Heat Index Calculator

How to use this tool

Type the air temperature, pick °F or °C, then give the moisture as relative humidity or as a dew point in the same unit. The dark band shows the National Weather Service heat index in both units with its category; the cards give the figure you did not enter, the full sun allowance and the humidex; the working box lists every step of the NWS procedure. The chart redraws for your temperature, and the NWS chart below it outlines your cell.

Humidity is the input people most often get wrong. Relative humidity falls as the day warms even when the moisture in the air does not: air with a 70 °F dew point reads 90% at dawn at 73 °F and 47% at 93 °F that afternoon. Pair the humidity with the temperature from the same hour, or enter the dew point, which stays put. A dew point is not a humidity either: a 75 °F dew point at 95 °F is 53% humidity, not 75%.

What the calculation is doing

The NWS starts with the simple formula HI = 0.5 × (T + 61 + 1.2 × (T − 68) + 0.094 × RH), T in °F and RH in percent: the average of the air temperature and a crude linear estimate. Below 80 °F that is the answer, so on a mild day the heat index barely leaves the thermometer. At 80 °F or more the Rothfusz regression takes over: 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. It is a curve fit to Steadman's 1979 apparent temperature tables with an error Rothfusz put at ±1.3 °F.

Two corrections follow. Below 13% humidity at 80 to 112 °F the NWS subtracts ((13 − RH) ÷ 4) × √((17 − |T − 95|) ÷ 17), because the regression overstates very dry heat. Above 85% humidity at 80 to 87 °F it adds ((RH − 85) ÷ 10) × ((87 − T) ÷ 5). The result is rounded to a whole degree, as on the NWS chart, and the category follows: Caution 80 to 89, Extreme Caution 90 to 102, Danger 103 to 124, Extreme Danger 125 and above. The NWS prints those ranges with shared end points (80 to 90, 90 to 103); a shared value goes to the higher category here.

Dew point and humidity are linked by the Magnus form from the NWS weather calculators: e_s = 6.11 × 10^{7.5T ÷ (237.3 + T)} hPa with T in °C, e = e_s × RH ÷ 100, and the dew point is the temperature whose saturation pressure equals e. The humidex follows Environment and Climate Change Canada: humidex = T + 0.5555 × (e − 10) with T in °C and e = 6.11 × exp(5417.753 × (1 ÷ 273.15 − 1 ÷ T_d)) from the dew point in kelvin.

What the heat index measures, and what it leaves out

The heat index is not a temperature anyone can measure. Steadman built it as an apparent temperature: the dry air temperature at which a reference person would lose heat at the same rate as in the actual humid air. That person is 5 ft 7 in and 147 lb, in long trousers and a short sleeved shirt, walking at 3.1 mph in shade with a 5 knot breeze. In direct sun the NWS says the heat index can run up to 15 °F higher, the figure that matters on a job site at noon, so the tool prints it beside every result. A stronger wind or lighter clothing pulls the felt temperature down, and neither is in the equation.

The humidex describes the same discomfort on a different scale, as the diagram shows at 32 °C. Built from vapour pressure rather than fitted to a body model, it climbs almost in a straight line with humidity while the heat index curves upward, so through the middle of the range it reads higher: 41 against 36 °C at 55% and 47 against 42 °C at 75%, meeting only near saturation at about 54. Environment and Climate Change Canada calls 40 to 45 great discomfort and above 45 dangerous, lower on the number line than the NWS Danger line of 103 °F (39.4 °C). Use each scale with its own categories and the two agree on the advice far more often than the raw numbers suggest.

Heat index in Celsius at common conditions

The same equation worked in Celsius, rounded to a whole degree. Off chart marks cells past 137 °F (58 °C), the top of the printed NWS chart, where the NWS says the regression is not reliable. In the cooler rows at 30% the heat index sits a degree below the air temperature, which is real: dry air lets sweat work.

A worked example you can check on paper

Take the tool default, 90 °F at 70% relative humidity. Simple formula first: 0.5 × (90 + 61 + 1.2 × (90 − 68) + 0.094 × 70) = 0.5 × (90 + 61 + 26.4 + 6.58) = 91.99 °F. That is 80 or more, so the regression applies. Term by term, with T = 90 and RH = 70: −42.379 + 184.411 + 710.033 − 1,415.959 − 55.386 − 268.604 + 696.696 + 376.094 − 78.983 = 105.922 °F. Humidity is between 13% and 85%, so neither correction applies: the heat index is 105.92 °F, reported as 106 °F, or (105.92 − 32) × 5 ÷ 9 = 41.07 °C, reported as 41 °C: Danger on the NWS scale.

For the dew point, convert the air temperature: (90 − 32) × 5 ÷ 9 = 32.22 °C. Then e_s = 6.11 × 10^{7.5 × 32.22 ÷ (237.3 + 32.22)} = 48.16 hPa, e = 48.16 × 0.70 = 33.71 hPa, log₁₀(33.71 ÷ 6.11) = 0.7417, and the dew point is 237.3 × 0.7417 ÷ (7.5 − 0.7417) = 26.04 °C, or 78.9 °F. For the humidex, e = 6.11 × exp(5417.753 × (1 ÷ 273.15 − 1 ÷ 299.19)) = 34.35 hPa, and humidex = 32.22 + 0.5555 × (34.35 − 10) = 45.7. Each figure appears in the tool's working box.

