Air Density Calculator — ρ from Temperature, Pressure & Humidity
Calculate the density of air at any temperature, atmospheric pressure and relative humidity. Useful for aeronautics, HVAC engineering, weather analysis and physics problems. The calculator uses the ideal gas law and the Magnus formula for vapour pressure.
Temperature unit
°C
hPa
%
Density of moist air at the given conditions
- 1
Temperature (K)
15 °C + 273.15 = 288.15 K - 2
Pressure (Pa)
1,013.25 hPa × 100 = 101,325 Pa - 3
Saturation vapour pressure
610.78 × 10^(7.5 × 15 ÷ (237.3 + 15)) = 1,705.23 PaMagnus formula gives the saturation vapour pressure at the given temperature. - 4
Actual vapour pressure
(50 ÷ 100) × 1,705.23 = 852.61 Pa - 5
Dry-air partial pressure
101,325 − 852.61 = 100,472.39 Pa - 6
Moist air density
100,472.39 ÷ (287.058 × 288.15) + 852.61 ÷ (461.495 × 288.15) = 1.2211
How does this calculator work?
Air density ρ = P_d/(287.058 × T_K) + e/(461.495 × T_K), where P_d is dry-air partial pressure (total P minus vapour pressure e from the Magnus formula) and T_K is temperature in Kelvin. ISA standard is 1.225 kg/m³ at 15 °C and 1013.25 hPa. Density falls with higher temperature, lower pressure, or higher humidity.
Formula
How this is calculated
Air density is calculated from the ideal gas law applied separately to the dry-air and water-vapour components of moist air. The total pressure P is split into the partial pressure of dry air P_d = P − e and the vapour pressure e, where e is found from the Magnus formula: e = 610.78 × 10^(7.5 T_C / (237.3 + T_C)) × (RH / 100). Each component contributes its own term to the density: ρ = P_d/(R_d × T) + e/(R_v × T), where R_d = 287.058 J/(kg·K) is the specific gas constant for dry air and R_v = 461.495 J/(kg·K) is the gas constant for water vapour.
Moist air is less dense than dry air at the same temperature and pressure because water molecules (M = 18 g/mol) are lighter than the average dry-air molecule (M ≈ 29 g/mol). This is why humid days feel heavier but the air is actually slightly less dense — a fact that matters in aviation (density altitude), ballistics and combustion engineering.
Assumptions and limitations: air is treated as an ideal gas, which is accurate to better than 0.1% at normal atmospheric conditions. The Magnus formula for saturation vapour pressure has a typical error below 0.1% in the range −40 °C to +60 °C. For pressures far from sea level (very high altitude or hyperbaric chambers) or for extreme temperatures, more precise equations of state (CIPM-2007, BIPM formula) should be used.
Frequently asked questions
Atmospheric pressure decreases with altitude because there is less air above pressing down. Lower pressure means fewer molecules per cubic metre — the ISA standard drops from 1.225 kg/m³ at sea level to about 0.909 kg/m³ at 3,000 m. Temperature also decreases with altitude (lapse rate ≈ 6.5 °C/km), which further reduces density. Both effects reduce lift on aircraft and combustion efficiency on engines.
A water molecule (H₂O, molar mass 18 g/mol) is lighter than the average dry-air molecule (mostly N₂ and O₂, average molar mass ≈ 29 g/mol). When water vapour replaces some dry-air molecules at the same total pressure, the average molecular mass of the mixture decreases, so density decreases. This counter-intuitive fact matters for meteorology — humid air rises more easily, helping drive thunderstorms.
Density altitude is the altitude in the ISA atmosphere that has the same air density as the actual conditions. On a hot, humid, high-elevation day, the air is much less dense than standard — a runway at Denver (1,600 m) on a 35 °C humid afternoon can have a density altitude of 3,000 m or higher. Aircraft and engines perform as if they were at that altitude, requiring longer takeoff rolls and reducing climb rates. Pilots use density altitude as a critical pre-flight safety check.
TG we-Calculate Editorial Team. (2026). Air Density Calculator — ρ from Temperature, Pressure & Humidity [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/air-density-calculator
TG we-Calculate Editorial Team. "Air Density Calculator — ρ from Temperature, Pressure & Humidity." TG we-Calculate. 2026. https://we-calculate.com/calculator/air-density-calculator.
TG we-Calculate Editorial Team, "Air Density Calculator — ρ from Temperature, Pressure & Humidity," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/air-density-calculator
@misc{wecalculate_air_density_calculator, title = {Air Density Calculator — ρ from Temperature, Pressure & Humidity}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/air-density-calculator}}, year = {2026}, note = {TG we-Calculate} }
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