Degree of Saturation (Moist Air)

Degree of saturation $\mu = W/W_s$ is the humidity ratio present divided by the humidity ratio the same air would have if it were saturated at the same temperature and pressure. It answers what sounds like the same question relative humidity answers, and it gives a slightly different number, and the gap between them is a genuinely useful thing to understand.

Both are proportions of this air's moisture against saturated air's moisture, but they measure with different rulers. Relative humidity is a ratio of PRESSURES, $\varphi = p_v/p_{ws}$. Degree of saturation is a ratio of MASSES. Because the humidity ratio has $(p - p_v)$ in its denominator, the two are related by $\mu = \varphi(p - p_{ws})/(p - \varphi p_{ws})$, and $\mu$ is always the slightly smaller of the pair. At 24 °C and 50 % RH at sea level, $\mu$ is 49.25 %. The gap widens as the air gets hot, because $p_{ws}$ becomes a larger fraction of the total pressure — at 40 °C and 50 % RH the two differ by nearly three points.

This matters when reading a chart you did not draw. Older psychrometric charts — and a number of European ones still in service — plot their curved family of lines as PERCENTAGE SATURATION, which is $\mu$. Nearly every modern chart plots relative humidity. The two families of lines look virtually identical, they are labelled almost identically, and they meet exactly at the 0 % and 100 % boundaries so there is no visual clue that anything differs in between. Read the legend before you trust an interpolated value.

Degree of saturation has one real advantage: it is linear in the quantity a coil actually moves. Since $W$ is what condenses out and $W_s$ is fixed by the temperature, $\mu$ tracks moisture content directly, which makes it convenient in humidification calculations where you are adding a known mass of water. Relative humidity keeps its place because materials — wood, paper, mould spores, human skin — respond to vapour pressure rather than to mass loading.

Both are PROPORTIONS, and this page types $\mu$ accordingly: a dimensionless quantity that carries a percent sign, not a humidity ratio. That is a real distinction. $W$ and $W_s$ are kilograms of water per kilogram of dry air and enter this page with a g/kg or grains-per-pound picker; their quotient is not water per kilogram of anything, and it would be meaningless to offer it in grains.

Getting $W_s$ is the step that catches people out, because it is not a lookup — it depends on pressure as well as temperature. Find the saturation vapour pressure at the dry-bulb temperature, then run it through the humidity-ratio relation at the barometric pressure you are actually at: $W_s = 0.62198 p_{ws}/(p - p_{ws})$. At 24 °C and sea level that gives 18.83 g/kg. At the same temperature in Denver it is nearer 22.5 g/kg, because the lower total pressure leaves more room for vapour. So the same air, unchanged, is a smaller fraction of saturation at altitude — one more reason altitude belongs in every psychrometric calculation rather than only in the density one.

A reading above 100 % means either that $W_s$ was evaluated at the wrong dry bulb — a common slip, since it must be the temperature the air is actually at and not the coil surface — or that the excess is genuinely already liquid, hanging as fog or running off the fins as condensate.