Heat index vs humidex for the same air

At 32 °C (89.6 °F) and 60 percent humidity, the NWS heat index is 37.1 °C (98.7 °F) and Environment Canada’s humidex is 42.5, 5.4 higher for the same air. At that humidity the humidex stays higher until about 38.1 °C. The heat index passes it there, but from 35.1 °C up the NWS formula is extrapolating past Steadman’s table.

Line chart of the NWS heat index and Environment Canada’s humidex against air temperature from 26 to 42 °C, with the relative humidity held at 60 percent. The humidex, a dashed line with squares, rises from 31.7 to 64.6. The heat index, a solid line with circles, rises from 26.9 to 71.2 °C and passes the humidex near 38.1 °C. A dotted line with diamonds marks the air temperature itself. Hatching from 35.1 °C marks air past the edge of Steadman’s table, where the NWS formula extrapolates. — The NWS heat index and Environment Canada’s humidex at 60 percent humidity; the dotted line is the air temperature itself. Every plotted point is a row of the table. Image © ScienceQuest, CC BY 4.0: free to reuse with credit and a link to this page, as the image licence explains.

Heat index and humidex at 60 percent humidity

The NWS heat index and Environment Canada’s humidex at 60 percent relative humidity, air from 26 to 42 °C, with each agency’s category. The chart plots its rows.
Air temperature	Heat index °C	Heat index °F	NWS category	Humidex	ECCC comfort	Difference
26 °C (78.8 °F)	26.9	80.5	Caution	31.7	Some discomfort	+4.8
28 °C (82.4 °F)	29.4	85.0	Caution	35.2	Some discomfort	+5.8
30 °C (86.0 °F)	32.8	91.1	Extreme Caution	38.8	Some discomfort	+6.0
32 °C (89.6 °F)	37.1	98.7	Extreme Caution	42.5	Great discomfort	+5.4
34 °C (93.2 °F)	42.2	107.9	Danger	46.5	Dangerous	+4.3
36 °C (96.8 °F)	48.1†	118.6†	Danger	50.7	Dangerous	+2.6
38 °C (100.4 °F)	55.0†	130.9†	Extreme Danger	55.0	Dangerous	0.0
40 °C (104.0 °F)	62.6†	144.8†	Extreme Danger	59.7	Dangerous	−2.9
42 °C (107.6 °F)	71.2†	160.1†	Extreme Danger	64.6	Dangerous	−6.6

Difference: the humidex minus the heat index in °C, between the printed values. Environment Canada works the humidex from the dew point. The dew points, from the humidity by Hyland and Wexler’s saturation pressure as the dew point calculator finds them, run from 17.6 °C at 26 °C to 32.6 °C at 42 °C. At 26 °C the simple formula gives 79.2 °F. The NWS calculator runs the regression above 79 °F, as this table does; by the equation page’s 80 °F the cell would read 79.2 °F (26.2 °C), with no category. Environment Canada adds “avoid exertion” to great discomfort and “possible heat stroke” to dangerous. † Past the edge of Steadman’s table, which at 60 percent is 35.1 °C: the NWS number is its regression extrapolated.

The same air at 40, 60 and 80 percent

Heat index (°C) and humidex at 40, 60 and 80 percent relative humidity, air from 26 to 40 °C
Air temperature	40 percent humidity		60 percent humidity		80 percent humidity
Air temperature	Heat index °C	Humidex	Heat index °C	Humidex	Heat index °C	Humidex
26 °C (78.8 °F)	25.7	27.9	26.9	31.7	27.7	35.6
28 °C (82.4 °F)	27.7	30.9	29.4	35.2	32.1	39.5
30 °C (86.0 °F)	29.7	33.9	32.8	38.8	37.7	43.7
32 °C (89.6 °F)	32.3	37.1	37.1	42.5	44.4†	48.0
34 °C (93.2 °F)	35.4	40.4	42.2	46.5	52.2†	52.7
36 °C (96.8 °F)	39.1	43.8	48.1†	50.7	61.2†	57.6
38 °C (100.4 °F)	43.4	47.4	55.0†	55.0	71.3†	62.8
40 °C (104.0 °F)	48.3	51.1	62.6†	59.7	82.5†	68.4

† Past the edge of Steadman’s table, which falls at 31.1 °C at 80 percent and 35.1 °C at 60 percent; at 40 percent it falls at 40.5 °C, beyond the last row. Environment Canada’s own Tables 2 and 3 print the same whole numbers in 19 of the 21 humidexes they share with this table; at 28 °C and 80 percent they print 39, against 39.5 here, and at 32 °C and 60 percent they print 42, against 42.5 here.

Where each agency’s warning starts

The air temperature at which the NWS heat index reaches Danger, 103 °F, and Environment Canada’s humidex enters great discomfort, 40, and dangerous, 46, at each humidity
Relative humidity	Air temperature where it starts			At the NWS line
Relative humidity	NWS Danger °C	Great discomfort °C	Dangerous °C	Humidex
30 percent	38.0	35.4	39.2	43.6
40 percent	36.1	33.5	37.0	44.1
50 percent	34.5	31.8	35.1	44.3
60 percent	33.0	30.4	33.5	44.4
70 percent	31.7	29.1	32.1	44.6
80 percent	30.6	28.0	30.9	44.9
90 percent	29.6†	27.0	29.7	45.3

NWS Danger starts at a heat index of 103 °F; Environment Canada’s great discomfort at a humidex of 40 and dangerous at 46. Environment Canada’s tables print the humidex as a whole number, so 39.5 counts as 40 and 45.5 as 46, as in the first table’s comfort column. The last column is the humidex of the air at the NWS line. † That line lies past the edge of Steadman’s table, so the 103 °F comes from the extrapolated regression.

