Heat Index Calculator (Feels-Like Temperature from Temperature and Humidity)

Enter the air temperature and either the relative humidity or the dew point. The heat index (feels-like temperature) is calculated in °C, °F and K, with the NWS risk level and a graph of humidity against the heat index.

Units

Air temperature

Temperature unit

Relative humidity (%)

Dew point (instead of relative humidity)

Dew point unit

Fill in only one of relative humidity and dew point (leave the other blank). This is the NWS heat index, which is a different index from the WBGT.

Result and graph

Enter the air temperature and the humidity (or dew point) in the fields on the left and press "Calculate". The result will appear here.

[ CLOSE ]

What you can do on this page
What is this calculation used for?
How to Use
Formulas and graphs
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Enter the air temperature and relative humidity, and you get the heat index, the feels-like temperature used by the US National Weather Service (NWS), on the spot
You can also use the dew point instead of the humidity (the dew point is converted to relative humidity automatically)
The result is shown in °F, °C and K, together with the NWS risk level (Caution, Extreme Caution, Danger or Extreme Danger)
A graph shows at a glance how much hotter the same temperature feels when the humidity is higher
A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

The heat index on this page is the feels-like temperature that the NWS uses in its heat forecasts. It assumes shade and a light wind; in direct sunshine it can feel up to about 15°F hotter, according to the NWS. The risk levels are general NWS guidelines, not medical advice. For heat advisories and warnings in your area, check your local NWS forecast. The heat index is a different index from the WBGT (wet bulb globe temperature), which also includes sun and wind.

What is this calculation used for?

Judging the heat risk of summer sports practice, humidity included

"It's 92°F today, a bit cooler than yesterday, so practice should be easier." If you ignore the humidity, this can be wrong. At 92°F and 75% humidity, the heat index is about 116°F, which falls in the NWS "Danger" category.
Seeing in numbers how much the humidity changes the risk helps coaches and players stop judging practice intensity and breaks by the temperature alone. Many schools and athletic associations follow their own heat policies (often based on the WBGT), so follow those for decisions such as canceling practice.

Heat safety for outdoor work

In the US, the heat index is widely used to plan heat safety for outdoor workers, and the OSHA-NIOSH Heat Safety Tool app is built on it. At 86°F, for example, the heat index is about 88°F at 50% humidity but about 100°F at 80% humidity, a difference of about 12°F from humidity alone.
This lets you adjust the work, such as slowing the pace and adding more breaks and water on muggy days, based on numbers rather than a hunch.

Comparing the heat of travel destinations

104°F in a dry desert city (20% humidity) has a heat index of about 103°F, while 92°F in a humid coastal city (75% humidity) has a heat index of about 116°F. The place that is 12°F cooler on the thermometer can feel far more dangerous.
The "Heat Index" and "Feels like" values in weather apps are this very index, so knowing what they show makes it easier to plan clothing and daytime activities on a trip.

Seeing why lowering the humidity helps

At a room temperature of 82°F and 70% humidity, the heat index is about 86°F. Lower the humidity to 40% with a dehumidifier or the air conditioner, and it drops to about 82°F. Without changing the thermostat, removing moisture alone makes it feel about 5°F cooler.
Knowing that lowering the humidity is an option, not only lowering the thermostat, helps you balance comfort and your electric bill.

Reading mugginess from the dew point in the forecast

The dew point in the forecast shows how much water vapor is in the air. At an air temperature of 86°F, for example, a dew point of 75°F is a relative humidity of about 70% (very muggy), while a dew point of 60°F is about 42% (fairly comfortable). Many US forecasters describe dew points in the 70s as oppressive.
Knowing that a high dew point comes with a muggy day lets you read the kind of heat ahead even without a humidity forecast. The calculator on this page also accepts the dew point as input.

