Air Pressure at Altitude Calculator

Calculates atmospheric pressure, temperature, and air density at a given altitude using the barometric formula for the standard atmosphere (troposphere, 0 to 11,000 m).

Quick Facts

Formula
P = P₀ × (1 − L·h/T₀)^(gM/RL)
The ISA barometric formula, assuming a fixed lapse rate L = 0.0065 K/m and valid through the troposphere (0-11,000 m).
Standard atmosphere
1013.25 hPa, 15°C at sea level
Default inputs use the ICAO standard; enter your local sea-level pressure and temperature for a closer real-world match.

Your Results

Calculated
Pressure at altitude
-
Absolute atmospheric pressure (hPa)
Pressure ratio
-
Multiples of standard sea-level pressure (1 atm)
Temperature at altitude
-
Using the standard lapse rate of 6.5°C per 1,000 m
Air density
-
Density of dry air at this pressure and temperature

Ready

Set an altitude and sea-level conditions, then press Calculate.

About the Air Pressure at Altitude Calculator

Atmospheric pressure decreases with altitude because there is progressively less air above you pushing down. This calculator applies the barometric formula from the International Standard Atmosphere (ISA) — the same model used in aviation, meteorology, and engineering — to estimate pressure, temperature, and density at any height in the troposphere.

The formula

For the troposphere (0 to about 11,000 m / 36,089 ft), the standard barometric formula is:

  • P = P₀ × (1 − L·h / T₀)gM/RL, where P₀ is sea-level pressure, T₀ is sea-level temperature in kelvin, h is altitude in meters, L is the standard temperature lapse rate (0.0065 K/m), g is standard gravity (9.80665 m/s²), M is the molar mass of dry air (0.0289644 kg/mol), and R is the universal gas constant (8.31447 J/(mol·K)).
  • Temperature at altitude: T = T₀ − L × h — temperature falls linearly at the standard lapse rate.
  • Air density: found from the ideal gas law, ρ = P / (Rspecific × T), using the specific gas constant for dry air (287.05 J/(kg·K)).

Reading the result

The pressure ratio compares your result to standard sea-level pressure (1013.25 hPa = 1 atm). A ratio near 1.0 means little altitude effect; a ratio well below 1.0 means meaningfully thinner air — relevant for aircraft performance, boiling points, and physiological effects at elevation. Because both pressure and temperature drop with height, air density falls even faster than pressure alone, which is why aircraft and engines lose performance at altitude.

Assumptions and limits

The formula assumes dry air, a constant lapse rate of 6.5°C per 1,000 m, and standard atmospheric composition. Real-world weather (humidity, temperature inversions, storm systems) causes actual pressure to deviate from this idealized model, and the fixed lapse rate no longer applies above roughly 11,000 m, where the stratosphere begins and temperature stops decreasing with height.

Frequently Asked Questions

What formula does this calculator use?
It uses the barometric formula from the International Standard Atmosphere (ISA) model: P = P0 x (1 - L x h / T0) ^ (g x M / (R x L)), where P0 is sea-level pressure, T0 is sea-level temperature in kelvin, L is the standard temperature lapse rate of 0.0065 K/m, h is altitude, g is gravitational acceleration, M is the molar mass of dry air, and R is the universal gas constant. This is the same model used in aviation altimetry and meteorology for the troposphere.
Why does air pressure drop as altitude increases?
Atmospheric pressure at any height equals the weight of the air column above it. As you go up, less air remains overhead, so pressure decreases. The decrease is not linear -- it falls off exponentially, dropping fastest near sea level and more slowly at greater heights.
What altitude range is this formula valid for?
The formula used here applies to the troposphere, from sea level up to about 11,000 meters (36,089 feet), which covers virtually all populated areas, mountains, and most commercial aircraft cruising altitudes. Above 11,000 m the temperature lapse rate changes and a different set of standard-atmosphere equations is required.
Why do my results differ from a weather report?
This calculator assumes standard atmospheric conditions (1013.25 hPa and 15 degrees C at sea level) unless you change the sea-level pressure and temperature inputs. Real-world weather systems, humidity, and local conditions cause actual pressure to vary from the standard model, so entering your local sea-level pressure and temperature will give a closer match.

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