Air Density Calculator
Calculate the density of air in kg/m³, lb/ft³ and other units from temperature, pressure and relative humidity. Enter the values and get partial pressures, molar mass and virtual temperature too.
Find the Density of Air from Temperature, Pressure and Humidity
Air Density Formula
Where:
- \(\rho\) — density of the moist air (kg/m³)
- \(p\) — total atmospheric pressure (converted to Pa)
- \(p_d\) — partial pressure of the dry air (Pa)
- \(p_v\) — partial pressure of the water vapour (Pa)
- \(T\) — absolute temperature (K)
- \(RH\) — relative humidity (%)
- \(e_s(T)\) — saturation vapour pressure over water (hPa), from the Magnus formula with \(T\) in °C
- \(R_d = 287.058\) J/(kg·K) — specific gas constant of dry air
- \(R_v = 461.495\) J/(kg·K) — specific gas constant of water vapour
The formula treats moist air as an ideal mixture of dry air and water vapour: each component contributes its own density according to the ideal gas law, using its own partial pressure and gas constant.
Air Density – Calculation Example
Example: air at 20 °C, standard sea-level pressure of 1013.25 hPa and 50 % relative humidity (the calculator's default values).
\[ e_s = 6.112\,\exp\!\left(\frac{17.62 \times 20}{243.12 + 20}\right) = 23.33\ \text{hPa} \\ p_v = 0.50 \times 23.33 = 11.66\ \text{hPa}, \quad p_d = 1013.25 - 11.66 = 1001.59\ \text{hPa} \\ T = 20 + 273.15 = 293.15\ \text{K} \\ \rho = \frac{100159}{287.058 \times 293.15} + \frac{1166}{461.495 \times 293.15} = 1.1904 + 0.0086 \]
Result: the air density is \(\rho \approx 1.1991\) kg/m³ (about 0.07486 lb/ft³). Completely dry air at the same temperature and pressure would weigh 1.2041 kg/m³, so the humidity makes this air about 0.42 % lighter.
How to use the calculator
- Enter the Air temperature (T) and pick its unit: °C, °F or K.
- Enter the Atmospheric pressure (p) and choose its unit: hPa, kPa, atm, inHg or mmHg. For standard sea-level conditions use 1013.25 hPa.
- Enter the Relative humidity (RH) in percent. Leave this field blank or enter 0 to compute dry air.
- Read the Air density (ρ) in kg/m³, g/L, lb/ft³, lb/in³ and oz/ft³, plus a comparison with dry air at the same conditions.
- Check the Moist air details table for the partial pressures, saturation vapour pressure, molar mass and virtual temperature.
What is air density and why does it vary?
Air density is the mass per unit volume of air, usually expressed in kilograms per cubic metre. Despite feeling weightless, a cubic metre of air at room temperature and sea-level pressure has a mass of about 1.2 kg. Density is not a fixed constant: it depends on temperature, pressure and humidity, and it changes constantly with the weather and with altitude.
The ideal gas law explains the two main effects. When pressure rises, molecules are pushed closer together and the air becomes denser. When temperature rises, the air expands and the same volume contains less mass, so hot air is less dense than cold air — the reason hot-air balloons rise and cold air sinks near the ground on winter nights.
Humidity works in the opposite direction to what many people expect: humid air is lighter than dry air. A molecule of water vapour (molar mass 18.0 g/mol) replaces heavier nitrogen and oxygen molecules (average 28.96 g/mol) in the mixture, so at the same pressure and temperature moist air has a lower density. At 30 °C and 100 % humidity the effect reaches roughly 1.5 %, which is small but measurable with precise instruments.
The result matters in many fields: aeronautics (lift, take-off distance, engine performance), motorsport and cycling (aerodynamic drag), ballistics, HVAC design, meteorology and the calibration of flow meters. Pilots, for example, use density altitude to quantify how much performance they lose on a hot day at a high-elevation airport.
Assumptions, limitations and practical tips
- Model: air is treated as an ideal-gas mixture of dry air and water vapour (a simplified CIPM-2007 approach). This is accurate to well under 0.5 % for everyday temperatures and pressures.
