acalculator

What is the heat index?

Type the air temperature and the relative humidity. The heat index calculator shows how hot it feels, in °F and °C, with the National Weather Service caution level.

Your numbers

Units
Heat index (°F)
109.3

At 100 °F and 40% relative humidity, the heat index is 109.3 °F (42.9 °C).

Danger

  1. Below the caution level
  2. Caution
  3. Extreme caution
  4. Danger
  5. Extreme danger
Heat index (°C)
42.9
Formula used
Rothfusz regression

Heat index (°F): 109.3. At 100 °F and 40% relative humidity, the heat index is 109.3 °F (42.9 °C).

How to calculate

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.

Example with the default inputs (Air temperature 100 °F, Relative humidity 40%): At 100 °F and 40% relative humidity, the heat index is 109.3 °F (42.9 °C).

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 %).

  • 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%.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Air temperature 100 °F, Relative humidity 40% gives Heat index (°F) 109.255562, Heat index (°C) 42.919757, Formula used Rothfusz regression.Source: NWS Weather Prediction Center, The Heat Index Equation (Rothfusz 1990 regression)
  2. Air temperature 90 °F, Relative humidity 50% gives Heat index (°F) 94.596941, Heat index (°C) 34.776078, Formula used Rothfusz regression.Source: NWS Weather Prediction Center, The Heat Index Equation (Rothfusz 1990 regression)
  3. Air temperature 75 °F, Relative humidity 50% gives Heat index (°F) 74.55, Heat index (°C) 23.638889, Formula used Steadman simple formula.
  4. Air temperature 100 °F, Relative humidity 10% gives Heat index (°F) 94.122483, Formula used Rothfusz regression, less the low-humidity adjustment.
  5. Air temperature 85 °F, Relative humidity 90% gives Heat index (°F) 101.780804, Formula used Rothfusz regression, plus the high-humidity adjustment.
  6. Air temperature 89.6 °F, Relative humidity 70% gives Heat index (°F) 104.736693, Heat index (°C) 40.409274.Source: NIST SP 811 (2008), 4.2.1.1: °F = 1.8 × °C + 32

How it works

T is the air temperature in °F and RH the relative humidity in percent. The steps are the NWS algorithm:

  1. Simple formula (Steadman): HI = 0.5 × (T + 61.0 + (T − 68.0) × 1.2 + RH × 0.094).
  2. If (HI + T) ÷ 2 is below 80 °F, the heat index is the simple formula's HI.
  3. Otherwise, the Rothfusz regression: HI = −42.379 + 2.04901523 T + 10.14333127 RH − 0.22475541 T RH − 0.00683783 T² − 0.05481717 RH² + 0.00122874 T² RH + 0.00085282 T RH² − 0.00000199 T² RH².
  4. Dry air: if RH < 13% and 80 °F ≤ T ≤ 112 °F, subtract ((13 − RH) ÷ 4) × √((17 − |T − 95|) ÷ 17).
  5. Humid air: if RH > 85% and 80 °F ≤ T ≤ 87 °F, add ((RH − 85) ÷ 10) × ((87 − T) ÷ 5).

The page also names the formula it used: "Steadman simple formula", "Rothfusz regression", "Rothfusz regression, less the low-humidity adjustment" or "Rothfusz regression, plus the high-humidity adjustment". The heat index in °C is (HI − 32) × 5 ÷ 9. A temperature typed in °C is converted exactly first: °F = °C × 9 ÷ 5 + 32.

NWS levels (°F): below 80, below the caution level; 80 up to 90, caution; 90 up to 103, extreme caution; 103 up to 125, danger; 125 and above, extreme danger. A value on a boundary takes the higher level.

Exact arithmetic. The temperature and humidity are read as the exact decimals typed (the page stores the temperature in kelvin and reads it back as the decimal with the fewest significant digits, in °F, °C or K, that gives the same stored number; on a tie, the unit listed first in the box's unit menu wins). Every step except the square root in step 4 is then exact. Rounding: both heat indexes show with 1 decimal, rounded half up from the exact value (74.55 °F shows as 74.6), with a trailing zero left off.

Assumptions

  • Shade and light wind; full sun can add up to 15 °F.
  • The NWS formulas as published; the regression fits Steadman’s tables and is not meant for extreme conditions.
  • 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); humidity from 0% to 100%.

Worked examples by hand

100 °F at 40%. Simple: 0.5 × (100 + 61 + 38.4 + 3.76) = 101.58; the average with 100 is 100.79, so the regression applies: −42.379 + 204.9015 + 405.7333 − 899.0216 − 68.3783 − 87.7075 + 491.496 + 136.4512 − 31.84 = 109.3 °F (42.9 °C), danger. The NWS chart shows 109 °F.

90 °F at 50%. Simple: 0.5 × (90 + 61 + 26.4 + 4.7) = 91.05; the average with 90 is 90.5, so the regression applies. −42.379 + 184.4114 + 507.1666 − 1011.3993 − 55.3864 − 137.0429 + 497.6397 + 191.8845 − 40.2975 = 94.6 °F (34.8 °C), extreme caution. The NWS chart shows 95 °F.

75 °F at 50%. Simple: 0.5 × (75 + 61 + 8.4 + 4.7) = 74.55 °F, shown as 74.6 °F (23.6 °C). The average with 75 is 74.8, below 80, so this is the answer.

100 °F at 10%. The regression gives 94.7526; the dry-air adjustment is (3 ÷ 4) × √(12 ÷ 17) = 0.6301, so the heat index is 94.1 °F.

85 °F at 90%. The regression gives 101.5808; the humid-air adjustment is (5 ÷ 10) × (2 ÷ 5) = 0.2, so 101.8 °F. The NWS chart shows 102 °F.

32 °C at 70%. 32 °C = 89.6 °F; the regression gives 104.7 °F (40.4 °C), danger.

Other questions people ask

What is the heat index?

The heat index is how hot the air feels when humidity is added to the temperature. Sweat evaporates more slowly in humid air, so the body cools less and it feels hotter. At 90 °F and 50% humidity the heat index is about 95 °F.

How is the heat index calculated?

The US National Weather Service first uses Steadman’s simple formula, 0.5 × (T + 61 + (T − 68) × 1.2 + RH × 0.094). If that result averaged with the temperature is 80 °F or more, it uses the Rothfusz regression instead, a formula in T and RH with nine terms, and adjusts it for very dry or very humid air. The steps are under How it works.

What heat index is dangerous?

The NWS uses four levels: caution from 80 to 90 °F (fatigue with long exposure), extreme caution from 90 to 103 °F (heat cramps and heat exhaustion possible), danger from 103 to 125 °F (heat exhaustion likely, heat stroke possible), and extreme danger at 125 °F and above (heat stroke highly likely).

Does sun change the heat index?

Yes. The heat index is for shade and light wind. The NWS notes that full sunshine can raise it by up to 15 °F. Strong hot winds can also make it feel worse.

Can the heat index be lower than the temperature?

Yes, in dry air. At 100 °F and 10% humidity the heat index is about 94.1 °F, because sweat evaporates quickly. On a mild day the simple formula can also give a little less than the air temperature.

Why is there no heat index for cold air?

The heat index was built for warm weather. The calculator takes temperatures from 40 °F to 130 °F; for cold air, the wind chill is the measure of how cold it feels.