The virtual temperature calculator answers one narrow question. Given a parcel of moist air at a known temperature, pressure and humidity, what temperature would a parcel of completely dry air have to be at the same pressure in order to have exactly the same density? That fictitious temperature is the virtual temperature, and it exists so that meteorologists can keep using the dry-air gas constant everywhere instead of tracking a gas constant that changes with humidity.
Arb Digital publishes several pages in this corner of atmospheric physics, and the boundaries between them are worth stating precisely. The air density calculator computes density directly, by splitting the air into a dry component and a vapour component and applying the gas law to each with its own constant — it never needs a virtual temperature and does not report one. The absolute humidity calculator reports the mass of vapour per cubic metre and grids the mixing ratio and vapour pressure alongside it, which are inputs to this page rather than outputs of it. What neither produces is the equivalent dry-air temperature, and that number is what makes buoyancy, lapse rate and sounding work tractable. This page produces it, shows the conversion chain that got there, and reports the density it implies so the two routes can be compared.
What This Virtual Temperature Calculator Does
Dry air and water vapour are different gases with different molar masses. Dry air averages about 28.96 grams per mole; water is 18.02. That is the whole physical story: a water molecule is lighter than the average air molecule it displaces, so replacing some of the air in a fixed volume at fixed pressure with vapour makes the parcel lighter. Humid air is less dense than dry air at the same temperature and pressure, which surprises almost everyone the first time they hear it.
Handling that properly means using a gas constant for the mixture that depends on how much vapour is present, and a variable gas constant is inconvenient in every equation it appears in. Virtual temperature is the standard workaround. Instead of adjusting the constant, you adjust the temperature: define Tv such that the dry-air gas constant applied at Tv gives the correct density of the moist parcel. Every subsequent equation — hydrostatic balance, the ideal gas law, buoyancy — then works with a single fixed constant.
The calculator accepts relative humidity, dew point, mixing ratio, specific humidity or vapour pressure, converts whichever you supply into a vapour pressure, and applies the definition. It reports the virtual temperature in Celsius and kelvin, the increment above the actual temperature, the mixing ratio and vapour pressure it derived along the way, and the moist air density that the virtual temperature implies.
How to Use It
- Enter the dry-bulb temperature. An ordinary thermometer reading in degrees Celsius, not a wet-bulb or apparent temperature.
- Enter station pressure. Use the pressure actually measured at the site. Sea-level-reduced pressure from a chart will give a wrong vapour fraction, particularly at altitude.
- Pick the moisture variable you have. Soundings usually give mixing ratio or dew point; surface observations usually give relative humidity. All routes converge on the same vapour pressure.
- Read the increment, not just the value. The difference between virtual and actual temperature is the number that tells you whether moisture matters here at all.
- Compare the two density bars. They show how much lighter the moist parcel is than dry air at the same temperature and pressure.
The Formula and a Worked Example
Written in terms of vapour pressure, the definition is exact:
Tv = T ÷ [1 − (e ÷ p)(1 − ε)]
where T is the absolute temperature, e the partial pressure of water vapour, p the total pressure and ε = Rd / Rv = 0.622, the ratio of the molar mass of water to that of dry air. The familiar approximation Tv ≈ T(1 + 0.608 q), with q the specific humidity as a fraction, follows from expanding that expression and is accurate to a few hundredths of a kelvin under ordinary conditions. This tool uses the exact form.
Saturation vapour pressure comes from the Buck relation, es = 6.1121 exp[(18.678 − T÷234.5)(T ÷ (257.14 + T))] with T in Celsius and es in hectopascals, which is the same relation the air density calculator uses so the two pages agree. Mixing ratio follows as w = ε e ÷ (p − e), and specific humidity as q = w ÷ (1 + w). The gas constants used here trace back to the molar masses and the universal gas constant published in the NIST reference on fundamental physical constants.
Work the default through by hand. At 30 °C, 1000 hPa and 80 per cent relative humidity, the saturation vapour pressure is 42.45 hPa, so e = 0.8 × 42.45 = 33.96 hPa. The mixing ratio is 0.622 × 33.96 ÷ (1000 − 33.96) = 0.02187, or 21.87 g/kg. The absolute temperature is 303.15 K, and (e÷p)(1−ε) = 0.03396 × 0.378 = 0.012838, so Tv = 303.15 ÷ 0.987162 = 307.09 K, which is 33.94 °C. The virtual increment is 3.94 K. Density from ρ = p ÷ (Rd Tv) is 100000 ÷ (287.058 × 307.09) = 1.1345 kg/m³, against 1.1492 kg/m³ for dry air at the same temperature — the moist parcel is 1.3 per cent lighter.
Why the Correction Is Small and Still Decides the Weather
Four kelvin sounds like a rounding error next to a daily temperature range, and for most purposes it is. The virtual increment matters because of where it is applied: to the density difference between a rising parcel and the environment it is rising through.
A convecting parcel accelerates upward in proportion to how much less dense it is than its surroundings. Those density differences are typically a fraction of a per cent. A one per cent density deficit is worth roughly three kelvin of virtual temperature excess, so a parcel that is moister than its environment but no warmer is still buoyant — and using actual temperature instead of virtual temperature in that comparison throws away a significant part of the signal. In warm, deep, moist environments the virtual correction can account for a meaningful fraction of the total buoyant energy available. That is why operational sounding analysis computes buoyancy from virtual temperature rather than temperature, and why the distinction is worth the arithmetic.
