Dew Point from Humidity Ratio

The dew point is the temperature at which this air, cooled without gaining or losing any moisture, first reaches saturation and begins to condense. This page finds it by running the chain backwards: humidity ratio to vapour pressure, then vapour pressure through the Magnus fit to the temperature whose saturation pressure equals it.

Notice what is missing from the answer: the air's own temperature. The dew point depends only on how much water the air is carrying and the pressure it is carrying it at. Heat the air and its relative humidity falls while its dew point sits exactly where it was. That makes the dew point a direct proxy for absolute moisture content, expressed in the most useful possible units — degrees, which you can compare directly against any surface temperature in the building.

That comparison is the entire practical value. Any surface at or below the dew point will be wet. This is the number that decides whether a chilled-water pipe needs insulation, whether a supply duct will drip into a ceiling, whether a slab will be damp in the morning, and whether the inside of a window will run. In summer, indoor dew points above about 16 °C are where mould risk starts climbing regardless of what the relative humidity reads, which is why building scientists increasingly specify dew point rather than RH — it is a single number that means the same thing in every room of the building at once.

Forecasters use it for the same reason: a dew point below 10 °C feels dry, 16 °C is noticeably humid, 21 °C is oppressive, and above 24 °C is dangerous for outdoor work — and those thresholds hold whatever the air temperature happens to be, which is exactly what a relative humidity figure cannot do.

Two limits are worth knowing. Below freezing this becomes a FROST POINT: the vapour deposits directly as frost rather than condensing as dew, and saturation over ice is lower than over supercooled water, so a sub-zero answer from this page — which carries the liquid-water fit — is approximate and should go to a sublimation curve if the number matters. And because both links of the chain use the Alduchov–Eskridge coefficients, expect the usual third-digit disagreement with a chart drawn from a different fit. The catalog's other dew-point page reaches the same quantity from relative humidity using the WMO coefficient set, and the two will differ by a few hundredths of a degree. Neither is wrong.

The pressure term is easy to overlook and does real work. Because the vapour pressure produced by a given humidity ratio scales with the total pressure, the SAME air carried up a mountain has a lower dew point than it had at the bottom — 12 g/kg condenses at 15 °C when the barometer reads 89.9 kPa, but not until 16.9 °C at sea level. That matters on any comparison between a measurement taken at altitude and a table printed for sea level.

One last framing worth carrying away. Humidity ratio, vapour pressure and dew point are three spellings of the same fact — how much water this air contains. Relative humidity and degree of saturation are a different kind of statement: that fact divided by a temperature-dependent ceiling. The first three stay put when you heat the air and the last two do not, and almost every confusion in psychrometrics comes from treating a member of one group as though it belonged to the other.