Formulas and graphs

Simple formula (heat index for milder conditions)

Graph

Standard notation (the usual math form)

\(HI\) \(=\) \(0.5\) \(\times\) \((\) \(T + 61\) \(+\) \((T - 68) \times 1.2\) \(+\) \(RH \times 0.094\) \()\)

In words (symbols replaced with words)

⑤ heat index \(HI\) \(=\) ④ factor \(0.5\) \(\times\) \((\) ① temp. \(T\) (°F) \(+\,61\) \(+\) ② (temp. \(T\) − 68) × 1.2 \(+\) ③ humidity term \(RH \times 0.094\) \()\)

The formula in words

① Add the air temperature \(T\) (°F) plus 61 ,

② the temperature adjustment (\(T\) − 68) × 1.2 and

③ the humidity term: relative humidity \(RH\) (%) × 0.094 ,

④ then multiply the total by the factor \(0.5\) (take half of it)

⑤ and you get the heat index \(HI\) (°F)

Quick example

The heat index at 77°F (25°C) and 40% relative humidity is

heat index \(HI\) \(=\) factor (0.5) \(\times\) \((\) temp. (77) + 61 \(+\) (77 − 68) × 1.2 \(+\) humidity (40) × 0.094 \()\)

\(0.5 \times (77 + 61 + 10.8 + 3.76) = 0.5 \times 152.56 = 76.28\ \ (^\circ F)\)

\((76.28 - 32) \times \dfrac{5}{9} = 24.6\ \ (^\circ C)\)

Key idea

All the heat index formulas are built for degrees Fahrenheit (°F). A temperature in °C must first be converted with \(T_{\mathrm{F}} = T_{\mathrm{C}} \times \dfrac{9}{5} + 32\) (25°C → 77°F). This simple formula is the first estimate. If the average of the air temperature \(T\) and this value \(HI\) is below 80°F (about 26.7°C), the value is used as is. In hotter conditions of 80°F or more, the heat index is calculated again with the Rothfusz regression below. This is the same procedure the NWS uses.

Rothfusz regression (heat index in hot weather, the standard NWS formula)

Graph

Standard notation (the usual math form)

\(HI\) \(=\) \(c_0\) \(+\) \(c_1 T + c_4 T^2\) \(+\) \(c_2 RH + c_5 RH^2\) \(+\) \(c_3 T RH + c_6 T^2 RH + c_7 T RH^2 + c_8 T^2 RH^2\)

In words (symbols replaced with words)

⑤ heat index \(HI\) \(=\) ① constant \(c_0\) \(+\) ② temperature terms \(+\) ③ humidity terms \(+\) ④ temp. × humidity terms

The formula in words

① Add the constant \(c_0\) ,

② the terms with the air temperature \(T\) only ,

③ the terms with the relative humidity \(RH\) only and

④ the terms that combine temperature and humidity (cross terms) ,

⑤ and you get the heat index \(HI\) (°F)

Quick example

The heat index at 86°F (30°C) and 70% relative humidity is (each group of terms with \(T = 86\) and \(RH = 70\) put in)

heat index \(HI\) \(=\) constant (−42.379) \(+\) temperature terms (125.643) \(+\) humidity terms (441.429) \(+\) cross terms (−429.624)

\(-42.379 + 125.643 + 441.429 - 429.624 \approx 95.07\ \ (^\circ F)\)

\((95.07 - 32) \times \dfrac{5}{9} \approx 35.0\ \ (^\circ C)\)