The correction also grows sharply with temperature, because saturation vapour pressure roughly doubles for every ten kelvin. At 0 °C saturated air has a virtual increment of about 0.6 K. At 30 °C saturated air is close to 5 K. Below freezing the correction is essentially negligible for any practical purpose, which is why it is easy to ignore in a temperate winter and impossible to ignore in the tropics.
The Three Temperatures That Get Confused
Virtual temperature sits in a family of derived temperatures that sound similar and mean entirely different things.
Virtual temperature is a density statement. It answers what dry air would need to be to weigh the same, at the same pressure. It is always at least as large as the actual temperature.
Potential temperature is a pressure statement. It answers what temperature a parcel would have if brought adiabatically to a reference pressure, usually 1000 hPa. It removes the effect of compression so parcels at different heights can be compared, and it says nothing about moisture. The two are routinely combined into virtual potential temperature, which does both jobs at once.
Wet-bulb temperature is an evaporation statement. It answers how cool a wetted thermometer becomes as water evaporates from it, and it is always lower than the actual temperature. It is a measurement, not a definition, and it is not a route to virtual temperature without first converting it into humidity. If your instrument gives wet bulb, convert to relative humidity or dew point with the relative humidity calculator before coming here, and use the dew point calculator if you need the saturation temperature itself.
Station Pressure, Altitude and Why It Bites
The vapour term in the definition is a ratio: e divided by p. That means the same absolute humidity produces a larger virtual increment at low pressure than at high pressure, because the vapour makes up a larger share of the total.
The practical trap is using sea-level pressure instead of station pressure. A weather report from a station a kilometre above sea level quotes a pressure reduced to sea level, which can be a hundred hectopascals above what the barometer actually reads. Entering that number understates the vapour fraction by about ten per cent and quietly shrinks the virtual increment. The same trap catches the density altitude calculator and every other page that needs a real local pressure. If you are working from an aviation report, the altimeter setting is a sea-level value and needs converting first. The relationship between height, pressure and standard atmosphere conditions is covered on the temperature at altitude calculator. For a general introduction to how the atmosphere is layered and measured, UCAR's Center for Science Education publishes an accessible overview of the layers of the atmosphere, and the derivation of the moisture variables used here appears in Penn State's METEO 300: Fundamentals of Atmospheric Science.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Entering sea-level pressure — the vapour term is a fraction of the total pressure, so a reduced pressure from a chart understates the correction at any station above sea level.
- Confusing mixing ratio with specific humidity — one is per kilogram of dry air and the other per kilogram of moist air. They differ by a couple of per cent in warm air, which is a meaningful slice of a four-kelvin correction.
- Expecting humid air to be denser — water vapour is lighter than the dry air it displaces, so virtual temperature is never below the actual temperature.
- Using virtual temperature where potential temperature belongs — one corrects for moisture, the other for pressure. Comparing parcels at different heights needs the second, and often both.
- Applying it below freezing and expecting a difference — saturation vapour pressure is tiny at low temperature, so the increment falls well under a kelvin and rounds away.
Related Free Tools From Arb Digital
For density computed directly from the partial pressures rather than through a virtual temperature, use the air density calculator. The absolute humidity calculator gives vapour mass per cubic metre along with the mixing ratio, the relative humidity calculator and dew point calculator convert between the common surface moisture variables, and the density altitude calculator turns a density into the altitude it corresponds to. For comfort and safety indices built on the same measurements, see the heat index calculator and the cloud base calculator. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
That page computes density directly, treating the air as a mixture of dry air and vapour and applying the gas law to each component with its own gas constant. It never forms a virtual temperature. This page produces the equivalent dry-air temperature itself, which is the quantity used in buoyancy, hydrostatic and sounding calculations so that a single fixed gas constant can be kept everywhere. The two are consistent and answer different questions.
Not for water vapour in air. Water has a lower molar mass than the average of dry air, so adding vapour at constant pressure lowers the density, and the equivalent dry-air temperature must therefore be higher. The increment is zero for completely dry air and grows with humidity. Suspended liquid water or ice would lower it, but that is a separate quantity called density temperature.
You can, and it gives the same answer. The reason virtual temperature exists is convenience: the dry-air gas constant appears in a great many atmospheric equations, and letting it vary with humidity would mean rewriting all of them. Folding the moisture correction into the temperature instead keeps every downstream equation unchanged with a single fixed constant.
Small in absolute terms and important where it is applied. Saturated air at 0 degrees Celsius has a virtual increment of roughly 0.6 kelvin; at 30 degrees Celsius it is close to 5 kelvin. It matters because it is used to compare a rising parcel against its environment, where the differences being resolved are themselves only a few kelvin.
Station pressure, meaning the absolute pressure your barometer actually reads at the measurement site. Sea-level-reduced pressure from a weather chart or an aviation altimeter setting has been adjusted upward for altitude, and using it makes the vapour fraction too small and the virtual increment too low. At sea level the two are nearly identical, so the error only appears with elevation.
Mixing ratio is the mass of water vapour per kilogram of dry air. Specific humidity is the mass of water vapour per kilogram of total moist air, so the same water is divided by a slightly larger number. They are related by q equals w divided by one plus w, and in warm humid air they differ by around two per cent, which is not negligible inside a correction of a few kelvin.
They correct for different things. Virtual temperature removes the density effect of moisture at fixed pressure. Potential temperature removes the effect of compression by bringing a parcel adiabatically to a reference pressure, usually 1000 hectopascals. Combining both gives virtual potential temperature, which is what is normally used when comparing parcels at different heights in a moist atmosphere.
This tool implements a standard published definition for teaching and estimation. It is not an operational forecasting product, and weather-critical decisions should rest on official observations and forecasts from a national meteorological service.