- Water vapour curve: the Magnus formula is used for saturation vapour pressure; it is accurate to about 0.2 % between roughly −45 °C and +60 °C. Above 100 °C at sea-level pressure, or near the dew point at very high humidity, results become less reliable.
- Pressure input: enter the actual (station) pressure, not the pressure reduced to sea level that weather reports usually quote. If you only have a sea-level value and you are at altitude, the result will be too high — pressure drops by about 12 hPa per 100 m near sea level.
- Other gases: the composition of dry air is assumed constant and CO₂ variations or pollution are neglected.
- Use in unit conversions: once you have the density, our Density Converter can translate it into any other density unit.
Related weather and air calculations
Relative humidity strongly influences how the air feels and how it behaves. To go deeper into the moisture side of the calculation, try the Dew Point Calculator or the Heat Index Calculator, which combine temperature and humidity to describe comfort. For the cold end of the scale, the Wind Chill Calculator estimates how cold the air feels when wind is factored in.
Frequently Asked Questions
What is a normal value for air density?
At sea level, 15 °C (59 °F) and standard pressure of 1013.25 hPa, dry air has a density of about 1.225 kg/m³ (0.0765 lb/ft³). In everyday conditions the value typically ranges from about 1.1 to 1.4 kg/m³. Cold, high-pressure winter weather gives the densest air, while hot, humid, high-altitude conditions give the least dense air. If your result falls far outside this range, double-check the units of your inputs.
How do I calculate air density by hand with the ideal gas law?
For dry air, use \( \rho = \frac{p}{R_d T} \) with \( R_d = 287.058 \) J/(kg·K). Convert pressure to pascals and temperature to kelvin: for example, at 101325 Pa and 293.15 K you get \( 101325 / (287.058 \times 293.15) \approx 1.204 \) kg/m³. For moist air, split the pressure into dry and vapour parts as shown on this page — treating the whole pressure as dry air overestimates the density slightly.
How do I convert air density between kg/m³ and lb/ft³?
Multiply kg/m³ by 0.062428 to get lb/ft³, or divide lb/ft³ by 0.062428 to go back. So 1.2 kg/m³ is about 0.0749 lb/ft³. Also useful: 1 kg/m³ equals 1 g/L and about 0.9988 oz/ft³, and standard air at 1.225 kg/m³ equals roughly 0.0765 lb/ft³ — a figure pilots often use for density altitude calculations.
How much does air density change with altitude?
Pressure drops by roughly 12 hPa per 100 m near sea level, so density falls quickly with height. At 1500 m the density is about 15 % lower than at sea level; at 3000 m it is down by roughly 30 %. Temperature usually also drops with altitude, which partly offsets the effect. If you cannot measure local station pressure, a barometric altimeter or a nearby weather station's reported pressure (corrected to your elevation) is a good source.
Why is humid air less dense than dry air?
It seems counterintuitive because humid air feels 'heavy', but water vapour molecules (molar mass 18.0 g/mol) are lighter than the nitrogen and oxygen they displace (average 28.96 g/mol). At fixed temperature and total pressure, replacing heavy molecules with light ones lowers the mixture's mass per volume. At 30 °C and 100 % humidity the effect is about 1.5 % — small, but enough for precision instruments, motorsport and ballistics to care about.
What are the most common mistakes when calculating air density?
The biggest one is entering the sea-level pressure from a weather report instead of the actual station pressure — at altitude this overestimates density by about 1 % per 80 m of elevation. Other frequent errors are forgetting to convert temperature to kelvin or pressure to pascals in manual calculations, and assuming humid air is denser than dry air. Also make sure the relative humidity is entered as a percentage (50, not 0.5).
What is density altitude and how does it relate to air density?
Density altitude is the altitude in the standard atmosphere at which the air density equals your actual density. Pilots use it because lift and engine power depend on density, not height. If your calculated density is 1.06 kg/m³, that corresponds to roughly 2500 m density altitude, meaning the aircraft performs as if it were at 2500 m even on the ground. Higher temperature, humidity or elevation all raise density altitude and reduce performance.