Key idea

The coefficients \(c_0\) to \(c_8\) were fitted statistically by Lans P. Rothfusz of the NWS so that the formula matches the feels-like temperatures of the original heat index table (they are regression coefficients): \(c_0 = -42.379\), \(c_1 = 2.04901523\), \(c_2 = 10.14333127\), \(c_3 = -0.22475541\), \(c_4 = -0.00683783\), \(c_5 = -0.05481717\), \(c_6 = 0.00122874\), \(c_7 = 0.00085282\), \(c_8 = -0.00000199\) This formula is used in hot conditions, when the average of the air temperature and the simple-formula value is 80°F or more. At the edges, the NWS adds one of these adjustments: • Low-humidity adjustment (\(RH < 13\%\) and \(80 \le T \le 112\)°F): subtract \(\dfrac{13 - RH}{4} \times \sqrt{\dfrac{17 - |T - 95|}{17}}\) from \(HI\) • High-humidity adjustment (\(RH > 85\%\) and \(80 \le T \le 87\)°F): add \(\dfrac{RH - 85}{10} \times \dfrac{87 - T}{5}\) to \(HI\) Thanks to the cross terms (temperature × humidity), one formula captures a real-life feeling: the more humid the air, the more each extra degree of heat is felt.

Converting the dew point to relative humidity (Magnus approximation)

Graph

Standard notation (the usual math form)

\(RH\) \(=\) \(100\) \(\times\) \(\exp\left(\dfrac{17.625\,T_d}{243.04 + T_d}\right)\) \(\div\) \(\exp\left(\dfrac{17.625\,T}{243.04 + T}\right)\)

In words (symbols replaced with words)

④ rel. humidity \(RH\) (%) \(=\) ③ to percent \(100\) \(\times\) ① dew point \(T_d\) (°C) term \(\div\) ② air temp. \(T\) (°C) term

The formula in words

① Take the dew point \(T_d\) term (it matches the water vapor the air actually holds now) ,

② divide it by the air temperature \(T\) term (it matches the most water vapor the air can hold at that temperature) ,

③ multiply by \(100\) to turn it into a percentage ,

④ and you get the relative humidity \(RH\) (%)

Quick example

The relative humidity at an air temperature of 86°F (30°C) and a dew point of 71.6°F (22°C) is (this formula uses °C; the dew point term ≈ 4.319 and the air temperature term ≈ 6.935)

relative humidity \(RH\) \(=\) 100 \(\times\) dew point term (4.319) \(\div\) air temp. term (6.935)

\(100 \times 4.319 \div 6.935 \approx 62.3\ \ (\%)\)

Key idea

\(\exp\) is the natural exponential function (a power of Euler's number \(e \approx 2.718\)). Each of the two terms is roughly proportional to the saturation vapor pressure at its temperature (the pressure of water vapor when the air holds as much as it can). They come from the Magnus approximation, which is widely used in meteorology (17.625 and 243.04 are the improved, more accurate coefficients published in 1996). "Water vapor the air holds now ÷ the most water vapor it can hold" is the very definition of relative humidity. So once you know the dew point, you can convert it to relative humidity and then calculate the heat index with the two formulas above. This formula works in °C, so convert °F first: \(T_{\mathrm{C}} = (T_{\mathrm{F}} - 32) \times \dfrac{5}{9}\).

The heat index is the feels-like temperature that the NWS calculates from air temperature and humidity. Milder conditions use the simple formula, and hot conditions (when the average of the air temperature and the simple value is 80°F or more) use the Rothfusz regression. At the same air temperature, the higher the humidity, the higher the heat index climbs.

Symbols and terms

Symbols

\(HI\)	H I	The heat index, a feels-like temperature found from air temperature and humidity. The formulas work in degrees Fahrenheit (°F); the calculator on this page also converts the result to °C and K.
\(T\)	tee	The air temperature. Note that the simple formula and the regression use °F, while the dew point conversion (Magnus approximation) uses °C.
\(RH\)	R H	Relative humidity, the "humidity" in the weather forecast. Put the percentage from 0 to 100 into the formula as is (for example, 70% humidity → 70).
\(T_d\)	tee sub dee	The dew point (°C in the conversion formula). It is the temperature at which water droplets (condensation) start to form when the air is cooled, and it shows how much water vapor is in the air.
\(c_0\)–\(c_8\)	c zero to c eight	The nine coefficients of the Rothfusz regression, constants fitted statistically to match the data.
\(\exp\)	exponential	The natural exponential function. \(\exp(x)\) is Euler's number \(e \approx 2.718\) raised to the power \(x\). Use the EXP function in Excel or math.exp in Python.

