What virtual temperature is
Virtual temperature is a meteorological quantity: the temperature dry air would need to have in order to match the density of a given parcel of moist air at the same pressure. Water vapor (molecular mass about 18) is lighter than the nitrogen and oxygen it displaces (average about 29), so humid air is less dense than dry air at the same temperature and pressure. Virtual temperature folds that effect into a single number, always at least as high as the real air temperature.
Use it wherever air density or buoyancy matters and humidity cannot be ignored: comparing the buoyancy of a rising parcel with its surroundings, computing pressure from the hypsometric equation, correcting sonic anemometer readings, or checking density altitude on a humid day. You supply the air temperature and the water vapor mixing ratio, expressed in grams of vapor per kilogram of dry air.
Formula and variables
Tv = T × (1 + 0.61 × w)
- T is the actual air temperature in kelvin. The calculator converts Celsius or Fahrenheit input for you (K = °C + 273.15).
- w is the mixing ratio as a plain fraction, so grams per kilogram is divided by 1000 first.
- 0.61 comes from the ratio of the molecular masses of dry air and water vapor, roughly (1 / 0.622) - 1. It is the widely used first-order approximation.
- Tv is the virtual temperature in kelvin. The panel also converts it to °C and °F and shows Tv - T.
Worked example
Take an air temperature of 25 °C with a mixing ratio of 15 g/kg. First T = 25 + 273.15 = 298.15 K. The mixing ratio as a fraction is 15 / 1000 = 0.015, so the correction factor is 1 + 0.61 × 0.015 = 1.00915. Then Tv = 298.15 × 1.00915 = 300.88 K, which is 27.73 °C or 81.91 °F. The virtual temperature exceeds the real temperature by 2.73 K, meaning the humid air behaves like dry air nearly 3 degrees warmer.
Common mistakes and how to interpret the result
- Using relative humidity instead of mixing ratio. Relative humidity is not the same thing. Convert it to a mixing ratio first using temperature and pressure.
- Entering the mixing ratio as a percentage. The field expects g/kg. A typical warm, humid day is 10 to 20 g/kg, while cold dry air can be below 1 g/kg.
- Confusing virtual temperature with feels-like temperature. Virtual temperature is a density quantity and says nothing about heat index or comfort.
- Expecting a big difference in dry air. At low humidity the correction is a fraction of a degree, so Tv is close to T.