How to compute the Humidex index: Canadian thermal comfort index (Masterton-Richardson 1979, Environment Canada) combining ambient temperature T (°C) and water vapor pressure e (hPa) derived from relative humidity or dew point. Formula: Humidex = T + (5/9) * (e - 10), where e = 6.11 * exp(5417.7530 * (1/273.16 - 1/Tdp_K)) and Tdp_K is dew point temperature in Kelvin. Environment Canada thresholds: 20-29 comfortable, 30-39 mild discomfort, 40-44 great discomfort, 45-53 dangerous, >=54 imminent heat stroke. Different from US NWS Heat Index (Steadman 1979) and OSHA WBGT. Essential tool for heat alerts, OSHA NIOSH worker safety heat stress, sports, elderly, children, cardiac patients summer waves.

Humidex and thermal index formulas

Humidex (Masterton-Richardson 1979): H = T + (5/9) * (e - 10), where e (hPa) = 6.11 * exp(5417.753 * (1/273.16 - 1/(Tdp+273.15))). Example T=32°C, Tdp=24°C: e=29.8 hPa, H=32+(5/9)*(29.8-10)=32+11=43 (great discomfort). Developed by Atmospheric Environment Service Canada to quantify thermal perception on hot humid days.

RH to Tdp conversion: alpha = (17.27*T)/(237.7+T) + ln(RH/100), Tdp = 237.7*alpha/(17.27-alpha). Example T=30°C, RH=70%: alpha=2.062-0.357=1.705, Tdp=237.7*1.705/(17.27-1.705)=24°C. Dew point Tdp is temperature at which air becomes saturated (RH=100%).

NWS Heat Index (Steadman 1979/Rothfusz 1990): US NWS American formula for hot humid perception valid T>=26.7°C (80°F). Polynomial HI_F = -42.379 + 2.049*T + 10.143*RH + interaction terms. Example T=32°C(89.6°F), RH=75%: HI ≈ 110°F = 43.3°C. Difference from Humidex: HI uses shadow temp 1.8 m altitude, Humidex uses pure vapor pressure.

WBGT (Wet Bulb Globe Temperature) OSHA NIOSH: indoor 0.7*Tw + 0.3*Tg, outdoor with sun 0.7*Tw + 0.2*Tg + 0.1*Td. Tw=wet bulb (psychrometer), Tg=globe (black sphere, solar radiation), Td=dry bulb. OSHA NIOSH thresholds: 25-27°C caution, 27-29°C work-rest limit 75/25, 29-31°C 50/50, 31-33°C 25/75, >33°C stop activity. For military sports ACSM Guidelines.

UTCI (Universal Thermal Climate Index): ISB (International Society Biometeorology) 2009 complex formula integrating T, RH, wind, MRT (mean radiant temperature). Range: 38 extreme hot. Modern scientific standard for outdoor thermal comfort, used in EU heat wave epidemiology studies.

History and context

Humidex index was developed by J.M. Masterton and F.A. Richardson (1979) at Atmospheric Environment Service of Canadian Meteorological Service, derived from earlier Thom 1959 Discomfort Index formula. Published as "Humidex: a method of quantifying human discomfort due to excessive heat and humidity" CLI 1-79. Officially adopted by Environment Canada (now ECCC Environment and Climate Change Canada) as primary heat alert index Quebec, Ontario, Maritimes. American Heat Index by Robert Steadman (1979) "The Assessment of Sultriness Part I" J. Appl. Meteor., refined Lans P. Rothfusz NWS Fort Worth 1990 with computerized polynomial. WBGT (Wet Bulb Globe Temperature) developed 1956 US Marine Corps Parris Island for recruit heat stroke prevention. ISO 7243 international standard 1989 (rev 2017) WBGT workers. UTCI Universal Thermal Climate Index COST 730 Action 2009-2013 EU 24 country cooperation. US: NCEP NWS, NOAA Climate Prediction Center, NIOSH workplace heat. Global air conditioning industry > $200 billion/year (Daikin, Mitsubishi Electric, Carrier, Trane, Honeywell). USA: Carrier, Trane, Lennox, Goodman HVAC manufacturers.

Humidex categories and recommended actions table

• Humidex < 20: cooler than summer comfort, pleasant
• 20-24: comfortable, no risk
• 25-29: comfortable for most
• 30-34: mild discomfort, hydrate
• 35-39: evident discomfort, slow outdoor activity
• 40-44: great discomfort, avoid prolonged effort, shade
• 45-53: dangerous, OSHA NIOSH heat stress alert, vulnerable groups indoors
• 54+: imminent heat stroke, medical emergency 911
• Environment Canada Heat Warning: H >= 30 + Night T >= 18 (2 days)
• OSHA WBGT 27.8°C (82°F): action level outdoor workers USA
• NWS Heat Advisory: HI 105°F (41°C) for 2+ hours
• Marathon cancellation WBGT 28+: ACSM Guidelines, 2007 Chicago Marathon collapsed runners

Worked numerical examples

Example 1 - heat wave Phoenix AZ 38°C 60% RH. T=38, RH=60. alpha=(17.27*38)/(237.7+38)+ln(0.6)=2.378-0.511=1.867. Tdp=237.7*1.867/(17.27-1.867)=28.8°C. e=6.11*exp(5417.753*(1/273.16-1/302))=39.6 hPa. Humidex=38+(5/9)*(39.6-10)=38+16.4=54 IMMINENT HEAT STROKE. NWS Phoenix excessive heat warning. OSHA workplace stop work threshold. CDC Centers Disease Control US heat-related deaths.