Terms

heat index	An index that combines air temperature and humidity to show, as a temperature, how hot it feels to people. It was developed by George Winterling in 1978 and is based on work by R. G. Steadman. The NWS uses it for summer heat advisories and warnings. It assumes shade and a light wind; the NWS notes that full sunshine can raise it by up to about 15°F. It was designed for hot, humid conditions (about 80°F and above, 40% humidity and above), so values in cooler or drier air are only a rough guide.
WBGT (wet bulb globe temperature)	A different heat stress index that includes sunshine, wind and humidity as well as air temperature. In the US it is used by the military, many sports and athletic associations and outdoor workplaces, and some NWS offices publish WBGT forecasts. It gives lower numbers than the heat index, so the two cannot be compared directly.
feels-like temperature	A temperature that shows how hot or cold it actually feels, rather than what the thermometer reads. In humid air, sweat evaporates slowly and the body loses heat less easily, so the same temperature feels hotter. The heat index puts this effect into a formula. Weather apps often show it as "Feels like".
relative humidity	How much water vapor the air holds, as a percentage of the most it can hold at that temperature. The "humidity" in the weather forecast is the relative humidity.
dew point	The temperature at which water vapor starts to turn into droplets (condensation starts) as air is cooled. The more water vapor in the air, the higher it is, so it is also a good guide to how muggy it feels (a high dew point is a muggy day).
saturation vapor pressure	The pressure of water vapor when the air holds as much as it can at that temperature. It rises with temperature. Meteorologists define relative humidity as "actual vapor pressure ÷ saturation vapor pressure × 100 (%)", and the Magnus approximation is an easy way to find the saturation vapor pressure from the temperature.
regression	A formula whose coefficients are chosen to fit a large set of data as closely as possible. The Rothfusz regression approximates the results of a model of human heat balance with a formula in air temperature and humidity.
°F (Fahrenheit)	The temperature unit used in the US. Water freezes at 32°F and boils at 212°F. To convert from Celsius, °F = °C × 9/5 + 32.
kelvin	The unit of absolute temperature used in science (symbol K). It is the Celsius temperature plus 273.15 (0°C = 273.15 K).

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.

Variables and substitution (Grades 6–7)	Being able to put numbers in for \(T\) and \(RH\) in a formula and calculate Following the order of operations, such as doing multiplication and division before addition and subtraction
Percentages (Grade 6)	Knowing that "70% humidity" is a percentage - the air holds 70% of the most water vapor it can hold
Temperature units (middle school science)	Knowing that there are several temperature units - Fahrenheit (°F), Celsius (°C) and kelvin (K) - and that formulas convert between them
Square roots (Grade 8)	Knowing what the square root \(\sqrt{\ }\) in the low-humidity adjustment is (a calculator or Excel can do the arithmetic)
Exponential functions (Algebra 2)	Having a general feel for \(\exp\) (powers of Euler's number \(e\)) in the dew point conversion (again, Excel or Python can do the arithmetic)

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table for the heat index with the simple formula

Air temperature (°F)	77
Air temperature (°C)	=(B1-32)*5/9
Relative humidity (%)	40
Heat index (°F)	=0.5(B1+61+(B1-68)1.2+B3*0.094)
Heat index (°C)	=(B4-32)*5/9

Table for the heat index with the Rothfusz regression

Air temperature (°F)	86
Air temperature (°C)	=(B1-32)*5/9
Relative humidity (%)	70
Heat index (°F)	=-42.379+2.04901523B1+10.14333127B3-0.22475541B1B3-0.00683783B1^2-0.05481717B3^2+0.00122874B1^2B3+0.00085282B1B3^2-0.00000199B1^2B3^2
Heat index (°C)	=(B4-32)*5/9

