Psychrometric Humidity Ratio Calculator

Humidity ratio W is the mass of water vapor carried per unit mass of dry air, and it follows directly from Dalton law of partial pressures applied to an ideal gas mixture. Treating moist air as dry air and vapor sharing the same volume and temperature, the mass ratio equals the molecular weight ratio times the pressure ratio. Water at 18.015 divided by dry air at 28.966 gives 0.621945, the vapor occupies partial pressure Pw, and the dry air occupies the remainder, so W equals 0.621945 times Pw divided by Patm minus Pw. Multiplying by 7,000 converts pounds of water per pound of dry air into grains per pound, the unit printed on North American psychrometric charts. Saturation pressure at the dry-bulb temperature comes here from an Antoine-type correlation, and multiplying it by relative humidity yields Pw. Because W is referenced to dry air rather than to the mixture, it is conserved through pure sensible heating or cooling and changes only when moisture is genuinely added or removed, which is what makes it the correct variable for latent load, coil selection, and desiccant work. Typical magnitudes: 75 degrees F at 50 percent relative humidity is about 0.0092 lb/lb or 65 grains per pound, while coastal air at 95 degrees F and 80 percent runs near 0.029 lb/lb or 200 grains. Barometric pressure is an explicit input because the same temperature and relative humidity at 5,000 feet produce a noticeably larger W than at sea level. The correlation degrades below freezing, where saturation must be taken over ice.

The physical foundation is John Dalton work in Manchester at the turn of the nineteenth century, which established that each gas in a mixture exerts its pressure independently and that the quantity of vapor air can hold depends on temperature rather than on the presence of the air itself. Saturation pressure data accumulated steadily through that century, and in 1888 Louis Charles Antoine published the three-constant logarithmic correlation between vapor pressure and temperature that still carries his name and is used in this calculator. Psychrometry became an engineering discipline in the early twentieth century. Willis Carrier, then working for the Buffalo Forge Company, presented Rational Psychrometric Formulae to the American Society of Mechanical Engineers in 1911, deriving the relations among wet-bulb temperature, vapor pressure, and moisture content and publishing the chart that made them usable at a drafting table. Richard Mollier developed the alternative enthalpy-moisture diagram favored across continental Europe. Responsibility for maintaining the reference formulations later passed to ASHRAE, which publishes them in the Handbook of Fundamentals with enhancement factors and tabulated properties for standard atmospheres, while the National Institute of Standards and Technology maintains the humidity standards used to calibrate measuring instruments. The grain, one seven-thousandth of a pound and originally a weight unit from the avoirdupois system, survived into this field because it produced conveniently sized whole numbers for building air.