Example 2 - dry tropical Riyadh 45°C 25% RH. T=45, RH=25. alpha=2.748-1.386=1.362. Tdp=20.4°C. e=24 hPa. Humidex=45+(5/9)*(24-10)=45+7.8=52.8 dangerous. Dry vs humid heat: identical T but Humidex 52.8 vs 60+ tropical humid. WBGT preferred for arid environments where evaporative cooling more effective.

Example 3 - moderate summer NYC 30°C 65% RH. T=30, RH=65. alpha=1.851-0.431=1.420. Tdp=22.8°C. e=27.7 hPa. Humidex=30+(5/9)*(27.7-10)=30+9.8=39.8 evident discomfort. Frequent breaks recommended, hydration. NWS NYC Heat Advisory threshold HI 100°F (37.8°C) 2+ hours typical July-August.

Example 4 - typical Toronto summer day 28°C 80% RH. T=28, RH=80. alpha=1.829-0.223=1.606. Tdp=24.1°C. e=29.9 hPa. Humidex=28+(5/9)*(29.9-10)=28+11=39 discomfort. Environment Canada doesn't issue warning under 30, only heat advisory. Compare NWS Heat Index US: HI = 31°C (88°F) caution zone. Systematic difference: Humidex generally higher 4-7 points than HI.

Example 5 - greenhouse agriculture USA. Tomato crop California, T=42°C inside greenhouse summer, RH=85%. alpha=(17.27*42)/(237.7+42)+ln(0.85)=2.591-0.163=2.428. Tdp=39.3°C. e=70.7 hPa. Humidex=42+(5/9)*(70.7-10)=42+33.7=75.7 (off-scale, extreme danger). Greenhouse workers severe risk, OSHA mandatory work-rest 25/75 cycle, ventilation, shading cooling pad. UFW United Farm Workers heat illness prevention training.

Limits and considerations

1. Humidex doesn't consider wind (cooling) and direct solar radiation (heating).
2. WBGT preferable for outdoor workers: includes global radiation + natural ventilation.
3. UTCI more scientifically accurate: integrates MRT mean radiant temperature, cloud cover, clothing.
4. NWS Heat Index (US) vs Humidex (Canada): average +4 point difference Humidex for RH>50%.
5. Danger thresholds not internationally uniform: 30 in Canada, 27 (Heat Index 80°F) in USA.
6. Dry arid heat (RH40°C): WBGT more relevant because includes dry bulb.
7. Individual acclimatization: 7-14 days cardiovascular adaptation reduces risk 50%.
8. Vulnerable groups: elderly >65, children <5, cardiac, hypertensive, nephropathic, psychiatric, dehydrated.
9. Drugs: anticholinergics, diuretics, beta-blockers reduce thermoregulation.
10. Extreme events: 2003 European heat wave (70,000 deaths), 2010 Russia (55,000), 2018 Japan (1,000).

Common errors

1. Confusing Humidex with NWS Heat Index (different formulas, different thresholds).
2. Substituting RH with dew point without converting (explicit formulas require Tdp).
3. Computing Humidex for T<20°C (formula derived for heat stress, irrelevant).
4. Ignoring wind and radiation (Humidex underestimates outdoor full-sun WBGT).
5. Applying Canadian thresholds without local cultural/climate adaptation.
6. Not considering acclimatization: European tourists in Florida August > native risk.
7. Neglecting patient drugs and comorbidities.
8. Underestimating pediatric/elderly risk (reduced thermoregulation).
9. Relying only on Humidex without WBGT cross-check for outdoor workers.
10. Ignoring nighttime hours: T_min >25°C riskier than high T_max daily under 35.

Practical applications

1. Heat alerts: NWS US, Environment Canada, Met Office UK heat waves.
2. Worker safety: OSHA NIOSH heat stress, ISO 7243 WBGT, NIOSH 2016 manual.
3. Sports medicine: ACSM Guidelines, marathon cancellation WBGT 28+, NCAA football.
4. Public health: CDC Heat-Related Deaths, NWS Excessive Heat Warning, Heat Health Watch.
5. Agriculture: California, Florida greenhouses, UFW heat illness prevention.
6. HVAC: Carrier, Trane, Lennox AC sizing, ASHRAE 55 thermal comfort.
7. Building energy: Energy Star, LEED green building, passive cooling design.
8. Transportation: NYC subway cooling stations, school bus AC requirements.
9. Climatology: NOAA climate change, IPCC heat wave projections decades.
10. Insurance: heat-related claims, parametric heat insurance products.

Support

Questions: info@calcoi.com. Educational tool for thermoregulation. For professional applications consult Masterton-Richardson 1979 CLI 1-79 Atmospheric Environment Service Canada, Environment Canada Humidex Heat Warning protocols, NWS Heat Index Steadman 1979/Rothfusz 1990, ISO 7243:2017 WBGT, UTCI Working Group COST 730 2009-13, CDC Heat & Health Tracker, OSHA NIOSH Heat Illness Prevention.

Updated July 2026