Explore atmospheric density effects with virtual temperature. Switch between humidity methods and unit systems easily. Validate results with formulas, examples, and export tools today.
| Case | T (°C) | p (hPa) | Moisture input | r (g/kg) | Tv (K) | Tv (°C) |
|---|---|---|---|---|---|---|
| 1 | 25 | 1000 | Mixing ratio | 10 | 300.02 | 26.87 |
| 2 | 10 | 950 | Relative humidity 70% | ~5.7 | 285.30 | 12.15 |
| 3 | 30 | 1013 | Dew point 22°C | ~16.7 | 306.80 | 33.65 |
Virtual temperature adjusts dry-bulb temperature so that moist air has the same density as dry air at the virtual temperature.
Mixing ratio from moisture variables (when needed):
Saturation vapor pressure uses a common Tetens-style exponential approximation over water.
Virtual temperature (Tv) is the dry-air temperature that would give the same air density as the actual moist air at the same pressure. Because water vapor is lighter than dry air, adding moisture lowers density, so Tv is typically higher than the measured air temperature.
At a fixed pressure, density is proportional to mean molecular weight. Replacing nitrogen and oxygen with water vapor decreases mean molecular weight, reducing density and increasing buoyancy. This correction matters for parcel calculations, thickness estimates, and stability diagnostics.
The exact form uses the mixing ratio r and the constant ε = 0.622. A common approximation is Tv ≈ T(1 + 0.61r) when r is small. For typical near-surface r values of 2–20 g/kg (0.002–0.020 kg/kg), the approximation is usually close, but the exact option is safer in humid air.
As a quick estimate, an r of 10 g/kg implies about a 0.61% increase in temperature in Kelvin. For T = 298.15 K (25°C), this is roughly 1.8 K. That difference can noticeably change computed density, buoyancy, and derived quantities like CAPE.
When you supply vapor pressure e and air pressure p, the calculator converts to mixing ratio using r = εe/(p − e). In practical weather data, p is often in hPa and e may be derived from dew point or relative humidity.
Relative humidity uses saturation vapor pressure computed from the air temperature, then multiplies by RH to obtain e. Dew point uses saturation vapor pressure at Td directly (e = es(Td)). Both routes end with the same r-to-Tv conversion, enabling consistent comparisons.
Tv appears in density calculations, buoyancy, and hydrostatic thickness relations. Many meteorological formulas use Tv (or virtual potential temperature) to represent the thermodynamic state more accurately than dry-bulb temperature alone, especially in warm and moist boundary layers.
For physical consistency, vapor pressure must be lower than total pressure, and specific humidity must be less than 1 kg/kg. Typical surface vapor pressures are a few to a few tens of hPa. If results look extreme, verify units and confirm pressure is entered correctly.
1) Is virtual temperature always higher than air temperature?
Usually yes, because water vapor reduces density. If the air is extremely dry (r ≈ 0), Tv and T are essentially the same within rounding.
2) Which input method should I choose?
Use the method that matches your data source. Radiosondes often provide pressure and humidity, stations provide RH, and thermodynamic tables may provide mixing ratio or specific humidity.
3) When should I use the exact option?
Choose exact when humidity is moderate to high, or when you need consistent density and buoyancy results. The approximation is fine for small r and quick checks.
4) Why does this calculator ask for pressure in some modes?
Pressure is required to convert vapor pressure to mixing ratio using r = εe/(p − e). Mixing ratio depends on how much water vapor exists relative to dry air.
5) What ranges are typical for mixing ratio?
Near the surface, r commonly ranges from about 2 to 20 g/kg. Dry continental air may be lower, while tropical maritime air can be higher.
6) Can Tv be used for buoyancy and stability calculations?
Yes. Tv improves density estimates used in buoyancy, thickness, and stability diagnostics. Many workflows go further by using virtual potential temperature for comparing parcels at different pressures.
7) My output looks unrealistic. What should I check first?
Confirm unit selections, especially hPa versus Pa, and ensure vapor pressure is less than total pressure. Also verify that temperature and dew point are sensible and not swapped.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.