What this calculator does
Air density measures how much mass is packed into a cubic metre of air, and it changes constantly with the weather. The density of air falls as it warms up, falls as pressure drops (which is why the air thins out at altitude), and falls very slightly as it gets more humid, because water vapour molecules are lighter than the nitrogen and oxygen they displace.
This calculator treats air as two overlapping gases sharing the same space: dry air and water vapour, each following the ideal gas law with its own specific gas constant. Adding their two partial pressures together gives a more accurate figure than treating air as a single dry gas, particularly on hot, humid days when the difference is largest.
The formula
Relative humidity and temperature first give the actual water vapour pressure, using the Tetens approximation for saturation vapour pressure. Subtracting that from total air pressure leaves the dry-air partial pressure. Each partial pressure is then divided by its own specific gas constant and the absolute temperature (kelvin), and the two results are added together to give the total air density.
| Term | Meaning |
|---|---|
| ρ (rho) | Air density, in kilograms per cubic metre. |
| Rd, Rv | Specific gas constants for dry air (287.05 J/(kg·K)) and water vapour (461.495 J/(kg·K)). |
| Psat | Saturation vapour pressure: the maximum water vapour pressure the air can hold at a given temperature before it condenses. |
The inputs explained
| Field | What to enter |
|---|---|
| Air temperature (°C) | The air temperature to calculate density at. |
| Air pressure (hPa) | Total air pressure, in hectopascals (the same units weather reports use; 1,013.25 hPa is standard sea-level pressure). |
| Relative humidity (%) | Relative humidity as a percentage. Set this to 0 for a dry-air-only figure. |
When to use it
Sizing an HVAC or ventilation system
Airflow equipment is rated by mass flow, not just volume, so the air density at the design temperature and altitude affects how much air a given fan or duct actually moves.
Aviation and drone performance
Aircraft and drones generate less lift and their engines produce less power in thinner air, which is why hot, high-altitude airports are the most demanding conditions for takeoff performance.
Ballistics and sports science
Projectile drag and the flight of a ball both depend on the density of the air they are moving through, so a shooter or a golfer at altitude sees a genuinely different result than at sea level.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the density of air change with temperature?
The same pressure and humidity, across a range of temperatures.
| Air temperature | Air density | Water vapour pressure |
|---|---|---|
| -10°C | 1.341 kg/m³ | 1.4 hPa |
| 0°C | 1.291 kg/m³ | 3.1 hPa |
| 10°C | 1.244 kg/m³ | 6.1 hPa |
| 20°C | 1.199 kg/m³ | 11.7 hPa |
| 30°C | 1.155 kg/m³ | 21.2 hPa |
| 40°C | 1.112 kg/m³ | 36.9 hPa |
How does the density of air change with pressure (altitude)?
A fixed temperature and humidity, across a range of air pressures, standing in for increasing altitude.
| Air pressure | Air density |
|---|---|
| 1013.25 hPa | 1.199 kg/m³ |
| 900 hPa | 1.064 kg/m³ |
| 800 hPa | 0.9454 kg/m³ |
| 700 hPa | 0.8266 kg/m³ |
| 600 hPa | 0.7078 kg/m³ |
| 500 hPa | 0.5889 kg/m³ |
Questions
Why does humid air weigh less than dry air, at the same temperature and pressure?
A water molecule (H₂O) is lighter than the nitrogen (N₂) and oxygen (O₂) molecules that make up most of dry air. When humidity rises, water vapour molecules displace some of that heavier nitrogen and oxygen at the same pressure, so the overall mixture ends up slightly lighter.
What is standard air density?
The commonly quoted figure of 1.225 kg/m³ is for dry air at 15°C and standard sea-level pressure of 1,013.25 hPa. Actual air density is rarely exactly this, since temperature, pressure and humidity all vary with weather and location.
Does this calculator account for altitude directly?
Not as a separate input, because altitude only matters through its effect on pressure. Enter the actual air pressure at the altitude in question (a weather station or aviation report will usually list it) rather than trying to convert altitude to density directly.
How big is the humidity effect compared with temperature and pressure?
Much smaller. Moving from 0% to 100% relative humidity at 20°C and standard pressure changes density by less than 1%, while a 30°C swing in temperature changes it by around 15%. Humidity is worth including for precision, but temperature and pressure dominate.
To compare against the density of liquid water instead of air, see the water density calculator. For density, mass and volume of any substance, use the density calculator.