About

Air density (ρ) determines aerodynamic lift, engine combustion efficiency, HVAC load, and sound propagation speed. Miscalculating it by even 2% compounds into significant errors in drag coefficients, ballistic trajectories, and fuel-air mixture ratios. This calculator implements the Ideal Gas Law for dry air and extends it via Dalton's Law of partial pressures for moist air, using the Magnus-Tetens approximation for saturation vapor pressure e_s. Inputs accept multiple unit systems. Altitude correction applies the barometric formula assuming ISA lapse rate of 6.5 K/km below 11 km.

The tool assumes air behaves as an ideal gas, which holds within 0.1% accuracy for pressures below 10 atm and temperatures above −40 °C. At extreme cold or high pressure the compressibility factor Z deviates from 1 and real-gas equations (van der Waals) become necessary. Humidity correction matters most at high temperatures: at 35 °C and 100% RH, moist air is roughly 1.2% less dense than dry air at the same conditions.

Formulas

Dry air density from the Ideal Gas Law:

ρ = PR_d ⋅ T

For moist air, saturation vapor pressure is computed via the Magnus-Tetens approximation:

e_s = 6.1078 × 10^{7.5 ⋅ T_cT_c + 237.3}

Actual vapor pressure:

e = RH100 × e_s

Moist air density via Dalton's Law of partial pressures:

ρ = P − eR_d ⋅ T + eR_v ⋅ T

Pressure at altitude (troposphere, h < 11000 m):

P_h = P₀ ⋅ (1 − L ⋅ hT₀)^{g ⋅ MR ⋅ L}

Where ρ = air density kg/m³, P = absolute pressure Pa, T = absolute temperature K, R_d = 287.058 J/(kg⋅K) specific gas constant for dry air, R_v = 461.495 J/(kg⋅K) specific gas constant for water vapor, e_s = saturation vapor pressure hPa, RH = relative humidity %, T_c = temperature in °C, L = 0.0065 K/m temperature lapse rate, g = 9.80665 m/s², M = 0.0289644 kg/mol molar mass of dry air, R = 8.31447 J/(mol⋅K) universal gas constant, T₀ = 288.15 K ISA sea-level temperature, P₀ = 101325 Pa ISA sea-level pressure.

Reference Data

Altitude m	Temperature °C	Pressure hPa	Density kg/m³	Speed of Sound m/s
0	15.00	1013.25	1.2250	340.3
500	11.75	954.61	1.1673	338.4
1000	8.50	898.76	1.1117	336.4
1500	5.25	845.56	1.0581	334.5
2000	2.00	794.95	1.0066	332.5
2500	−1.25	746.83	0.9569	330.6
3000	−4.50	701.09	0.9091	328.6
3500	−7.75	657.64	0.8632	326.6
4000	−11.00	616.40	0.8191	324.6
4500	−14.25	577.28	0.7768	322.6
5000	−17.50	540.20	0.7361	320.5
5500	−20.75	505.06	0.6971	318.5
6000	−24.00	471.81	0.6597	316.5
6500	−27.25	440.35	0.6238	314.4
7000	−30.50	410.61	0.5895	312.3
7500	−33.75	382.48	0.5566	310.2
8000	−37.00	355.99	0.5252	308.1
8500	−40.25	331.06	0.4951	306.0
9000	−43.50	307.60	0.4663	303.8
9500	−46.75	285.56	0.4389	301.7
10000	−50.00	264.88	0.4127	299.5
10500	−53.25	245.49	0.3877	297.4
11000	−56.50	226.99	0.3639	295.2
12000	−56.50	193.30	0.3099	295.2
14000	−56.50	141.01	0.2261	295.2
16000	−56.50	103.52	0.1660	295.2
18000	−56.50	75.65	0.1216	295.2
20000	−56.50	55.29	0.0889	295.2
25000	−51.60	25.49	0.0401	298.4
30000	−46.64	11.97	0.0184	301.7

Frequently Asked Questions

Water vapor (molar mass 18.015 g/mol) is lighter than both nitrogen (28.014 g/mol) and oxygen (31.998 g/mol). When water vapor displaces these heavier molecules in a given volume, the total mass decreases. At 35 °C and 100% RH, moist air is approximately 1.2% less dense than dry air at identical temperature and pressure.

The ideal gas law assumes negligible intermolecular forces and molecular volume. For air, this holds within 0.1% for pressures below roughly 10 atm and temperatures above −40 °C. At cryogenic temperatures or pressures exceeding 50 atm, the compressibility factor Z deviates significantly from 1, and real-gas equations such as van der Waals or Peng-Robinson should be used.

The ISA model divides the atmosphere into layers. In the troposphere (0 - 11 km), temperature decreases linearly at 6.5 K/km. Above 11 km (lower stratosphere), temperature remains constant at −56.5 °C up to about 20 km. The pressure formula for an isothermal layer is exponential: P = P_b ⋅ exp(−gM(h − h_b) ÷ (RT_b)), which differs from the power-law form used in the troposphere.

If you supply a measured barometric pressure (e.g., from a local weather station already corrected to sea level, known as QNH), do not also apply altitude correction as this would double-count the effect. Use altitude correction only when starting from ISA sea-level standard pressure of 1013.25 hPa. If you have a station-level (uncorrected) pressure reading taken at your altitude, enter it directly and set altitude to 0.

Density altitude is the altitude in the ISA at which the air density equals the actual density at your location. High temperature, high humidity, and low pressure all increase density altitude. An aircraft at 1000 m on a hot humid day may experience a density altitude of 2500 m, meaning reduced engine power, lower propeller efficiency, and longer takeoff rolls. This calculator provides density altitude as a derived output.

The dry-air calculation uses R_d = 287.058 J/(kg⋅K), specific to the standard dry air mixture (78% N₂, 21% O₂, 1% Ar). For pure gases, replace with the appropriate specific gas constant: R_specific = R ÷ M where M is the molar mass. For example, pure CO₂ uses 188.92 J/(kg⋅K). The humidity correction is air-specific and should be disabled for other gases.