Mistakes that catch people out

Typing the dew point into the humidity box. A 75 °F dew point at 95 °F is 53% humidity and a heat index of 107 °F. Read as 75% humidity it becomes 128 °F. Switch the humidity setting to dew point instead.

Forgetting the sun. The heat index is a shade figure. In full sun the NWS allows up to 15 °F more, so the 106 °F of the default example is 121 °F for someone working in the open.

Trusting the last degree. The regression has an error of ±1.3 °F against Steadman's tables, and the tables describe one reference person. A reading of 102 against a Danger line of 103 is not a safe margin; it is the same conditions within the method's precision.

Pushing the equation past its chart. Above 112 °F, or wherever the result passes 137 °F, the NWS says the regression can give meaningless values. The tool still computes them and says so in the note; read them as extreme rather than precise. Below 80 °F the regression is not used and no category applies.

Popular calculations

Each address opens the calculator with those figures filled in.

Fahrenheit readings with relative humidity

Celsius readings

From the dew point

Dry heat, saturated air and the edge of the scale

How this was checked

The engine was compared with the 135 cells of the printed NWS heat index chart, from the NWS Heat Safety one pager and confirmed cell for cell against the Wikipedia transcription. The procedure on the Weather Prediction Center equation page reproduces 125 cells exactly. Eight cells at 80 to 86 °F with 90% humidity or more come out 1 to 2 °F higher because the chart was drawn before the NWS added the high humidity adjustment, and 90 °F at 45% and 70% are rounding differences of 0.51 and 0.92 °F. Wikipedia's worked example, 96 °F at 65% giving 121 °F, comes out at 121.03, and 100 °F at 50% gives 118.32, the printed 118. The regression was recomputed as a nested polynomial in humidity and from the published Celsius coefficient fit; both agree with the engine to better than 0.001 °F at 6,565 points across 80 to 112 °F and 0 to 100% humidity.

The dew point conversion was checked by round trip, humidity to dew point and back, at 6,100 combinations, returning the input to within a millionth of a percentage point, and against the Alduchov and Eskridge form of the Magnus equation, which differs by at most 0.17 °C between 0 and 45 °C. The humidex reproduces the Environment and Climate Change Canada definition and the published examples of 34 for 30 °C with a 15 °C dew point and 42 with a 25 °C dew point. The category boundaries were tested either side of 80, 90, 103 and 125 °F, and every address above was opened and checked for a distinct title, the right answer and clean CSV, image and print output at desktop, tablet and phone widths.

Common questions

What is the heat index?

The National Weather Service measure of how hot it feels when humidity is combined with the air temperature, from Steadman's apparent temperature model as fitted by Rothfusz in 1990. At 90 °F and 70% humidity it is 106 °F (41 °C): the air feels like 106 °F would in dry conditions.

How is the heat index calculated?

The NWS computes the simple formula 0.5 × (T + 61 + 1.2 × (T − 68) + 0.094 × RH) first, T in °F, and below 80 °F that is the answer. At 80 °F or more it uses the nine term Rothfusz regression, corrected below 13% humidity (80 to 112 °F) or above 85% (80 to 87 °F), then rounds to a whole degree.

Why does this calculator give 106 °F for 90 °F and 70% when the NWS chart says 105?

The regression gives 105.92 °F, which rounds to 106. The printed chart shows 105, one of only two cells that round the other way, and the gap is well inside the ±1.3 °F error of the regression. Both are Danger, and the tool stars the cell with the printed value.

Is the heat index for sun or shade?

Shade, with a light wind of about 5 knots, because that is how Steadman defined the scale. The NWS says full sunshine can raise the heat index by up to 15 °F, so a shade value of 106 °F can feel like 121 °F in the open at midday.

What heat index is dangerous?

The NWS calls 80 to 90 °F Caution, where fatigue is possible with prolonged exposure or activity; 90 to 103 °F Extreme Caution, where heat cramps, exhaustion and heat stroke become possible; 103 to 124 °F Danger, where cramps or exhaustion are likely and heat stroke possible; and 125 °F or higher Extreme Danger, where heat stroke is highly likely. All of it assumes shade.

What is the difference between the heat index and the humidex?

Both describe the same discomfort on different scales. The humidex is the air temperature in °C plus 0.5555 × (vapour pressure − 10) from the dew point, with no units. Through the middle of the humidity range it reads higher: at 32 °C and 75% the heat index is 42 °C and the humidex 47. Read each against its own scale.

Related Calculators and Reference

• Humidex Calculator: the Canadian scale with its own comfort ranges.
• Wind Chill Calculator: the cold weather counterpart, from temperature and wind speed.
• Temperature Converter: for readings that arrive in the wrong unit.
• Water Intake Calculator: how much to drink when the heat index climbs.
• Dew Point Calculator: dew point, humidity and vapour pressure in more detail.
• Density Altitude Calculator: hot, humid air and aircraft performance.
• NWS Weather Prediction Center, The Heat Index Equation: the regression and both adjustments as published.