Table for relative humidity from the dew point (Magnus approximation)

Air temperature (°F)	86
Dew point (°F)	71.6
Relative humidity (%)	=100EXP(17.625((B2-32)5/9)/(243.04+(B2-32)5/9))/EXP(17.625((B1-32)5/9)/(243.04+(B1-32)*5/9))

After pasting, the number cells are your inputs and the cells starting with "=" are calculated automatically.
The first table (simple formula) is for milder conditions, when the average of the air temperature and the simple value is below 80°F. With the example values (77°F, 40%), B4 shows about 76.28 (°F) and B5 about 24.6 (°C).
The second table (regression) is for hot conditions of 80°F or more. With the example values (86°F, 70%), B4 shows about 95.07 (°F) and B5 about 35.0 (°C). The adjustments for very low humidity (below 13%) and very high humidity (above 85%) are left out. For exact values, use the calculator on this page or the Python code.
The third table converts the dew point to relative humidity. The formula converts °F to °C inside, because the Magnus approximation works in °C. With the example values (86°F air, 71.6°F dew point), B3 shows about 62.28 (%).

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table for the heat index with the simple formula

Air temperature (°F)	77
Air temperature (°C)	=(B1-32)*5/9
Relative humidity (%)	40
Heat index (°F)	=0.5(B1+61+(B1-68)1.2+B3*0.094)
Heat index (°C)	=(B4-32)*5/9

Table for the heat index with the Rothfusz regression

Air temperature (°F)	86
Air temperature (°C)	=(B1-32)*5/9
Relative humidity (%)	70
Heat index (°F)	=-42.379+2.04901523B1+10.14333127B3-0.22475541B1B3-0.00683783B1^2-0.05481717B3^2+0.00122874B1^2B3+0.00085282B1B3^2-0.00000199B1^2B3^2
Heat index (°C)	=(B4-32)*5/9

Table for relative humidity from the dew point (Magnus approximation)

Air temperature (°F)	86
Dew point (°F)	71.6
Relative humidity (%)	=100EXP(17.625((B2-32)5/9)/(243.04+(B2-32)5/9))/EXP(17.625((B1-32)5/9)/(243.04+(B1-32)*5/9))

The same formulas as in Excel work as is (EXP and "^" for powers work the same). Copy the whole table, paste it into cell A1, and replace the input values with your own.

How to calculate it in Python

import math

air_temperature_f = 86    # air temperature (°F)
relative_humidity = 70    # relative humidity (%)

# To start from the dew point, remove the # from the next two lines (Magnus approximation, which works in °C)
# dew_point_f = 71.6        # dew point (°F)
# relative_humidity = 100 * math.exp(17.625 * ((dew_point_f - 32) * 5 / 9) / (243.04 + (dew_point_f - 32) * 5 / 9)) / math.exp(17.625 * ((air_temperature_f - 32) * 5 / 9) / (243.04 + (air_temperature_f - 32) * 5 / 9))

t_f = air_temperature_f
rh = relative_humidity

heat_index_f = 0.5 * (t_f + 61 + (t_f - 68) * 1.2 + rh * 0.094)   # simple formula
if (t_f + heat_index_f) / 2 >= 80:       # if the average is 80°F or more, use the Rothfusz regression
    heat_index_f = (-42.379 + 2.04901523 * t_f + 10.14333127 * rh
                    - 0.22475541 * t_f * rh - 0.00683783 * t_f ** 2
                    - 0.05481717 * rh ** 2 + 0.00122874 * t_f ** 2 * rh
                    + 0.00085282 * t_f * rh ** 2 - 0.00000199 * t_f ** 2 * rh ** 2)
    if rh < 13 and 80 <= t_f <= 112:     # low-humidity adjustment
        heat_index_f -= (13 - rh) / 4 * math.sqrt((17 - abs(t_f - 95)) / 17)
    elif rh > 85 and 80 <= t_f <= 87:    # high-humidity adjustment
        heat_index_f += (rh - 85) / 10 * (87 - t_f) / 5

heat_index_c = (heat_index_f - 32) * 5 / 9
heat_index_k = heat_index_c + 273.15
print(f"Heat index: {heat_index_f:.1f} °F ({heat_index_c:.1f} °C / {heat_index_k:.1f} K)")

