Dew Point and Frost Point Calculator

Calculator

1. select the desired temperature scale from the dropdown menu
2. enter the air temperature
3. the relative humidity value

Results

1. Dew Point: the temperature at which air becomes saturated with moisture results in condensation.
2. Frost Point: If the dew point temperature is below freezing (0°C), the frost point is shown instead, predicting when ice will form via sublimation

Formulas

The dew point and frost point are calculated using the Magnus-Tetens formula. The steps are as follows:

1. Calculate \( \alpha \):

\[ \alpha = \frac{A \cdot T}{B + T} + \ln\left(\frac{\text{RH}}{100}\right) \]

• \( T \): Air temperature (°C)
• \( \text{RH} \): Relative humidity (%)
• \( A = 17.62 \), \( B = 243.12 \): Constants

2. Calculate the Dew Point (\( T_d \)):

\[ T_d = \frac{B \cdot \alpha}{A - \alpha} \]

3. Frost Point Adjustment (if \( T_d < 0 \)):

If the dew point temperature is below freezing (0°C), the frost point (\( T_f \)) is calculated as: \[ T_f = T_d - \left(0.66 \cdot T_d + 0.16\right) \]

Example Calculations

Example 1: Dew Point Calculation

Given:

• Air temperature (\( T \)) = 21°C
• Relative humidity (\( \text{RH} \)) = 60%

Step 1: Calculate \( \alpha \):

\[ \alpha = \frac{17.62 \cdot 21}{243.12 + 21} + \ln\left(\frac{60}{100}\right) \] \[ \alpha = \frac{370.02}{264.12} + \ln(0.6) \] \[ \alpha \approx 1.4 - 0.511 = 0.889 \]

Step 2: Calculate \( T_d \):

\[ T_d = \frac{243.12 \cdot 0.889}{17.62 - 0.889} \] \[ T_d = \frac{216.08}{16.731} \] \[ T_d \approx 12.91^\circ\text{C} \]

Result: The dew point is approximately \( 12.91^\circ\text{C} \).

Example 2: Frost Point Calculation

Given:

• Air temperature (\( T \)) = -4°C
• Relative humidity (\( \text{RH} \)) = 60%

Step 1: Calculate \( \alpha \):

\[ \alpha = \frac{17.62 \cdot -4}{243.12 - 4} + \ln\left(\frac{60}{100}\right) \] \[ \alpha = \frac{-70.48}{239.12} + \ln(0.6) \] \[ \alpha \approx -0.2947 - 0.5108 = -0.8055 \]

Step 2: Calculate \( T_d \):

\[ T_d = \frac{243.12 \cdot -0.8055}{17.62 - (-0.8055)} \] \[ T_d = \frac{-195.74}{18.4255} \] \[ T_d \approx -10.62^\circ\text{C} \]

Step 3: Adjust to Frost Point (\( T_f \)):

\[ T_f = T_d - (0.66 \cdot T_d + 0.16) \] \[ T_f = -10.62 - (0.66 \cdot -10.62 + 0.16) \] \[ T_f = -10.62 - (-6.9992 + 0.16) \] \[ T_f = -10.62 - (-6.8392) \] \[ T_f \approx -3.78^\circ\text{C} \]

Result: The frost point is approximately \( -3.78^\circ\text{C} \).

Conclusion

These calculations demonstrate how the Magnus-Tetens formula is used to compute dew and frost points for given atmospheric conditions.