Heat Index Calculator
Free heat index calculator (NWS Rothfusz 1990). Enter temperature and humidity for apparent temperature in °F and °C with a danger rating.
Heat Index Calculator
Background.
This heat index calculator uses the US National Weather Service Rothfusz 1990 regression to turn any pair of air temperature and relative humidity into the apparent temperature — the number meteorologists call the 'feels like' temperature, and the same number the NWS uses to decide when to issue a Heat Advisory (HI 100–104 °F sustained) or an Excessive Heat Warning (HI 105 °F or higher sustained). Enter the temperature in either Fahrenheit or Celsius, enter the relative humidity from a thermometer-hygrometer or your phone's weather app, and the calculator returns the heat index in °F (the canonical NWS reporting scale), the same value in °C for international use, and a danger level from 0 (normal) through 4 (extreme danger).
The reason heat index is worth calculating, and the reason it deserves a calculator rather than a one-line formula, is that the human body cools itself almost entirely by evaporating sweat, and the rate of sweat evaporation depends mostly on how dry the surrounding air is, not on how hot it is. At 90 °F (32 °C) with 20% relative humidity, sweat evaporates so fast that the apparent temperature is essentially 87 °F (31 °C) — comfortable enough to garden or run errands. At the same 90 °F with 70% relative humidity, sweat barely evaporates at all, and the apparent temperature is around 105 °F (40.6 °C) — straight into the NWS 'danger' zone, where heat exhaustion is likely within an hour of moderate activity and heat stroke is a realistic possibility. The 15 °F gap between those two scenarios is invisible on the thermometer; only the heat index reveals it.
The polynomial we use was published by Lans Rothfusz at the NWS Southern Region Headquarters in 1990 as Technical Attachment SR 90-23. It is a multivariable regression fit to the original Steadman (1979) physiological model of human thermal balance — a model that explicitly built in core body temperature of 37 °C, skin temperature of 35 °C, normal indoor clothing thermal resistance, a 4 km/h walking pace, and standard sweating efficiency assumptions, then solved an iterative balance of conductive, convective, evaporative, and radiative heat loss. Rothfusz's regression captures the Steadman model to within about ±1.3 °F across the temperature range 80–110 °F and relative humidity range 40–100% without requiring iteration, which is why it became the operational standard at every NWS forecast office in the United States and the formula behind every TV weather graphic, smartphone weather app, and OSHA heat-safety guideline that quotes a 'feels like' temperature.
The Rothfusz polynomial is augmented by two adjustment terms, also from NWS: a low-humidity adjustment that pulls the heat index down when relative humidity is below 13% (desert air, very low dew point), and a high-humidity adjustment that pushes it up when humidity exceeds 85% in the 80–87 °F range (the muggy summer-evening range where evaporation is already so impaired that small changes in humidity have outsized effects). Below 80 °F the Rothfusz polynomial is not used; instead the NWS applies a simpler Steadman-derived form HI = 0.5 × (T + 61 + (T − 68) × 1.2 + R × 0.094) and only re-applies the full polynomial if that simple result clears the 80 °F threshold.
Why does this matter for you, the user? Three reasons. First, the heat index is the variable that should drive your behavioural decisions on hot days: when to push a workout indoors, when to keep children and elderly relatives out of the sun, when to delay roofing or paving work, when to start drinking water before you feel thirsty. The dry-bulb thermometer cannot answer those questions; it does not know how much you sweat. Second, heat index is the variable used in occupational safety standards — the US OSHA Technical Manual, the US Army Wet Bulb Globe Temperature flag system, and most US state heat-illness prevention regulations cite the NWS heat index thresholds directly. Third, the heat index puts a quantitative number on the climate-change conversation. Mean dew points across the Gulf of Mexico and the Indian subcontinent are rising about 0.5 °C per decade; the Sherwood and Huber (2010) PNAS paper used this calculator's underlying physics to identify a wet-bulb 35 °C limit beyond which the unacclimatised human body cannot dissipate metabolic heat at all, and showed that this limit is now plausibly reachable in the warmest decades of the century.
The rest of this page walks through the Rothfusz polynomial in full, the low-humidity and high-humidity adjustments, the simple-formula sub-80 °F path, the four NWS danger thresholds with concrete symptom descriptions, why the heat index differs from the wet-bulb temperature, and worked examples at 90 °F / 70% RH (HI ≈ 105 °F, danger) and 95 °F / 70% RH (HI ≈ 124 °F, on the danger / extreme-danger border).
What is heat index calculator?
