Virtual Temperature Calculator — Moist Air Density
Enter air temperature, relative humidity and station pressure to compute the virtual temperature — the temperature a parcel of dry air would need to have the same density as the actual moist air.
°C
%
hPa
Tv is always ≥ T because moist air is less dense than dry air at the same temperature and pressure.
- 1
Saturation vapour pressure (eₛ)
6.1078 × exp(17.2694 × 20 ÷ (20 + 237.29)) = 23.382Tetens formula: maximum water vapour pressure the air can hold at this temperature. - 2
Actual vapour pressure (e)
(60 ÷ 100) × 23.382 = 14.029 - 3
Mixing ratio (w)
0.622 × 14.029 ÷ (1,013.25 − 14.029) = 0.008733Mass of water vapour per kg of dry air (kg/kg). - 4
Virtual temperature (Tv)
293.15 × (1 + 0.008733 ÷ 0.622) ÷ (1 + 0.008733) − 273.15 = 21.54
How does this calculator work?
Virtual temperature Tv = T(K) × (1 + w/0.622) / (1 + w), where w is the mixing ratio in kg/kg derived from relative humidity and station pressure. Tv is always ≥ T because moist air is less dense than dry air; the excess is typically 0.5–5 K under normal atmospheric conditions. Meteorologists use Tv to simplify buoyancy calculations without tracking moisture separately.
Formula
How this is calculated
Water vapour (H₂O, molar mass ≈ 18 g/mol) is lighter than dry air (effective molar mass ≈ 28.97 g/mol), so a parcel of moist air at the same temperature and pressure is less dense than dry air. The virtual temperature Tv is a convenient fiction: it is the temperature at which a dry air parcel would have the same density as the actual moist air. Because Tv always equals or exceeds T (moist air appears warmer to a density-based instrument), meteorologists use it to simplify the equation of state and buoyancy calculations without tracking water-vapour concentration separately.
The calculation proceeds in four steps. (1) The Tetens formula gives the saturation vapour pressure es = 6.1078 × exp(17.2694 T / (T + 237.29)) hPa from the Celsius temperature T. (2) The actual vapour pressure is e = (RH/100) × es. (3) The mixing ratio w = 0.622 × e / (P − e) in kg/kg expresses the mass of water vapour per kilogram of dry air. (4) The exact virtual temperature formula Tv(K) = T(K) × (1 + w/0.622) / (1 + w) converts back to Celsius. For typical atmospheric mixing ratios (< 30 g/kg) the simpler approximation Tv ≈ T + 0.608 × T(K) × w differs by less than 0.1 K.
Virtual temperature is widely used in convective meteorology: a rising air parcel is positively buoyant when its Tv exceeds that of the surrounding environment (the basis of convective available potential energy, CAPE). It also enters the density altitude calculation used in aviation and the derivation of the Lifted Index. Station pressure — not sea-level pressure — must be used because density is computed at the actual elevation of the air parcel.
Frequently asked questions
Water vapour is lighter than dry air, so adding moisture to air at constant T and P makes the parcel less dense. To restore that density with dry air, you would need to heat it up — that higher equivalent temperature is the virtual temperature. The excess Tv − T is usually less than 5 K for typical atmospheric conditions.
Dew-point temperature is the temperature to which air must be cooled at constant pressure for condensation to begin — it indicates moisture content directly. Virtual temperature is the temperature dry air would need to match moist air's density — it is used in buoyancy and density calculations, not as a moisture indicator.
Always use actual station (barometric) pressure measured at your location, not the sea-level pressure reported by weather services. Sea-level pressure is corrected upward to remove elevation effects and would give incorrect mixing ratios and virtual temperatures for locations above sea level.
Also known as
TG we-Calculate Editorial Team. (2026). Virtual Temperature Calculator — Moist Air Density [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/virtual-temperature-calculator
TG we-Calculate Editorial Team. "Virtual Temperature Calculator — Moist Air Density." TG we-Calculate. 2026. https://we-calculate.com/calculator/virtual-temperature-calculator.
TG we-Calculate Editorial Team, "Virtual Temperature Calculator — Moist Air Density," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/virtual-temperature-calculator
@misc{wecalculate_virtual_temperature_calculator, title = {Virtual Temperature Calculator — Moist Air Density}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/virtual-temperature-calculator}}, year = {2026}, note = {TG we-Calculate} }
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