How this instrument works
Virtual temperature answers a narrower question than 'how hot is the air': it asks what temperature perfectly dry air would need in order to match the density of the actual, water-vapor-laden sample at the same pressure. A water molecule (molar mass 18.02) is lighter than the nitrogen-and-oxygen mixture it displaces (molar mass 28.97), so swapping some dry air for vapor lowers density without moving the thermometer at all — and the ideal gas law only balances again if the temperature term is nudged upward to compensate. That upward nudge is Tᵥ.
The formula's shape traces straight back to the ideal gas law, p = ρRT, applied separately to dry air and to the moist mixture. Matching the two densities at equal pressure and solving for the equivalent dry-air temperature yields the exact relation Tᵥ = T(w + ε) ⁄ [ε(1 + w)], where ε = Rd ⁄ Rv = 0.622 is the ratio of the dry-air and water-vapor gas constants. Expanded as a series in the mixing ratio w and truncated after the first term, that collapses to Tᵥ ≈ T(1 + 0.61w) — a linear stand-in accurate to a few thousandths of a kelvin across the mixing ratios Earth's atmosphere actually produces, which is why forecasters and textbooks reach for the short form instead of the fraction.
The approximation is a vapor-only correction: it says nothing about cloud droplets or ice crystals riding in the same parcel, which add mass without adding gas molecules and so push real density the opposite way. That is why the hypsometric equation and CAPE soundings that lean on virtual temperature to compute layer thickness and updraft buoyancy switch to a related quantity, density temperature, once condensate is present. Push the mixing ratio input past roughly 0.04 kg/kg — wetter than any real surface air mass gets — and the linear formula starts to visibly diverge from the exact fraction it approximates.
- Enter Air temperature — the actual thermometer or sounding reading, in °C (switch to °F if that's your source).
- Enter Water vapor mixing ratio, kg/kg — mass of vapor per mass of dry air, from a sounding, psychrometric chart, or humidity sensor.
- Read Virtual temperature — it sits at or above the entered Air temperature, since a mixing ratio can't be negative.
- Carry that Virtual temperature into a hypsometric-equation or parcel-buoyancy calculation anywhere it calls for a dry-air temperature.
Worked example — a humid 25 °C afternoon
Take air reading 25 °C with a water vapor mixing ratio of 0.015 kg/kg — fifteen grams of vapor per kilogram of dry air, typical of a muggy coastal afternoon. Converting to kelvin, T = 298.15 K, and the formula gives Tᵥ = 298.15 × (1 + 0.61 × 0.015) = 298.15 × 1.00915 = 300.8780725 K.
Converting back to Celsius, Tᵥ = 27.7280725 °C, which this instrument computes to full precision even though the display rounds it. The air behaves, density-wise, as though it were completely dry at 27.73 °C instead of the 25 °C the thermometer shows — nearly 2.73 °C of density-equivalent warmth contributed by water vapor's lower molecular weight, enough to shift a thickness or buoyancy calculation that assumes dry air.
Questions
Why is virtual temperature always higher than the measured air temperature?
A parcel of moist air replaces some of its nitrogen and oxygen molecules, mass for mass, with lighter water vapor molecules (18.02 g/mol versus roughly 28.97 g/mol for dry air), so it packs less mass into the same volume than a dry parcel at the identical temperature and pressure. Warming dry air thins it out to match that lower mass — the 0.61w term only ever adds heat, since a mixing ratio can't be negative, so Tᵥ equals T only for perfectly dry air.
Where does the 0.61 coefficient come from?
It falls out of the exact relation Tᵥ = T(w + ε) ⁄ [ε(1 + w)], where ε = Rd ⁄ Rv = 0.622 is the ratio between the dry-air and water-vapor gas constants. Expanding that fraction as a series in w and stopping after the linear term gives Tᵥ ≈ T(1 + w(1 − ε)/ε) = T(1 + 0.608w), which textbooks and this instrument round to 0.61. The rounding barely matters, since Earth's atmospheric mixing ratios rarely exceed about 0.03 kg/kg.
How is mixing ratio different from specific humidity in this formula?
Mixing ratio w weighs water vapor mass against dry-air mass alone; specific humidity q weighs it against the total mass of the moist sample, so q = w ⁄ (1 + w). The two sit close enough at ordinary atmospheric values that some references quote Tᵥ = T(1 + 0.608q) instead of the 0.61w form used here — entering a specific-humidity figure into this instrument's mixing ratio field will read too low by roughly the small gap between w and q.
Why not just use the actual air temperature in dry-air equations?
Because relations like the hypsometric equation and the ideal gas law as commonly written are built around the dry-air gas constant, Rd, and moist air does not satisfy p = ρRdT at its own measured temperature. Substituting Tᵥ for T restores the balance, so a sounding's thickness calculation or a thunderstorm parcel's buoyancy check comes out right without rewriting the gas constant for every different water vapor content encountered.
Does virtual temperature account for cloud droplets or ice?
No — the formula only corrects for water vapor, a gas, not for liquid droplets or ice crystals suspended in the same air. Condensate adds mass to a parcel without adding gas molecules, pushing real density the opposite direction from vapor's effect. Soundings that need to include cloud water switch to a related figure, density temperature, which subtracts a liquid-water-content term rather than adding a vapor term.
What mixing ratio values are realistic to enter?
Surface air on Earth ranges from close to 0 kg/kg over cold, dry continents to roughly 0.020–0.030 kg/kg in humid tropical air, occasionally reaching 0.035–0.040 kg/kg in the warmest, most saturated conditions on the planet. A value above about 0.04 kg/kg is physically implausible at ordinary surface pressure and temperature and usually signals a units slip, such as typing grams per kilogram where kilograms per kilogram was expected.