The heat index, also called the apparent temperature or 'feels like' temperature, is the equivalent dry-bulb temperature at 20% relative humidity that would produce the same physiological heat stress on a moderately-clothed adult walking in the shade as the actual temperature and humidity do. It is a single number that combines two variables — air temperature and relative humidity — into the operational quantity that actually predicts heat-illness risk. The concept was formalised by Robert Steadman in his 1979 Journal of Applied Meteorology paper 'The Assessment of Sultriness, Part I', which built a multi-equation thermal balance model of a 1.7 m, 67 kg adult at 37 °C core temperature, with normal indoor clothing resistance and a 4 km/h walking pace, and solved for the apparent temperature implicitly. Lans Rothfusz at the NWS Southern Region published a multivariable regression of Steadman's iterative model in 1990 (Technical Attachment SR 90-23) — the closed-form polynomial this calculator uses — so forecasters could compute heat index in real time without iteration. The NWS classifies heat index into four bands above the 80 °F threshold: 80–89 °F is 'caution' (fatigue possible with prolonged exposure and physical activity); 90–102 °F is 'extreme caution' (heat cramps, heat exhaustion, and sunstroke possible); 103–124 °F is 'danger' (heat cramps and heat exhaustion likely, heat stroke probable with continued exposure); 125 °F and above is 'extreme danger' (heat stroke imminent). These thresholds drive NWS heat advisory products: a Heat Advisory is typically issued when daytime heat index is forecast to reach 100–104 °F for two or more consecutive days, and an Excessive Heat Warning when it is forecast to reach 105 °F or higher. Heat index assumes shade and light wind; in full sun, NWS guidance is to add up to 15 °F (about 8 °C) to the calculated value. Heat index is not the same as wet-bulb temperature, wet-bulb globe temperature (WBGT), or humidex (the Canadian analogue); each makes different assumptions about clothing, sun exposure, and metabolic rate, and they cannot be substituted for each other without a careful conversion.
How to use this calculator.
- Enter the current air temperature into the first field. Use a shaded thermometer reading, your car or thermostat display, or the temperature listed in your local forecast — do not use the 'feels like' or heat-index value; that would be circular.
- Select whether you entered Fahrenheit or Celsius. Celsius inputs are converted internally to Fahrenheit (using Tf = Tc × 9/5 + 32) before the Rothfusz polynomial runs, because the regression coefficients are defined in °F. The °C output is then back-converted from the °F result.
- Enter the relative humidity from 1 to 100. Most consumer hygrometers and phone weather apps report this directly. If you only have dew point, look up the corresponding RH with a Magnus-Tetens calculator first.
- Read the heat index in °F (the primary output, matching NWS reporting convention) and the same value in °C below it. The danger level output translates the °F value onto the four NWS bands: 0 normal (< 80 °F), 1 caution (80–89), 2 extreme caution (90–102), 3 danger (103–124), 4 extreme danger (≥ 125).
- If you are planning outdoor activity in full sun, add up to 15 °F (8 °C) to the calculated heat index per NWS guidance. The Rothfusz regression assumes shade; direct sun substantially increases the apparent temperature and the heat-illness risk.
- Cross-check the result against your local NWS forecast or weather app. If the calculator returns 105 °F or higher and the local forecast is silent, double-check your inputs (temperature unit, humidity reading) — at that danger level an active heat advisory is normally already in effect.
The formula.
The NWS heat index is computed in three branches depending on the dry-bulb temperature T (in °F) and the relative humidity R (in %, 1–100).
--- Branch 1: T ≥ 80 °F — full Rothfusz polynomial ---
HI = −42.379 + 2.04901523 · T + 10.14333127 · R − 0.22475541 · T · R − 0.00683783 · T² − 0.05481717 · R² + 0.00122874 · T² · R + 0.00085282 · T · R² − 0.00000199 · T² · R²
This is the multivariable regression Lans Rothfusz published in NWS Technical Attachment SR 90-23 (1990). It is a least-squares fit to the Steadman (1979) iterative thermal-balance model, with residual error of about ±1.3 °F across 80 ≤ T ≤ 110 °F and 40 ≤ R ≤ 100%.
--- Adjustment A: low-humidity correction ---
If R < 13% and 80 ≤ T ≤ 112 °F: HI −= ((13 − R) / 4) · √((17 − |T − 95|) / 17)
This pulls the heat index down in very dry conditions (desert air), where sweat evaporation is extremely efficient and the Rothfusz regression mildly over-predicts apparent temperature. The triangular weight peaks at T = 95 °F and falls to zero at T = 78 °F and T = 112 °F.
--- Adjustment B: high-humidity correction ---
If R > 85% and 80 ≤ T ≤ 87 °F: HI += ((R − 85) / 10) · ((87 − T) / 5)
This pushes the heat index up in the muggy late-evening range (80–87 °F with very high humidity), where the Rothfusz regression mildly under-predicts because sweat evaporation is already so impaired that small humidity increases have outsized effects on perceived temperature.
--- Branch 2: T < 80 °F — simple Steadman form ---
HIsimple = 0.5 · (T + 61 + (T − 68) · 1.2 + R · 0.094)
If HIsimple < 80 °F: the heat index is reported as just T (no humidity effect; the air is cool enough that humidity is not a heat-stress factor).
If HIsimple ≥ 80 °F: the full Rothfusz polynomial (Branch 1, with both adjustments) is re-applied. This handles the transitional zone where the dry-bulb is below 80 °F but the simple humidity-aware result already clears the 80 °F threshold.
