Why air density matters
The mass of air in a given volume determines how much lift a wing produces, how much power an engine makes, how far a baseball flies and how much drag a cyclist faces. It changes with temperature, pressure and humidity.
The formula
The calculator treats air as a mixture of dry air and water vapor:
- Saturation vapor pressure (Tetens): Es = 6.1078 × 10^(7.5 T ÷ (T + 237.3)) hPa.
- Actual vapor pressure: Pv = RH × Es.
- Density: ρ = (P − Pv) ÷ (287.058 × Tk) + Pv ÷ (461.495 × Tk), with pressures in pascals and Tk in kelvin.
- Density altitude: DA = 44,330.8 × (1 − (ρ ÷ 1.225)^0.234969) meters.
Worked example
At the standard sea-level conditions of 59 °F (15 °C), 29.92 inHg (1,013.25 hPa) and dry air, the density is 1.225 kg/m³ (0.0765 lb/ft³), 100% of standard, and the density altitude is zero.
Now take a summer afternoon in Denver: 90 °F, station pressure 24.9 inHg, 30% humidity. The density drops to about 0.96 kg/m³, only 78% of standard, and the density altitude climbs above 8,200 ft.
Effect of each factor
| Change | Effect on density |
|---|---|
| +10 °F (5.6 °C) | about −2% |
| −1 inHg (−34 hPa) | about −3.4% |
| From 0% to 100% humidity at 86 °F | about −1.5% |
| +1,000 ft of elevation | about −3% |
Humid air is lighter, not heavier, because water molecules are lighter than the nitrogen and oxygen they displace.
Density altitude for pilots
Aircraft performance depends on density altitude, not on the elevation printed on the chart. Every 1,000 ft of density altitude above sea level reduces engine power by roughly 3% for a normally aspirated engine and lengthens the takeoff roll. “High, hot and humid” days are the classic trap at mountain airports.
Other uses
- Baseball: a fly ball travels a few percent farther in thin air, one reason Coors Field in Denver is known as a hitter’s park.
- Cycling and running: lower density means less aerodynamic drag, which is why hour records are often attempted at altitude.
- HVAC and engines: fan airflow, combustion air and turbocharger maps are all corrected for density.
Which pressure to enter
Use the actual pressure at your location (station pressure). Weather reports usually give the altimeter setting or sea-level pressure, which is corrected to sea level and would overstate the density at altitude. The boiling point at altitude calculator can estimate the station pressure from your elevation.