Hong Life CalculatorsUnderstanding the virtual temperature calculator — concept and principle
Moist air is lighter than dry air at the same temperature and pressure. Meteorologists handle this with the virtual temperature: the temperature dry air would need to have the same density. This calculator finds the virtual temperature from air temperature and water-vapour mixing ratio, and uses it to give the moist-air density at your pressure.
How it is calculated
Tv = T × (1 + r ÷ ε) ÷ (1 + r)
Approximation: Tv ≈ T × (1 + 0.61 r)
Specific humidity q = r ÷ (1 + r)
Density ρ = p ÷ (Rd × Tv)
- T in kelvin (°C + 273.15), r mixing ratio in kg/kg (g/kg ÷ 1000), ε = 0.622, Rd = 287.05 J/(kg·K), p in Pa (hPa × 100).
The principle
A water molecule (about 18 g/mol) is lighter than the average air molecule (about 29 g/mol). When water vapour replaces some of the air at the same pressure, the mixture's average molecular mass falls and so does its density. The ratio ε = 0.622 is the ratio of these molecular masses. Rather than using a different gas constant for every humidity, meteorologists keep the dry-air gas law and raise the temperature instead: a higher temperature also lowers density. That adjusted value is Tv. Because buoyancy depends on density, Tv is what matters for whether a parcel of air rises.
Worked example
Default inputs: 30 °C, mixing ratio 20 g/kg, pressure 1013.25 hPa.
- T = 303.15 K, r = 0.020.
- Tv = 303.15 × (1 + 0.020 ÷ 0.622) ÷ 1.020 = 303.15 × 1.03215 ÷ 1.020 = 306.76 K = 33.61 °C.
- Excess Tv − T = 3.61 °C; the simple approximation gives 33.7 °C.
- Specific humidity = 0.020 ÷ 1.020 = 19.61 g/kg.
- Moist-air density = 101,325 ÷ (287.05 × 306.76) = 1.1507 kg/m³, compared with 1.1644 kg/m³ for dry air.
| Air temperature (°C) | Virtual temperature (°C) |
|---|---|
| 7.5 | 10.84 |
| 15 | 18.43 |
| 22.5 | 26.02 |
| 30 | 33.61 |
| 37.5 | 41.2 |
| 45 | 48.79 |
| 60 | 63.97 |
How to read the result
The virtual temperature excess is small in cold, dry air (a fraction of a degree) and can reach several degrees in hot, humid tropical air. That difference affects buoyancy calculations, thunderstorm instability indices and aircraft performance: humid air gives lower density, so aircraft need longer take-off runs, which is why density altitude calculations include humidity.
Common mistakes
- Entering the mixing ratio in g/kg into a formula that expects kg/kg.
- Using °C instead of kelvin in the ratio.
- Confusing mixing ratio with relative humidity; convert humidity to mixing ratio first.
- Assuming moist air is heavier because it "feels heavy".
Frequently asked questions
Is humid air really lighter than dry air?
Yes, at the same temperature and pressure, because water molecules are lighter than nitrogen and oxygen molecules.
What is a mixing ratio?
The mass of water vapour per mass of dry air, often in g/kg.
How accurate is Tv ≈ T(1 + 0.61r)?
Very close at ordinary humidities; here it differs by under 0.1 °C.
Where is virtual temperature used?
In atmospheric soundings, buoyancy and stability analysis, and computing air density for aviation.
Sources: American Meteorological Society, Glossary of Meteorology, "Virtual temperature"