--- Conversion ---
If the user entered Celsius, the calculator first converts Tc → Tf = Tc × 9/5 + 32, runs the formula, then converts HIf → HIc = (HIf − 32) × 5/9 for the secondary output. All polynomial coefficients are anchored in °F because that is the unit Rothfusz fit them in; converting them to °C would introduce rounding error.
--- Danger level ---
The single-integer dangerLevel output applies the NWS published thresholds: 0 if HI < 80 °F, 1 if 80 ≤ HI < 90, 2 if 90 ≤ HI < 103, 3 if 103 ≤ HI < 125, 4 if HI ≥ 125.
A worked example.
A textbook muggy-summer-afternoon example: the dry-bulb thermometer reads 90 °F (32.2 °C) and the relative humidity is 70% — typical for a July afternoon in Houston, Memphis, or Tampa. Enter temperature = 90, temperatureUnit = F, humidityPercent = 70. The calculator plugs T = 90 and R = 70 into the Rothfusz polynomial: HI = −42.379 + 2.04901523 × 90 + 10.14333127 × 70 − 0.22475541 × 90 × 70 − 0.00683783 × 90² − 0.05481717 × 70² + 0.00122874 × 90² × 70 + 0.00085282 × 90 × 70² − 0.00000199 × 90² × 70². Working term by term: −42.379 + 184.411 + 710.033 − 1,415.959 − 55.386 − 268.604 + 696.654 + 376.072 − 87.689 ≈ 106.0 °F (the precise computed value is about 105 °F after all coefficients accumulate at full precision). Neither adjustment applies (R = 70 is not below 13 nor above 85), so the final heat index is about 105 °F. Converting to Celsius: (105 − 32) × 5/9 ≈ 40.6 °C. That falls into the NWS 'danger' band (103–124 °F), so the danger level output is 3. Interpreting these numbers: even though the thermometer reads only 90 °F, the combination with 70% humidity produces an apparent temperature 15 °F higher because sweat evaporation is sharply impaired. At this danger level, heat exhaustion is likely within an hour of moderate outdoor activity, heat cramps are probable, and heat stroke is possible — especially for children, the elderly, anyone on diuretics, and outdoor workers. NWS guidance would normally trigger a Heat Advisory at this combination if it persisted for two days. If the same 90 °F day had been only 30% RH (a Phoenix afternoon rather than a Houston afternoon), the heat index would drop to about 87 °F — just barely in the 'caution' band. And if the temperature climbed to 95 °F at the same 70% RH, the heat index jumps to about 124 °F — right at the danger / extreme-danger border, with heat stroke probable within 30 minutes of activity. The non-linear sensitivity is why a 5 °F jump in actual temperature, on a muggy day, can take the apparent temperature from 105 °F to 124 °F.
Frequently asked questions.
What is the difference between heat index and wet-bulb temperature?
Why does the heat index calculator switch formulas below 80 °F?
What are the warning signs of heat exhaustion and heat stroke?
Why are children and the elderly at higher heat-index risk than healthy adults?
Is it safe to exercise when the heat index is above 90 °F?
What does the heat index assume about sun exposure and wind?
What was the highest heat index ever measured?
How does heat index relate to OSHA workplace safety rules?
Does indoor heat index matter?
Is the heat index different in metric (Celsius) units?
References& sources.
- [1]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. The original NWS publication of the multivariable regression polynomial and the low-humidity / high-humidity adjustment terms this calculator implements.
- [2]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. The peer-reviewed thermal-balance model — core temperature 37 °C, skin 35 °C, clothing resistance, 4 km/h walking pace, sweating efficiency — that Rothfusz's regression approximates.
- [3]NOAA National Weather Service. Heat Forecast Tools and Heat Index Chart. NWS Climate Prediction Center / Weather Prediction Center. The authoritative reference for the four NWS heat index danger bands (caution / extreme caution / danger / extreme danger) and the Heat Advisory / Excessive Heat Warning issuance thresholds.
- [4]Centers for Disease Control and Prevention. About Extreme Heat — Warning Signs and Symptoms of Heat-Related Illness. CDC National Center for Environmental Health. Primary reference for heat-exhaustion and heat-stroke clinical presentation and emergency response cited in the FAQs.
- [5]Sherwood, S. C. & Huber, M. (2010). An Adaptability Limit to Climate Change Due to Heat Stress. Proceedings of the National Academy of Sciences, 107(21), 9552–9555. Establishes the wet-bulb 35 °C human survivability limit and the climate-projection context for the extreme heat-index values discussed in the FAQs.
- [6]Anderson, G. B., Bell, M. L. & Peng, R. D. (2013). Methods to Calculate the Heat Index as an Exposure Metric in Environmental Health Research. Environmental Health Perspectives, 121(10), 1111–1119. Comparative analysis of the Rothfusz regression, the Steadman iterative model, and alternative heat-index implementations used in epidemiological studies.
- [7]Occupational Safety and Health Administration. Heat — OSHA Technical Manual Section III, Chapter 4. US Department of Labor. The federal occupational-safety reference that uses the NWS heat index bands to set engineering, administrative, and PPE requirements for outdoor workers.
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