TL;DR
- •The heat index combines air temperature and relative humidity into one "feels like" number your body actually experiences.
- •High humidity slows sweat evaporation, so the same thermometer reading can feel much hotter than the air temperature alone.
- •Above 80°F, the National Weather Service uses the Rothfusz regression: nine terms built from temperature, humidity, and their squares and cross-products.
- •On a 90°F afternoon with 70% humidity, the formula yields a heat index near 106°F, a gap of about 16 degrees from humidity alone.
- •Heat index is defined for shade with light wind; direct sun can add another 10-15°F on top.
When it is 90°F outside but your weather app says it feels like 105°F, that gap is not hype - it is the heat index, a number that combines air temperature and relative humidity to describe how hot your body actually experiences the air.
Below we walk through the National Weather Service Rothfusz regression term by term, work a real 90°F / 70% humidity example by hand, and map the result to the official caution-to-extreme-danger scale.
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Open Heat Index CalculatorThe basics
What Is the Heat Index?
You've seen it on every weather app: the actual temperature, and then the "feels like" number. When it's 90°F outside but feels like 105°F, that feels like temperature is called the heat index - a single number that combines air temperature and relative humidity to describe how hot the human body actually experiences the air.
Why does humidity matter so much? Because your body cools itself by sweating. When sweat evaporates off your skin, it carries heat away with it. But when the air is already loaded with moisture (high humidity), your sweat can't evaporate as quickly - so that cooling system breaks down, and your body temperature climbs.
Key Idea
The heat index only applies in the shade with light winds. Direct sun can make you feel an additional 10-15°F hotter on top of the heat index. Breezy conditions reduce it.
The Math
The Rothfusz Regression Formula
Meteorologists use a formula developed by R.G. Rothfusz for the National Weather Service. It sounds intimidating at first - but it's really just addition and multiplication with a bunch of constants. Here it is:
The Rothfusz Formula
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)
Where T = air temperature in °F | RH = relative humidity (as a percentage, e.g. 70 not 0.70) | HI = Heat Index in °F
Those nine terms might look wild, but notice the pattern: each term is just a constant (a fixed number) multiplied by some combination of T and RH. The formula was built by analyzing thousands of data points and finding the equation that best matched how people actually reported feeling in different conditions.
What the Variables Mean
T
Temperature (°F)
Air temperature in the shade. Must be at least 80°F for the formula to apply.
RH
Relative Humidity (%)
How much moisture is in the air vs. how much it could hold. 0-100.
T²
Temperature Squared
T × T. This captures the non-linear way heat stress grows.
RH²
Humidity Squared
RH × RH. Very high humidity has a disproportionately large effect.
Why "Regression"?
A regression formula is a math technique where scientists feed a computer lots of real-world data (temperature readings + how hot people said it felt) and the computer finds the equation that fits all those data points best. It's the same math behind things like predicting house prices or sports statistics.
Try It
A Worked Example
Let's calculate the heat index for the same conditions shown in the example above: T = 90°F, RH = 70%. This is exactly the kind of afternoon when a heat advisory might be issued.
Step-by-Step
-
1
Find the squared and combined terms we'll need:
T² = 90 × 90 = 8,100
RH² = 70 × 70 = 4,900
T × RH = 90 × 70 = 6,300
T² × RH = 8,100 × 70 = 567,000
T × RH² = 90 × 4,900 = 441,000
T² × RH² = 8,100 × 4,900 = 39,690,000 -
2
Calculate each of the 9 terms:
Term 1 (constant): −42.379
Term 2 (2.04901523 × T): 2.04901523 × 90 = +184.411
Term 3 (10.14333127 × RH): 10.14333127 × 70 = +710.033
Term 4 (−0.22475541 × T × RH): −0.22475541 × 6,300 = −1,415.959
Term 5 (−0.00683783 × T²): −0.00683783 × 8,100 = −55.386
Term 6 (−0.05481717 × RH²): −0.05481717 × 4,900 = −268.604
Term 7 (+0.00122874 × T² × RH): 0.00122874 × 567,000 = +696.875
Term 8 (+0.00085282 × T × RH²): 0.00085282 × 441,000 = +376.094
Term 9 (−0.00000199 × T² × RH²): −0.00000199 × 39,690,000 = −78.983 -
3
Add all nine terms together:
−42.379 + 184.411 + 710.033 − 1,415.959 − 55.386 − 268.604 + 696.875 + 376.094 − 78.983 ≈ 106°F
So on a 90°F day with 70% humidity, your body feels like it's dealing with 106°F - a full 16 degrees hotter than the thermometer reads. That's the difference between a manageable afternoon and a dangerous one.
What It Means
The National Weather Service Heat Index Scale
Once the heat index is calculated, meteorologists use it to issue warnings. Here's what each level means for your body:
Caution
80-90°F
Fatigue possible with prolonged exposure. Drink water and take breaks.
Extreme Caution
90-103°F
Heat cramps and heat exhaustion are possible. Limit outdoor activity.
Danger
103-124°F
Heat cramps likely. Heat exhaustion probable. Stay in cool spaces.
Extreme Danger
125°F+
Heatstroke highly likely. Avoid all outdoor activity. Seek air conditioning immediately.
The Shortcut
When Meteorologists Use a Simpler Formula
The full Rothfusz equation is only used when the temperature is above 80°F and the humidity is between 40-100%. For milder conditions, the National Weather Service uses a much simpler formula called the Steadman approximation:
Steadman Simple Formula
HI = 0.5 × { T + 61.0 + [(T − 68.0) × 1.2] + (RH × 0.094) }
Used when the result from this formula averages with the actual temperature to give a value below 80°F.
This is the version a student could reasonably calculate by hand in a few steps. Weather services use both formulas and pick the appropriate one based on conditions - a great example of how real-world math involves choosing the right tool for the job.
Math in the Real World
Every heat advisory issued by your local weather service started with exactly this calculation. Meteorologists run the formula for thousands of grid points across the country every hour - that's computers doing arithmetic at massive scale, the same basic operations you'd do by hand.
Key Takeaways
What We Learned
The heat index is a real-world polynomial - a formula with multiple terms that each capture a different piece of how temperature and humidity interact in the human body. A few important things to remember:
- The heat index only applies when temps are above 80°F.
- Higher humidity = higher heat index, because sweat can't evaporate to cool you down.
- The formula uses squared terms (T² and RH²) because the relationship isn't perfectly linear - extreme humidity is disproportionately dangerous.
- Scientists built the formula by analyzing real data - that technique is called regression analysis.
- The difference between "actual" and "feels like" can be 15°F or more - in our example, 90°F felt like 106°F, a 16-degree gap from humidity alone.
Try the Heat Index Calculator
Try the Heat Index Calculator
Plug in any temperature and humidity and see the math work in real time.
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