Relative Humidity from Vapour Pressure

Relative humidity is the most quoted and least understood number in building science. Its definition is simple enough: the vapour pressure actually present divided by the saturation vapour pressure at the same temperature, $\varphi = p_v/p_{ws}$. The trouble is entirely in that denominator, because the denominator moves.

Relative humidity is a ratio to a moving target. The saturation pressure roughly doubles for every 11 °C of warming, so heating air without adding one molecule of water sends its RH down while the actual moisture content is completely untouched. Cool the same air and RH climbs, again with no moisture change at all, until at the dew point it reaches 100 % and water starts falling out. This means a relative humidity reading tells you almost nothing about how much water is present unless you also know the temperature — and it is quoted constantly as though it did.

Two practical consequences follow. First, dry winter indoor air is not caused by heating removing moisture; heating removes nothing. Outdoor air at −10 °C and 80 % RH carries about 1.6 g/kg, and once warmed to 21 °C that identical air reads near 11 % RH. Second, RH is nonetheless the right variable for a great many questions, because most of the things we care about respond to relative humidity rather than absolute content: mould germinates above roughly 80 % surface RH, wood and paper equilibrate their moisture content against RH, static electricity becomes a nuisance below about 30 %, and human comfort tracks it. Materials do not count grams; they respond to how close the air is to saturation at their own temperature.

The chronic field error is comparing an RH reading in one place with an RH reading in another at a different temperature and concluding something about moisture migration. Two rooms at 50 % RH and 18 °C and 24 °C hold quite different amounts of water, and the difference will drive vapour from one to the other. If you want to reason about where moisture is going, convert both to humidity ratio or dew point first — those are the quantities that compare directly across temperatures.

Readings above 100 % deserve a note rather than a refusal. Supersaturation is genuinely real: it is what fog and mist and the visible plume from a cooling tower are, and cloud physics runs on it. In a duct, though, it almost always means one of two things — either $p_{ws}$ was evaluated at the wrong temperature, which must be the same dry-bulb the vapour is sitting at, or the air really has hit its dew point and the excess is already condensing on the nearest cold surface.

One further subtlety in the definition. Strictly, relative humidity is defined against the saturation pressure of pure water, while the vapour in real air is very slightly more soluble than that idealisation allows; ASHRAE carries an enhancement factor of about 1.004 at ordinary conditions to account for it. Almost nobody applies it, because 0.4 % is well inside the accuracy of any field instrument — but it is one more reason to expect small disagreements between references and to stop hunting for the source of a half-percent gap.