in content.mdx"
    },
    {
      "given": {
        "t": 305.37222222222226,
        "rh": 50
      },
      "expect": {
        "heatIndexF": 94.5969412,
        "heatIndexC": 34.776078444444444,
        "formula": "Rothfusz regression"
      },
      "source": "NWS Weather Prediction Center, The Heat Index Equation (Rothfusz 1990 regression); NWS heat index chart: 95 °F at 90 °F and 50%; hand calculation in content.mdx"
    },
    {
      "given": {
        "t": 297.03888888888895,
        "rh": 50
      },
      "expect": {
        "heatIndexF": 74.55,
        "heatIndexC": 23.63888888888889,
        "formula": "Steadman simple formula"
      },
      "source": "NWS Weather Prediction Center, The Heat Index Equation: 0.5 × (75 + 61 + 7 × 1.2 + 50 × 0.094) = 74.55; the average with 75 °F is below 80"
    },
    {
      "given": {
        "t": 310.9277777777778,
        "rh": 10
      },
      "expect": {
        "heatIndexF": 94.1224826621874,
        "formula": "Rothfusz regression, less the low-humidity adjustment"
      },
      "source": "NWS Weather Prediction Center, The Heat Index Equation: subtract ((13 − RH) ÷ 4) × √((17 − |T − 95|) ÷ 17) when RH < 13% and 80 ≤ T ≤ 112 °F; hand calculation in content.mdx"
    },
    {
      "given": {
        "t": 302.5944444444445,
        "rh": 90
      },
      "expect": {
        "heatIndexF": 101.7808036,
        "formula": "Rothfusz regression, plus the high-humidity adjustment"
      },
      "source": "NWS Weather Prediction Center, The Heat Index Equation: add ((RH − 85) ÷ 10) × ((87 − T) ÷ 5) when RH > 85% and 80 ≤ T ≤ 87 °F; NWS heat index chart: 102 °F"
    },
    {
      "given": {
        "t": 305.15,
        "rh": 70
      },
      "expect": {
        "heatIndexF": 104.7366926232,
        "heatIndexC": 40.409273679555554
      },
      "source": "NIST SP 811 (2008), 4.2.1.1: °F = 1.8 × °C + 32; NWS Weather Prediction Center, The Heat Index Equation; hand calculation in content.mdx"
    }
  ],
  "sources": [
    "National Weather Service, Weather Prediction Center, The Heat Index Equation (Rothfusz regression and adjustments). https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml",
    "Rothfusz, L. P. (1990). The Heat Index “Equation” (or, More Than You Ever Wanted to Know About Heat Index). NWS Southern Region Technical Attachment SR 90-23.",
    "Steadman, R. G. (1979). The Assessment of Sultriness. Part I: A Temperature-Humidity Index Based on Human Physiology and Clothing Science. Journal of Applied Meteorology 18(7), 861–873. https://doi.org/10.1175/1520-0450(1979)018<0861:TAOSPI>2.0.CO;2",
    "National Weather Service, What is the heat index? (heat index chart, caution levels, and up to 15 °F more in full sun). https://www.weather.gov/ama/heatindex"
  ],
  "related": [
    "wind-chill",
    "dew-point"
  ],
  "changelog": [
    {
      "date": "2026-09-30",
      "note": "Metric heads the result with the heat index in °C and names °C first."
    }
  ]
}