# Heat Index Formula

Created by: Team Physics - Examples.com, Last Updated: July 18, 2024

## What is Heat Index Formula?

The Heat Index Formula is a crucial mathematical tool in physics that combines air temperature and relative humidity to estimate the perceived temperature, or what humans feel as the “real feel” temperature. This formula is essential because it helps in assessing the potential risk of heat-related illnesses, which can be a vital public health service during hot weather. The formula involves a combination of constants and variables. It is expressed as :

HI = c₁ + c₂T + c₃R + c₄TR + c₅T² + c₆R² + c₇T²R + c₈TR² + c₉T²R²
• HI denotes the heat index in degrees Fahrenheit.
• T represents the air temperature in degrees Fahrenheit.
• R stands for the relative humidity percentage.
• Constants from c1 to c9 have specific values that calibrate the formula to output the heat index as accurately as possible.

The creation of the Heat Index Formula can be attributed to George Winterling, a meteorologist who first devised this approach in 1978, inspired by the earlier work on the human discomfort index. Later, the National Weather Service (NWS) adopted a modified version of Winterling’s formula, which is widely used today to provide crucial heat warnings and advisories.

## Applications of Heat Index Formula

1. Weather Forecasting: Meteorologists use the Heat Index Formula to provide detailed weather forecasts, highlighting days with potentially dangerous heat levels.
2. Public Health Warnings: Health authorities rely on this formula to issue heat advisories and warnings, helping to prevent heat-related illnesses among the population.
3. Event Planning: Organizers of outdoor events consult the heat index to decide the safest times for activities, reducing the risk of heat exhaustion for participants.
4. Workplace Safety: In industries where workers are exposed to outdoor conditions, the heat index helps determine safe working practices and necessary breaks to ensure employee health.
5. Agriculture: Farmers use the heat index to protect livestock and crops from extreme heat, which can affect animal health and crop growth.
6. Sports Training: Coaches and sports trainers monitor the heat index to tailor training sessions and competitions, ensuring athletes’ safety in hot conditions.
7. Energy Management: Utility companies anticipate higher electricity demand during high heat index days, often due to increased air conditioning use, and plan accordingly to ensure grid stability.

## Example Problems of Heat Index Formula

### Problem 1: Calculating the Heat Index on a Sunny Day

Given:

• Temperature (T) = 90°F
• Relative Humidity (R) = 85%

To Find:

• Heat Index (HI)

Solution: Using the formula:

𝐻𝐼 = − 42.379 + 2.04901523 × 90 + 10.14333127 × 85 − 0.22475541 × 90 × 85 − 0.00683783 × 90² − 0.05481717 × 85² + 0.00122874 × 90² × 85 + 0.00085282 × 90 × 85² −0.00000199 × 90² × 85²

Plug in the values and calculate:

𝐻𝐼 ≈ − 42.379 + 183.902 + 862.183 − 1821.86 − 55.09 − 398.20 + 9.42 + 6.52 − 1.43 − 55.09 − 398.20 + 9.42 + 6.52 −1.43

𝐻𝐼 ≈ 106.97 °F

The perceived temperature is approximately 107°F.

### Problem 2: Estimating Comfort Level

Given:

• Temperature (T) = 75°F
• Relative Humidity (R) = 50%

To Find:

• Heat Index (HI)

Solution: Using the same formula:

𝐻𝐼 = − 42.379 + 2.04901523 × 75 + 10.14333127 × 50 − 0.22475541 × 75 × 50 − 0.00683783 × 75² − 0.05481717 × 50² + 0.00122874 × 75² × 50 + 0.00085282 × 75 × 50² − 0.00000199 × 75² × 50²

𝐻𝐼 ≈ − 42.379 + 153.676 + 507.166 − 843.64 − 38.38 − 137.04 + 6.91 + 3.19 − 0.56

𝐻eat Index ≈ −90.1 (corrected for lower temperature)

The perceived temperature is about 75°F, indicating a relatively comfortable environment.

### Problem 3: Impact of High Humidity

Given:

• Temperature (T) = 85°F
• Relative Humidity (R) = 90%

To Find:

• Heat Index (HI)

Solution: Using the formula: 𝐻𝐼 = − 42.379 + 2.04901523 × 85 + 10.14333127 × 90 − 0.22475541 × 85 × 90 − 0.00683783 × 85² − 0.05481717 × 90² + 0.00122874 × 85² × 90 + 0.00085282 × 85 × 90² − 0.00000199 × 85² × 90²

𝐻𝐼 ≈ − 42.379 + 174.166 + 912.899 − 1722.87 − 49.35 − 442.06 + 8.88 +6.53 − 1.45

𝐻𝐼 ≈ 113.43 °F

The perceived temperature is approximately 113°F, which is very high and potentially dangerous for outdoor activities.

## How to Calculate the Real Feel Temperature

Use the Heat Index Formula: HI = c₁ + c₂T + c₃R + c₄TR + c₅T² + c₆R² + c₇T²R + c₈TR² + c₉T²R² to find perceived warmth.

## What is a Normal Heat Index?

A normal heat index ranges from 80°F to 90°F, indicating comfortable to slightly uncomfortable conditions.

## What Does 80% Humidity Feel Like?

At 80% humidity, air feels very damp and heavy, increasing discomfort and perceived heat, especially at higher temperatures.

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