Relative Humidity Calculator - Calculate Relative Humidity from Temperature and Dew Point

Calculator

1. select the temperature scale
2. enter the air temperature
3. select the temperature scale
4. enter the dew point temperature

Results

1. the calculated relative humidity as a percent value (RH%)

Formula

Relative humidity (RH%) is calculated using the Magnus-Tetens formula:

\[ RH = 100 \times \frac{e(T_d)}{e(T)} \]

where:

• \( RH \) = Relative Humidity (%)
• \( e(T) = 6.112 \times e^{(A \cdot T) / (B + T)} \)
• \( e(T_d) = 6.112 \times e^{(A \cdot T_d) / (B + T_d)} \)
• \( T \) = Temperature (°C)
• \( T_d \) = Dew Point (°C)
• Constants: \( A = 17.62 \), \( B = 243.12 \)

Example Calculations

Example 1: Temperature = 25°C, Dew Point = 10°C

Step 1: Compute \( e(T) \) and \( e(T_d) \):

\[ e(25) = 6.112 \times e^{(17.62 \times 25) / (243.12 + 25)} \] \[ e(25) \approx 6.112 \times e^{1.75} \approx 31.67 \] \[ e(10) = 6.112 \times e^{(17.62 \times 10) / (243.12 + 10)} \] \[ e(10) \approx 6.112 \times e^{0.64} \approx 12.28 \]

Step 2: Compute RH%

\[ RH = 100 \times \frac{12.28}{31.67} \approx 38.8% \]

Example 2: Temperature = 30°C, Dew Point = 20°C

Step 1: Compute \( e(T) \) and \( e(T_d) \):

\[ e(30) = 6.112 \times e^{(17.62 \times 30) / (243.12 + 30)} \] \[ e(30) \approx 6.112 \times e^{2.03} \approx 42.43 \] \[ e(20) = 6.112 \times e^{(17.62 \times 20) / (243.12 + 20)} \] \[ e(20) \approx 6.112 \times e^{1.34} \approx 23.37 \]

Step 2: Compute RH%

\[ RH = 100 \times \frac{23.37}{42.43} \approx 55.1% \]

Conclusion

This tool provides reliable humidity calculations for meteorology, HVAC, and climate control applications.