*Relative humidity (RH) and temperature (T) data from an RH&T sensor like the DHT22 can be used to compute not only absolute humidity AH but also dewpoint temperature T*_{D}

There has been a fair amount of interest in my formula which computes AH from measured RH and T, since it adds value to the output of RH&T sensors. To further extend this value, I have developed another formula which computes dewpoint temperature T_{D} from measured RH and T.

Formula for computing dewpoint temperature T_{D}

In this formula (P Mander 2017) the measured temperature T and the computed dewpoint temperature T_{D} are expressed in degrees Celsius, and the measured relative humidity RH is expressed in %

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**Strategy for computing T**_{D} from RH and T

1. The dewpoint temperature T_{D} is defined in the following relation where RH is expressed in %

2. To obtain values for P_{sat}, we can use the Bolton formula^{[REF, eq.10]} which generates saturated vapor pressure P_{sat} (hectopascals) as a function of temperature T (Celsius)

These formulas are stated to be accurate to within 0.1% over the temperature range –30°C to +35°C

3. Substituting in the first equation yields

Taking logarithms

Rearranging

Separating T_{D} terms on one side yields

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**Spreadsheet formula for computing T**_{D} from RH and T

**1)** Set up data entry cells for RH in % and T in degrees Celsius.

**2)** Depending on whether your spreadsheet uses a full point (.) or comma (,) for the decimal separator, copy the appropriate formula below and paste it into the computation cell for T_{D}.

Formula for T_{D} (decimal separator = .)

=243.5*(LN(RH/100)+((17.67*T)/(243.5+T)))/(17.67-LN(RH/100)-((17.67*T)/(243.5+T)))

Formula for T_{D} (decimal separator = ,)

=243,5*(LN(RH/100)+((17,67*T)/(243,5+T)))/(17,67-LN(RH/100)-((17,67*T)/(243,5+T)))

**3)** Replace T and RH in the formula with the respective cell references. (see comment)

Your spreadsheet is now complete. Enter values for RH and T, and the T_{D} computation cell will return the dewpoint temperature. If an object whose temperature is at or below this temperature is present in the local space, the thermodynamic conditions are satisfied for water vapor to condense (or freeze if T_{D} is below 0°C) on the surface of the object.

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© P Mander August 2017

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