Runs with the standard library (math) only. It follows the NWS procedure - the simple formula first, then (in hot conditions) the regression plus the edge adjustments. Change the temperature and humidity at the top and run it.

How to write it in LaTeX and other math languages (copy and paste)

Simple formula (heat index for milder conditions)

HI = 0.5 × (T + 61 + (T − 68) × 1.2 + RH × 0.094)

HI = 0.5 \left( T + 61 + (T - 68) \times 1.2 + RH \times 0.094 \right)

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>HI</mi>
    <mo>=</mo>
    <mn>0.5</mn>
    <mo>&#x00D7;</mo>
    <mo>(</mo>
    <mi>T</mi><mo>+</mo><mn>61</mn>
    <mo>+</mo>
    <mo>(</mo><mi>T</mi><mo>&#x2212;</mo><mn>68</mn><mo>)</mo>
    <mo>&#x00D7;</mo><mn>1.2</mn>
    <mo>+</mo>
    <mi>RH</mi><mo>&#x00D7;</mo><mn>0.094</mn>
    <mo>)</mo>
  </mrow>
</math>

HI = 0.5 (T + 61 + (T - 68) * 1.2 + RH * 0.094)

hi = 0.5*(t + 61 + (t - 68)*1.2 + rh*0.094)

HI := 0.5*(T + 61 + (T - 68)*1.2 + RH*0.094);

HI = 0.5*(T + 61 + (T - 68)*1.2 + RH*0.094);

HI = 0.5(T + 61 + (T - 68) × 1.2 + RH × 0.094)

Rothfusz regression (heat index in hot weather, the standard NWS formula)

HI = −42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²·RH + 0.00085282T·RH² − 0.00000199T²·RH²

HI = -42.379 + 2.04901523\,T + 10.14333127\,RH - 0.22475541\,T \cdot RH - 0.00683783\,T^2 - 0.05481717\,RH^2 + 0.00122874\,T^2 RH + 0.00085282\,T\,RH^2 - 0.00000199\,T^2 RH^2

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>HI</mi>
    <mo>=</mo>
    <mo>&#x2212;</mo><mn>42.379</mn>
    <mo>+</mo><mn>2.04901523</mn><mi>T</mi>
    <mo>+</mo><mn>10.14333127</mn><mi>RH</mi>
    <mo>&#x2212;</mo><mn>0.22475541</mn><mi>T</mi><mo>&#x22C5;</mo><mi>RH</mi>
    <mo>&#x2212;</mo><mn>0.00683783</mn><msup><mi>T</mi><mn>2</mn></msup>
    <mo>&#x2212;</mo><mn>0.05481717</mn><msup><mi>RH</mi><mn>2</mn></msup>
    <mo>+</mo><mn>0.00122874</mn><msup><mi>T</mi><mn>2</mn></msup><mi>RH</mi>
    <mo>+</mo><mn>0.00085282</mn><mi>T</mi><msup><mi>RH</mi><mn>2</mn></msup>
    <mo>&#x2212;</mo><mn>0.00000199</mn><msup><mi>T</mi><mn>2</mn></msup><msup><mi>RH</mi><mn>2</mn></msup>
  </mrow>
</math>

