About

Atmospheric pressure decreases non-linearly with altitude. The relationship follows the barometric formula derived from the hydrostatic equation and the ideal gas law. In the troposphere (below 11 km), the ICAO International Standard Atmosphere defines a temperature lapse rate L = 0.0065 K/m and sea-level conditions of T₀ = 288.15 K and P₀ = 101325 Pa. Getting the pressure wrong affects altimeter calibration, engine performance calculations, and cabin pressurization design. An error of 1 hPa corresponds to roughly 8.5 m of altitude error. This tool computes pressure using both the standard barometric formula (with lapse rate) and the simplified exponential model (isothermal assumption). Note: the barometric formula is valid only in the troposphere. Above 11 km the lapse rate changes and the stratospheric model applies. Real conditions deviate from ISA due to weather, latitude, and seasonal variation.

Formulas

The standard barometric formula for the troposphere (0 - 11 km) uses the temperature lapse rate to model pressure decrease:

P = P₀ × (1 − L × hT₀)^{g × MR × L}

The simplified exponential (isothermal) model assumes constant temperature throughout the column:

P = P₀ × exp(−g × M × hR × T)

Where: P = pressure at altitude Pa, P₀ = sea-level pressure (101325 Pa ISA), L = temperature lapse rate (0.0065 K/m), h = altitude above sea level m, T₀ = sea-level temperature (288.15 K ISA), T = temperature at altitude K (for isothermal model), g = gravitational acceleration (9.80665 m/s²), M = molar mass of dry air (0.0289644 kg/mol), R = universal gas constant (8.31447 J/(mol⋅K)). The exponent g × MR × L evaluates to approximately 5.2559 under ISA conditions.

Reference Data

Altitude	ISA Temp	ISA Pressure	Pressure	Density	Typical Context
-422 m	290.9 K	106,410 Pa	1050.4 hPa	1.274 kg/m³	Dead Sea shore
0 m	288.15 K	101,325 Pa	1013.25 hPa	1.225 kg/m³	Sea level (ISA reference)
500 m	284.90 K	95,461 Pa	954.61 hPa	1.167 kg/m³	Low hills, many cities
1,000 m	281.65 K	89,875 Pa	898.75 hPa	1.112 kg/m³	Low mountains
1,609 m	277.69 K	83,436 Pa	834.36 hPa	1.047 kg/m³	Denver, CO (Mile High City)
2,000 m	275.15 K	79,501 Pa	795.01 hPa	1.007 kg/m³	High plateaus
2,500 m	271.90 K	74,682 Pa	746.82 hPa	0.957 kg/m³	High-altitude cooking affected
3,000 m	268.65 K	70,109 Pa	701.09 hPa	0.909 kg/m³	Altitude sickness onset
3,658 m	264.37 K	64,557 Pa	645.57 hPa	0.851 kg/m³	La Paz, Bolivia
4,000 m	262.15 K	61,640 Pa	616.40 hPa	0.819 kg/m³	High-altitude trekking
5,000 m	255.65 K	54,020 Pa	540.20 hPa	0.736 kg/m³	Everest Base Camp
5,500 m	252.40 K	50,506 Pa	505.06 hPa	0.697 kg/m³	Approx. half sea-level pressure
6,000 m	249.15 K	47,181 Pa	471.81 hPa	0.660 kg/m³	Severe altitude sickness zone
7,000 m	242.65 K	41,060 Pa	410.60 hPa	0.590 kg/m³	High Himalayan peaks
8,000 m	236.15 K	35,600 Pa	356.00 hPa	0.525 kg/m³	Death zone begins
8,849 m	230.63 K	31,440 Pa	314.40 hPa	0.475 kg/m³	Summit of Mt. Everest
10,000 m	223.15 K	26,436 Pa	264.36 hPa	0.413 kg/m³	Unpressurized flight limit
11,000 m	216.65 K	22,632 Pa	226.32 hPa	0.364 kg/m³	Tropopause / Jet cruise altitude
12,192 m	216.65 K	19,330 Pa	193.30 hPa	0.311 kg/m³	Commercial airliner (40,000 ft)
15,000 m	216.65 K	12,044 Pa	120.44 hPa	0.194 kg/m³	Lower stratosphere

Frequently Asked Questions

The standard barometric formula assumes a constant temperature lapse rate L = 0.0065 K/m. At 11,000 m (the tropopause), the lapse rate drops to 0 K/m and the atmosphere becomes isothermal at 216.65 K. Above the tropopause, the exponential (isothermal) model must be used instead. This calculator warns you when input altitude exceeds the tropospheric boundary.

Near sea level, a 1 hPa difference corresponds to approximately 8.5 m (28 ft) of altitude. This is derived from the hypsometric equation. In aviation, altimeters are calibrated to the local QNH pressure setting. Failing to update this setting when flying between regions with different sea-level pressures causes systematic altitude errors that can violate separation minimums.

The barometric (hypsometric) model accounts for temperature decreasing linearly with altitude at rate L. This produces the power-law formula and is more accurate in the troposphere. The exponential (isothermal) model assumes constant temperature T throughout the air column, yielding a simpler exponential decay. The exponential model overestimates pressure at high altitudes because it ignores cooling. For altitudes below 3,000 m, both models agree within about 1%.

The ISA assumes T₀ = 288.15 K (15 °C) at sea level. On a hot day (35 °C), the air column expands, and pressure at a given geometric altitude is higher than ISA predicts. In cold conditions (−20 °C), the column contracts and pressure is lower. This calculator lets you override the sea-level temperature to model these deviations. Pilots call this density altitude and it directly affects aircraft performance.

Yes. Commercial aircraft cabins are typically pressurized to an equivalent altitude of 1,800 - 2,400 m (6,000 - 8,000 ft). Enter the cabin altitude to determine the cabin pressure differential relative to ambient. The difference between cabin pressure and outside pressure at cruise altitude (10,000 - 12,000 m) determines structural load on the fuselage. Typical differential is around 55 - 62 kPa.

The barometric formula uses the molar mass of dry air (M = 0.0289644 kg/mol). Water vapor has a lower molar mass (0.01802 kg/mol), so humid air is actually less dense than dry air at the same temperature and pressure. The effect is small, typically 1 - 2% on density, and even less on pressure at altitude. This calculator assumes dry air. For precise meteorological work, apply a virtual temperature correction.