Relative Humidity Calculator

1. What is the Relative Humidity Calculator?

Definition: This calculator computes the relative humidity (\( \text{RH} \)) of air based on the air temperature and dew point temperature, using the Magnus-Tetens formula with revised coefficients by Alduchov and Eskridge. Relative humidity is the ratio of the actual vapor pressure to the saturation vapor pressure at a given temperature, expressed as a percentage.

Purpose: It is used in meteorology, HVAC design, and environmental science to assess the moisture content of the air, predict condensation, and ensure comfort or safety in various applications.

2. How Does the Calculator Work?

The calculator uses the following formula:

Formula: \[ RH = 100 \times \frac{e^{\frac{\beta \times D_p}{\lambda + D_p}}}{e^{\frac{\beta \times T}{\lambda + T}}} \] where:

\( RH \): Relative humidity (%)
\( D_p \): Dew point temperature (°C, °F, K)
\( T \): Air temperature (°C, °F, K)
\( \beta \): Magnus coefficient, 17.625
\( \lambda \): Magnus coefficient, 243.04 °C

Unit Conversions:

Temperature (Air Temperature, Dew Point):
- 1 °C = 1 °C
- 1 °F = (T - 32) × 5/9 °C
- 1 K = T - 273.15 °C

Steps:

Enter the air temperature in °C, °F, or K (default is 25°C, step size 0.00001).
Enter the dew point in °C, °F, or K (default is 15°C, step size 0.00001).
Convert temperature and dew point to Celsius (°C).
Calculate the relative humidity using the Magnus-Tetens formula with the revised coefficients.
Display the result, using scientific notation if the absolute value is less than 0.001, otherwise rounded to 4 decimal places.

3. Importance of Relative Humidity Calculation

Calculating relative humidity is crucial for:

Meteorology: Predicting weather conditions such as fog, dew, or frost formation, and assessing the likelihood of precipitation.
HVAC Systems: Ensuring optimal indoor humidity levels for comfort and preventing mold growth by controlling condensation.
Aviation: Assessing the risk of icing on aircraft surfaces, as relative humidity indicates how close the air is to saturation.

4. Using the Calculator

Examples:

Example 1: Calculate the relative humidity with a temperature of 25°C and dew point of 15°C:
- Enter Temperature = 25 °C.
- Enter Dew Point = 15 °C.
- Numerator: \( e^{\frac{17.625 \times 15}{243.04 + 15}} = e^{\frac{262.875}{258.04}} = e^{1.0189} = 2.7695 \).
- Denominator: \( e^{\frac{17.625 \times 25}{243.04 + 25}} = e^{\frac{440.625}{268.04}} = e^{1.6433} = 5.1708 \).
- Relative humidity: \( RH = 100 \times \frac{2.7695}{5.1708} = 100 \times 0.5355 = 53.5519\% \).
- Result: \( \text{RH} = 53.5519\% \).
Example 2: Calculate the relative humidity with a temperature of 86°F and dew point of 59°F:
- Enter Temperature = 86 °F, convert to °C: \( (86 - 32) \times 5/9 = 30 \, \text{°C} \).
- Enter Dew Point = 59 °F, convert to °C: \( (59 - 32) \times 5/9 = 15 \, \text{°C} \).
- Numerator: \( e^{\frac{17.625 \times 15}{243.04 + 15}} = e^{1.0189} = 2.7695 \).
- Denominator: \( e^{\frac{17.625 \times 30}{243.04 + 30}} = e^{\frac{528.75}{273.04}} = e^{1.9362} = 6.9289 \).
- Relative humidity: \( RH = 100 \times \frac{2.7695}{6.9289} = 100 \times 0.3996 = 39.9637\% \).
- Result: \( \text{RH} = 39.9637\% \).

5. Frequently Asked Questions (FAQ)

Q: What is relative humidity?
A: Relative humidity (\( \text{RH} \)) is the ratio of the actual vapor pressure to the saturation vapor pressure at a given temperature, expressed as a percentage. It indicates how close the air is to saturation, where condensation (e.g., dew, fog) begins to form.

Q: Why use the Magnus-Tetens formula?
A: The Magnus-Tetens formula provides an accurate approximation for calculating relative humidity within the temperature range of -40°C to 50°C, with revised coefficients by Alduchov and Eskridge improving its precision for meteorological applications.

Q: How does dew point affect relative humidity?
A: The dew point (\( D_p \)) is the temperature at which air becomes saturated, and condensation begins. A smaller difference between the air temperature (\( T \)) and the dew point indicates higher relative humidity, as the air is closer to saturation.