HI = -42.379 + 2.04901523 T + 10.14333127 RH - 0.22475541 T RH - 0.00683783 T^2 - 0.05481717 RH^2 + 0.00122874 T^2 RH + 0.00085282 T RH^2 - 0.00000199 T^2 RH^2

hi = -42.379 + 2.04901523*t + 10.14333127*rh - 0.22475541*t*rh - 0.00683783*t^2 - 0.05481717*rh^2 + 0.00122874*t^2*rh + 0.00085282*t*rh^2 - 0.00000199*t^2*rh^2

HI := -42.379 + 2.04901523*T + 10.14333127*RH - 0.22475541*T*RH - 0.00683783*T^2 - 0.05481717*RH^2 + 0.00122874*T^2*RH + 0.00085282*T*RH^2 - 0.00000199*T^2*RH^2;

HI = -42.379 + 2.04901523*T + 10.14333127*RH - 0.22475541*T*RH - 0.00683783*T^2 - 0.05481717*RH^2 + 0.00122874*T^2*RH + 0.00085282*T*RH^2 - 0.00000199*T^2*RH^2;

HI = -42.379 + 2.04901523T + 10.14333127RH - 0.22475541T RH - 0.00683783T^2 - 0.05481717RH^2 + 0.00122874T^2 RH + 0.00085282T RH^2 - 0.00000199T^2 RH^2

Converting the dew point to relative humidity (Magnus approximation)

RH = 100 × exp(17.625Td / (243.04 + Td)) ÷ exp(17.625T / (243.04 + T))

RH = 100 \times \dfrac{\exp\left(\dfrac{17.625\,T_d}{243.04 + T_d}\right)}{\exp\left(\dfrac{17.625\,T}{243.04 + T}\right)}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>RH</mi>
    <mo>=</mo>
    <mn>100</mn>
    <mo>&#x00D7;</mo>
    <mfrac>
      <mrow>
        <mi>exp</mi>
        <mo>(</mo>
        <mfrac>
          <mrow><mn>17.625</mn><msub><mi>T</mi><mi>d</mi></msub></mrow>
          <mrow><mn>243.04</mn><mo>+</mo><msub><mi>T</mi><mi>d</mi></msub></mrow>
        </mfrac>
        <mo>)</mo>
      </mrow>
      <mrow>
        <mi>exp</mi>
        <mo>(</mo>
        <mfrac>
          <mrow><mn>17.625</mn><mi>T</mi></mrow>
          <mrow><mn>243.04</mn><mo>+</mo><mi>T</mi></mrow>
        </mfrac>
        <mo>)</mo>
      </mrow>
    </mfrac>
  </mrow>
</math>

RH = 100 exp((17.625 T_d)/(243.04 + T_d)) / exp((17.625 T)/(243.04 + T))

rh = 100*Exp[17.625*td/(243.04 + td)]/Exp[17.625*t/(243.04 + t)]

RH := 100*exp(17.625*Td/(243.04 + Td))/exp(17.625*T/(243.04 + T));

RH = 100*exp(17.625*Td/(243.04 + Td))/exp(17.625*T/(243.04 + T));

RH = 100 exp(17.625T_d/(243.04 + T_d))/exp(17.625T/(243.04 + T))

How to have ChatGPT do the calculation

You are a weather calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing).

Find the heat index (NWS method) at an air temperature of 86°F and a relative humidity of 70%.
Steps:
1. Calculate the simple formula HI = 0.5 × (T + 61 + (T − 68) × 1.2 + RH × 0.094)
2. If the average of the air temperature and the simple value is 80°F or more, recalculate with the Rothfusz regression
   HI = -42.379 + 2.04901523T + 10.14333127RH - 0.22475541T·RH - 0.00683783T² - 0.05481717RH² + 0.00122874T²RH + 0.00085282T·RH² - 0.00000199T²RH²
   (apply the low-humidity adjustment if RH < 13% and T is 80 to 112°F, or the high-humidity adjustment if RH > 85% and T is 80 to 87°F)
3. Give the result in both °F and °C (°C = (°F − 32) × 5/9)

Show the formulas you used and the numbers from the execution result.

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula