Dew Point (Magnus Approximation)

The dew point is the temperature air must be cooled to before its water vapour starts condensing. Unlike relative humidity, which is a ratio that swings all day as the temperature moves, the dew point is close to an absolute measure of how much water is actually in the air. That is why forecasters and HVAC technicians reach for it: 70 % humidity means something entirely different in November than in July, while a dew point of 20 °C means sticky everywhere on earth.

The formula is a Magnus fit, an empirical curve for saturation vapour pressure with coefficients chosen to match laboratory measurements. This page uses the Sonntag values $b = 17.62$ and $c = 243.12\,^\circ\mathrm{C}$ recommended by the World Meteorological Organization, good to about 0.1 °C between −45 and 60 °C. Other coefficient sets published by Tetens, Buck and Alduchov appear in textbooks and give answers a tenth of a degree apart, which is a fair statement of how well anyone knows this curve.

Two things fall straight out of the algebra. The dew point can never exceed the air temperature, since that would require more than 100 % humidity, and when the two are equal the air is saturated and fog or dew is imminent. Cooling a surface below the dew point is precisely how a cold glass sweats, why ductwork needs insulation, and how a dehumidifier works.