Dew Point from Relative Humidity

$DP = (B_1*(ln(( RH )/100) + (A_1* t )/(B_1 + t )))/(A_1 -ln(( RH )/100)-A_1* t /(B_1+ t ))$

$(t)"Ambient Temperature"$

$(RH)"Relative Humidity"$

The Science

This Dew Point Temperature equation computes the Dew Point Temperature given the Relative Humidity and ambient temperature. The Dew Point Temperature is the temperature air needs to cool to cause the water vapor already in the air to condense out as dew on surfaces. While there are many ways in which to estimate the Dew Point Temperature, Lawrence (2005) derived this formula based on the empirical formula by Magnus (1844) along with a definition of Relative Humidity. Constants A₁ and B₁ used in this equation were determined by Alduchov and Eskridge (1996). There are two different definitions of Relative Humidity. This formula assumes Relative Humidity is defined as the ratio of water vapor pressure (e) to the equilibrium vapor pressure over a plane of water ("saturation" vapor pressure (e_s)) converted to a percent. If the alternative definition of Relative Humidity based on the water vapor mixing ratio is used, then this equation may report a slight error of up to ~3% of the dew point depression.

The Math

The Dew Point Temperature from percent relative humidity formula is:

`DP (^oC) =(B₁*(ln(RH/100) + (A₁*t)/(B₁ +t)))/(A₁-ln(RH/100)-A₁*t/(B₁+t))`

where

DP is the dew point temperature
t is the ambient temperature °C
RH is the Relative Humidity
A₁ is a constant equal to 17.625
B₁ is a constant equal to 243.04 °C

Weather (Meteorology) Calculators

Heat Index: Approximates the heat index based on the temperature and relative humidity
Canadian Humidity Index (HUMIDEX): Computes the Canadian Humidity Index (HUMIDEX) based on the dry-bulb ambient temperature and the dew-point temperature.
Australian Apparent Temperature (AT): Computes the apparent temperature based on the dry ambient temperature, the relative humidity and the wind speed at ten meters.
Relative Humidity: Computes the relative humidity based on the actual density of vapor and the saturated density.
Dew Point from Relative Humidity: Computes the dew point based on the relative humidity and ambient temperature.
Summer Simmer Index: Computes the Summer Simmer Index based on the air temperature and relative humidity.
Wind Chill Index (North America): Computes the wind chill index based on the air temperature and the velocity of the wind.
Wet-Bulb Globe Temperature (WBGT): Computes the wet-bulb globe temperature index based on dry-bulb (air) temperature, globe thermometer temperature and the wet-bulb temperature.
Humature Index: Estimates the humidity index based on the temperature and dew point.
Antoine Equation: Computes the apparent vapor pressure of pure substances based on temperature and coefficients for the substance.
Barometric Formula (Tropospheric) calculator computes the normal barometric pressure based on the altitude (h) using the Exponential Atmosphere formula.
Planetary Temperature: Estimates a planet's temperature based on the luminosity of its star, distance to the star, average albedo and infrared optical depth of atmosphere.
Snow Water Equivalent (SWE): Computes the volume of liquid water contained in rain or snow pack defined by area, depth and snow type or rain.

References

Lawrence, M. G. (2005). The relationship between relative humidity and the dewpoint temperature in moist air: A simple conversion and applications. Bulletin of the American Meteorological Society, 86(2), 225-233.

Magnus, G. (1844). Versuche über die Spannkräfte des Wasserdampfs. Annalen der Physik, 137(2), 225-247.

Alduchov, O. A., & Eskridge, R. E. (1996). Improved Magnus form approximation of saturation vapor pressure. Journal of Applied Meteorology, 35(4), 601-609.