Virtual temperature (Tv) is the temperature of dry air that has the same density as moist air at the same pressure. Because water vapor is lighter than dry air, Tv is always ≥ the actual temperature. This tool computes Tv from relative humidity, dew point, specific humidity, or mixing ratio — in both directions (forward & inverse).
Anchor example (verified high-precision): T = 30 °C, RH = 70%, p = 1013.25 hPa → es = 42.4558 hPa, e = 29.7190 hPa, q = 18.4480 g/kg, Tv = 306.5614 K (33.4114 °C).
Results will appear here along with the intermediate calculation chain.
Results will appear here along with the intermediate calculation chain.
Results will appear here along with the intermediate calculation chain.
Results will appear here along with the intermediate calculation chain.
Relation: q = r/(1+r) and r = q/(1−q).
Shows why virtual temperature is useful: at the same T and p, moist air is lighter than dry air.
Results will appear here.
1. Saturation vapor pressure (Tetens/Magnus, Alduchov & Eskridge 1996 coefficients over water):
es(T) = 6.112 × exp(17.67 × T / (T + 243.5)) — T in °C, es in hPa.
2. Actual vapor pressure: from RH: e = RH × es / 100; from dew point: e = es(Td).
3. Specific humidity: q = 0.622 × e / (p − 0.378 × e) (kg/kg).
4. Virtual temperature: Tv = TK × (1 + 0.61 × q) — TK absolute temperature (K).
5. Density: ρ = p / (Rd × T) with Rd = 287.058 J/(kg·K); for moist air use Tv as T.
References: Tetens, O. (1930) Über einige meteorologische Begriffe; Alduchov, O. A. & Eskridge, R. E. (1996) Improved Magnus form approximation of saturation vapor pressure, J. Appl. Meteor.; standard meteorological Tv definition (WMO).
Virtual temperature (Tv) is the temperature of dry air that has the same density as moist air at the same pressure. Because water vapor molecules (H2O, 18 g/mol) are lighter than nitrogen/oxygen molecules (~28.8 g/mol), moist air is always lighter than dry air at the same temperature and pressure — so Tv is always ≥ the actual temperature. Formula: Tv = TK × (1 + 0.61 × q). Example: T = 30 °C, RH = 70%, p = 1013.25 hPa → Tv = 306.5614 K (33.4114 °C), i.e. 3.41 °C higher than the actual temperature.
Four steps: (1) saturation vapor pressure via Tetens es = 6.112 × exp(17.67 × T/(T + 243.5)) (T in °C, result in hPa); (2) actual vapor pressure e = RH × es / 100; (3) specific humidity q = 0.622 × e / (p − 0.378 × e); (4) Tv = (T + 273.15) × (1 + 0.61 × q). Anchor example: es = 42.4558 hPa → e = 29.7190 hPa → q = 18.4480 g/kg → Tv = 306.5614 K.
Ideal gas law: ρ = p / (Rd × T). For moist air, T is replaced with Tv. Example: T = 30 °C, p = 1013.25 hPa, RH = 70% → moist air ρ = 1.1514 kg/m³ vs dry air ρ = 1.1644 kg/m³ — a difference of -1.1128%. This is why meteorology uses Tv: a single “substitute” temperature makes air-parcel buoyancy calculations simple.
Actual vapor pressure equals the saturation vapor pressure at the dew point: e = es(Td) — plug Td into the Tetens formula, then continue to q and Tv as usual. Example: T = 30 °C, Td = 24 °C → e = 29.8325 hPa (≈ 70.27% RH). Mode 2 of this calculator also works in reverse: finding Td from a T and Tv pair.
temperature-converter is a temperature unit conversion hub (°C/°F/K/°R/°Ré) — not meteorology. This page computes meteorological virtual temperature Tv = T(1 + 0.61q) for buoyancy/atmosphere analysis. For aviation density altitude (which uses Tv as an internal humidity correction step), use density-altitude-lab.
Air-parcel buoyancy calculations, storm convection energy (CAPE), aviation density altitude, altimeter corrections, and numerical weather models — all use Tv so the ideal gas law stays valid for moist air.
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