How this instrument works
Saturation vapor pressure, Pws, is the maximum pressure water vapor can exert in air at a given temperature before it starts condensing out as liquid. It rises steeply and non-linearly with temperature because the underlying physics, the Clausius–Clapeyron relation, has no simple closed-form solution. In 1930 the meteorologist O. Tetens published an exponential fit, Pws = 0.6108·e^(17.27T ⁄ (T+237.3)), that reproduces the true curve to within about 1% across the range most weather and engineering work cares about, 0 °C to 50 °C.
Multiply Pws by relative humidity to get Pv, the vapor pressure actually present, then compare its mass share against dry air's: w = 622·Pv ⁄ (P−Pv). The subtraction matters — total pressure P is the sum of dry-air pressure and vapor pressure, Dalton's law of partial pressures, so the vapor's own share has to come out of P before the ratio is fair. The constant 622 is 1000 times the ratio of water's molar mass to dry air's, converting a pressure ratio into grams of vapor per kilogram of dry air.
Mixing ratio's whole appeal is what it ignores: temperature. Warm a sealed parcel of air with no water added and its relative humidity drops even though nothing about its moisture content changed; mixing ratio reads exactly the same before and after. That stability is why the Tetens constants used here, fitted for saturation over liquid water, quietly stop applying below 0 °C, where ice rather than liquid sets the equilibrium — a separate ice-phase formula with different constants covers that range.
- Enter Air temperature in °C — the reading that drives the Tetens saturation formula.
- Enter Relative humidity as a percent, 0 to 100, of the air's current moisture against its capacity at that temperature.
- Enter Atmospheric pressure in kPa; use 101.325 for standard sea level, or your local station pressure at altitude.
- Read Saturation vapor pressure (Pws), the intermediate result, then read Mixing ratio for the final answer in grams of water vapor per kilogram of dry air.
Worked example — 25 °C air at 50% relative humidity
Take air at 25.0 °C, 50% relative humidity, and standard sea-level pressure of 101.325 kPa. The Tetens formula first gives saturation vapor pressure: Pws = 0.6108·e^(17.27×25 ⁄ (25+237.3)) = 3.16778 kPa, the ceiling this air could hold before water started condensing out of it.
Actual vapor pressure follows from relative humidity: Pv = 3.16778 × 0.50 = 1.58389 kPa. Feeding that into w = 622·Pv ⁄ (P−Pv) = 622 × 1.58389 ⁄ (101.325 − 1.58389) returns 9.87736 g of water vapor per kilogram of dry air — the figure a meteorologist would log to track this air mass, unaffected by whatever the thermometer does next.
Questions
Why does mixing ratio use grams per kilogram while forecasts quote percent humidity?
Relative humidity is a ratio of how full the air is against its capacity at the current temperature, so it rises and falls with temperature alone even when no water is added or removed. Mixing ratio instead weighs the vapor's mass against dry air's mass directly, so it holds steady through a temperature swing. Forecasters tracking one air mass across a day, or up through a rising cloud, need that steadiness — percent humidity alone would make it look like moisture appeared or vanished.
What is the Tetens formula and where does it come from?
It is an empirical fit, published by O. Tetens in 1930, standing in for the Clausius–Clapeyron relation that governs how saturation vapor pressure rises with temperature. That underlying physics has no clean closed-form solution; Tetens's exponential, Pws = 0.6108·e^(17.27T⁄(T+237.3)), reproduces it to roughly 1% between 0 °C and 50 °C, close enough for weather work and HVAC sizing without solving a differential equation each time.
Why does the formula subtract Pv from atmospheric pressure instead of just dividing by P?
Total atmospheric pressure is the sum of dry air's pressure and water vapor's own partial pressure, by Dalton's law. To weigh vapor mass against dry-air mass alone, vapor's share Pv has to be removed from the total first, leaving P−Pv as the true dry-air pressure. Dividing by P instead would silently overstate the dry-air amount and understate the mixing ratio, an error that grows larger as humidity climbs toward saturation.
Does this calculator still work below freezing or at high altitude?
The constants 17.27 and 237.3 are fitted for saturation over liquid water and lose accuracy below 0 °C, where vapor equilibrates against ice instead — a separate ice-phase Tetens variant with different constants covers that range. Altitude is not a problem: enter the lower local atmospheric pressure directly, since the formula only assumes the constant 622, which comes from a fixed molar-mass ratio and holds at any elevation.
Who actually reads mixing ratio instead of relative humidity?
Meteorologists plot it on skew-T diagrams to trace a rising air parcel whose relative humidity climbs toward 100% purely from cooling, with mixing ratio confirming no moisture was actually added. HVAC engineers size dehumidification equipment in grams of water removed per kilogram of air handled, and grain-storage or greenhouse operators use it to judge how much moisture a ventilation airstream truly carries rather than how close it sits to saturation.
Why is the constant 622 used instead of 0.622?
Both express the same physics: 0.622 is the ratio of water's molar mass, about 18.02 g/mol, to dry air's, about 28.97 g/mol, which converts a vapor-to-dry-air pressure ratio into a mass ratio. Multiplying by 1000 and writing it as 622 simply delivers the answer directly in grams per kilogram, the unit meteorologists conventionally read mixing ratio in, instead of kilograms per kilogram.