Dew Point Temperature Estimate (Magnus Formula)
Dew Point Temperature Estimate (Magnus Formula)
The dew point — the temperature to which air must be cooled for water vapor in it to begin condensing — is a practical, intuitive way to describe how much moisture air is holding, widely used in weather forecasting, building condensation risk checks, and HVAC design, and it can be estimated quickly from dry bulb temperature and relative humidity using the empirical Magnus formula rather than full psychrometric tables. Because the Magnus formula is a curve fit calibrated with temperature in Celsius and relative humidity as a plain percentage number, mixing in real physical units for either quantity would break the empirical constants — so both are treated here as plain numbers by convention, with the result likewise a plain number representing degrees Celsius.
The Magnus formula gives alpha = ln(RH/100) + a·T/(b+T), then the dew point is Td = b·alpha/(a - alpha). where T is the dry-bulb air temperature and RH is the relative humidity (both plain numbers by convention: T in Celsius, RH as a percentage), and a and b are empirical Magnus constants.
Inputs
a_mag := 17.27=17.27
b_mag := 237.7=237.7
T_air := 25=25
RH_air := 60=60
This intermediate term combines the log of the relative humidity fraction with a temperature-dependent term, packaging both moisture and temperature effects into the single variable the dew point formula is built from.
alpha_mag := ln(RH_air/100) + a_mag·T_air/(b_mag+T_air)=1.13
Solving the Magnus formula for temperature at the saturation condition gives the dew point — the temperature at which this same air, cooled with no change in moisture content, would become saturated.
Td_dew := b_mag·alpha_mag/(a_mag - alpha_mag)=16.68
Results
At 25°C and 60% relative humidity the Magnus formula gives a dew point close to 16.7°C, matching the commonly cited reference value for these conditions and confirming the correlation is being applied correctly. A dew point this far below the dry-bulb temperature (about 8°C of spread) indicates moderately dry comfortable air; as relative humidity climbs toward 100% the dew point converges on the dry-bulb temperature, and a dew point above roughly 20°C generally starts to feel humid and uncomfortable regardless of the actual air temperature. Dew point is also the temperature at which condensation will start forming on any surface that cold, which is the basis for condensation-risk checks on windows and cold water pipes.
Assumptions & limitations
- Empirical correlation valid over a limited temperature and humidity range (roughly 0–60°C).
- T and RH treated as plain numbers per the formula's Celsius/percent convention, not physical units.
- Assumes standard atmospheric pressure conditions.
- Not valid for extrapolation to conditions well outside typical atmospheric ranges.