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Humidity at a Glance

Most Relevant Equations with Sample Code

This summary provides on overview on the most-used humidity-related formulas. The sample code is optimized for microprocessors (e.g. the common logarithm “log10” is used rather than the natural logarithm “ln”). For an in-depth study of the equations please refer to our complimentary paper “Introduction to Humidity” available on www.sensirion.com/humidity.

1 Relative humidity

Condition: Constant absolute humidity (e.g. closed systems). RH1 RH2 t1 t2 m Tn relative humidity at position 1 relative humidity at position 2 temperature in °C at position 1 temperature in °C at position 2 17.62 243.12 °C

  t1 − t 2 RH 2 = RH 1 exp m ⋅ Tn (Tn + t 1 )(Tn + t 2 )   

Sample code:

RH2 = RH1*exp(4283.78*(t1-t2)/(243.12+t1)/(243.12+t2));

2 Dew point

Definition: The dew point is the temperature to which a given parcel of air must be cooled, at constant barometric pressure, for water vapor to condense into water.

 RH  m ⋅ t ln +  100%  Tn + t t d (t , RH ) = Tn ⋅   RH  m ⋅ t  m − ln +    100%  Tn + t 

Sample code:

td t RH m Tn

dew point temperature in °C actual temperature in °C actual relative humidity in % 17.62 243.12 °C

H = (log10(RH)-2.0)/0.4343+(17.62*t)/(243.12+t); td = 243.12*H/(17.62-H);

3 Absolute humidity

Definition: The absolute humidity is the mass of water vapor in a particular volume of dry air. The unit is g/m3.

 RH  m ⋅t  ⋅ A ⋅ exp   T + t   100%  n   d v (t , RH ) = 216.7 ⋅   273.15 + t      

Sample code:

dv t RH m Tn A

absolute humidity in g/m3 actual temperature in °C actual relative humidity in % 17.62 243.12 °C 6.112 hPa

dv = 216.7*(RH/100.0*6.112*exp(17.62*t/(243.12+t))/(273.15+t));

Version 1.0 – Aug. 2008

Humidity at a Glance

4 Mixing ratio

Definition: The mixing ratio is the mass of water vapor in a particular mass of dry air. The unit is g/kg.

r (t , RH ) =

622 ⋅ p−

 m⋅t  RH ⋅ A ⋅...