# How to Calculate Relative Humidity From Dewpoint

Written by luc braybury
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Relative humidity refers to the amount of water vapour in the air and represents the amount of humidity that can remain in the air at a given temperature, expressed as a percentage. That is, it is a measure of how humid the air is relative to the air temperature. The dew point is the temperature at which air can not hold all of the water vapour it contains and releases it in the form of condensation. Dew point is always equal or lower than the air temperature. Relative humidity is determined by the equation: ((Actual Vapor Pressure) / (Saturation Vapor Pressure)) * 100%

Skill level:
Moderately Easy

## Instructions

1. 1

Obtain the current temperature and dew point from a weather source. This can most easily be found from a local weather station or with your own measuring devices, if available.

2. 2

Use a special equation called the Clausius-Clapeyron equation to determine the vapour pressure and saturation vapour pressure. The equation is: Ln(Es / 6.11) = (L / Rv)(1/273 - 1 / T), where Es = saturation vapour pressure, L = latent heat of vaporisation = 2.453 * 10^6 J/kg, Rv = gas constant for moist air = 461 J/kg and T = temperature in Kelvins.

3. 3

Substitute dew point temperature for T in the Clausius-Clapeyron equation to determine the vapour pressure. For example, if the dew point is 23.9 degrees Celsius, you must first convert it to Kelvins. To do this you must convert from Fahrenheit to Celsius then Celsius to Kelvins. Celsius = (Fahrenheit - 32) / 1.8 so the dew point conversion becomes: Celsius = (75 - 32) / 1.8 = 24 degrees. To convert Celsius to Kelvins simply add 273.15 to the Celsius temperature. In the example this becomes: 24 + 273.15 = 297.15.

4. 4

Determine vapour pressure by solving the Clausius-Clapeyron equation using the predetermined dew-point temperature, in Kelvins. For example, with a dew-point temperature of 297.15K, the equation becomes: Ln(Es / 6.11) = (2.453 * 10^6 / 461) * ((1 / 273) - (1 / 291.15)). This becomes: Ln(Es / 6.11) = 1.22. Solving for Es, first raise each side by the power of the natural exponent e, to get rid of the natural log Ln. The equation becomes: Es / 6.11 = e^1.22; Ex = (e^1.22 * 6.11) = 20.1.

5. 5

Substitute the air temperature for T in the Clausius-Clapeyron equation to determine the saturation vapour pressure. First convert the temperature to Celsius then Kelvins. For example, if the air temperature is 26.7 degrees Celsius, converting to Celsius it becomes: (80 - 32) / 1.8 = 27 degrees Celsius. Converting this to Kelvins finds: 27 + 273.15 = 300.15K.

6. 6

Determine saturated vapour pressure by solving the Clausius-Clapeyron equation using the predetermined air temperature, in Kelvins. For example, with a dew-point temperature of 300.15K, the equation becomes: Ln(Es / 6.11) = (2.453 * 10^6 / 461) * ((1 / 273) - (1 / 300.15)). This becomes: Ln(Es / 6.11) = 1.76. Solving for Es, first raise each side by the power of the natural exponent e, to get rid of the natural log Ln. The equation becomes: Es / 6.11 = e^1.76; Ex = (e^1.76 * 6.11) = 35.5.

7. 7

Find the relative humidity by substituting the values for actual vapour pressure and saturation vapour pressure into the equation: Relative humidity = ((actual vapour pressure) / (saturation vapour pressure)) * 100%. For example, with an actual vapour pressure of 20.1 and a saturation vapour pressure of 35.5, the equation becomes: relative humidity = (20.1 / 35.5) * 100% = 56.62. Therefore, relative humidity is 56.62%.

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