Follow your local heat warning, which may use either index or another. This page compares two formulas and gives no safety advice.

Why the formulas disagree

The heat index starts from a model of one person. Rothfusz fitted the NWS regression to Steadman’s 1979 table of apparent temperatures, and that table assumes an adult 5 ft 7 in tall and 147 pounds, in long trousers and a short-sleeved shirt, walking at 3.1 mph in a 5 knot wind, in shade. Environment Canada’s humidex (Masterton and Richardson, 1979) has no body model: it adds 0.5555 to the air temperature for every hPa of vapour pressure above 10 hPa, the vapour pressure of air with a dew point of 7.0 °C.

At 60 percent and 26 °C the humidex reads 5.7 above the air and the heat index 0.9. From 34 to 42 °C the heat index climbs faster, from 42.2 to 71.2 °C, while the humidex goes from 46.5 to 64.6.

Most of that climb sits past 35.1 °C at 60 percent, where Steadman’s model gives no answer. Lu and Romps (2022) showed that it turns unphysical in air that hot and humid, and the NWS says its regression is not valid beyond the range of Steadman’s data. The NWS calculator prints a number there by extending the fit past its data, so the crossing near 38.1 °C comes from that extrapolation. Each agency warns on its own scale. At 60 percent the NWS reaches Danger, 103 °F, at 33.0 °C, where the humidex reads 44.4, great discomfort; Environment Canada’s dangerous band starts at 33.5 °C.

The formulas

NWS simple formula, used while it gives 79 °F or less [2]: $\mathrm{HI} = 0.5\,[\,T + 61.0 + 1.2\,(T - 68.0) + 0.094\,\mathrm{RH}\,]$
Rothfusz regression, when the simple formula gives more than 79 °F [3]: $\begin{aligned}\mathrm{HI} = {}& -42.379 + 2.04901523\,T + 10.14333127\,R - 0.22475541\,TR - 0.00683783\,T^2 \\ & - 0.05481717\,R^2 + 0.00122874\,T^2R + 0.00085282\,TR^2 - 0.00000199\,T^2R^2\end{aligned}$
Humidex [6]: $H = T + 0.5555\,(e - 10),$ $e = 6.11\,\exp\!\left[5417.7530\left(\frac{1}{273.15} - \frac{1}{T_d}\right)\right]$
Dew point from the relative humidity, Hyland and Wexler (1983) [9]: $p_{ws}(T_d) = \frac{\mathrm{RH}}{100}\,p_{ws}(T),\qquad \ln p_{ws}(\theta) = \frac{C_8}{\theta} + C_9 + C_{10}\theta + C_{11}\theta^2 + C_{12}\theta^3 + C_{13}\ln\theta$

θ is a temperature in kelvin and p ws a saturation pressure in Pa; C8 to C13 are Hyland and Wexler’s constants over liquid water, as ASHRAE Handbook Fundamentals (2017) gives them.

Where each formula holds

Each formula’s sample, the people it holds for, and where it does not apply
Formula	Fitted in	Holds for	Not for
NWS heat index (Rothfusz 1990, on Steadman 1979)	Steadman’s table, which ends at the edge of his model in hot, humid air (31.1 °C at 80 percent, Lu and Romps 2022), for one adult walking in shade in a 5 knot wind	A heat index of about 80 °F (26.7 °C) or more inside Steadman’s table, to ±1.3 °F	Full sunshine, which the NWS says can add up to 15 °F; air past Steadman’s edge, 35.1 °C at 60 percent, where the fit extrapolates
Humidex (Environment Canada)	A vapour pressure from the dew point, then 0.5555 per hPa above 10 hPa added to the air temperature	Air of 20 °C or more with a humidex at least 1 above it, the hours Environment Canada reports	Air below 20 °C; reading the number as °F, or against the NWS categories

Calculators and simulators

Sources

NOAA National Weather Service, Weather Prediction Center. The Heat Index Equation. https://www.wpc.ncep.noaa.gov/html/heatindex_equation.shtml
NOAA National Weather Service, Weather Prediction Center. Heat Index Calculator. https://www.wpc.ncep.noaa.gov/html/heatindex.shtml
Rothfusz LP. The heat index “equation” (or, more than you ever wanted to know about heat index). NWS Southern Region Technical Attachment SR 90-23, 1 July 1990. https://www.weather.gov/media/ffc/ta_htindx.PDF
Steadman RG. The assessment of sultriness. Part I: A temperature-humidity index based on human physiology and clothing science. J Appl Meteor 1979;18(7):861 to 873. doi:10.1175/1520-0450(1979)018<0861:TAOSPI>2.0.CO;2
NOAA National Weather Service, Amarillo. What is the heat index? https://www.weather.gov/ama/heatindex
Environment and Climate Change Canada. Climate glossary: Humidex. https://climate.weather.gc.ca/glossary_e.html
Government of Canada. How to use the Humidex. Table 1: Reference legend for Humidex range and degree of comfort; Tables 2 and 3: Humidex for relative humidity from 100% to 65% and from 60% to 20%. https://www.canada.ca/en/services/environment/weather/severeweather/humidex.html
Lu Y-C, Romps DM. Extending the heat index. J Appl Meteor Climatol 2022;61(10):1367 to 1383. doi:10.1175/JAMC-D-22-0021.1
Hyland, R. W., and A. Wexler (1983). Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K. ASHRAE Transactions 89(2A): 500 to 519. https://www.ashrae.org/technical-resources/ashrae-transactions