Air Pressure at Altitude Calculator
Calculate atmospheric pressure, temperature, and air density at any elevation using the International Standard Atmosphere model.
Enter an altitude and surface conditions to instantly compute the air pressure, temperature, and density at that elevation.
Air Pressure at Altitude Calculator
Calculate atmospheric pressure, temperature, and air density at any elevation using the International Standard Atmosphere model.
About the Air Pressure at Altitude Calculator
Atmospheric pressure is the force per unit area exerted by the weight of the air column above a given point. As altitude increases, the thickness of the air column above you decreases, so atmospheric pressure falls. This relationship is not linear — it follows an exponential-like curve described by the barometric formula derived from the hydrostatic equation and the ideal gas law.
This calculator uses the International Standard Atmosphere (ISA) model and the hypsometric (barometric) formula to compute pressure at a given altitude. The ISA defines a standard temperature lapse rate of 6.5 K per 1000 metres (3.56 °F per 1000 feet) in the troposphere, which extends from sea level to approximately 11 km (36,089 ft). The formula used is P(h) = P₀ × ((T₀ + L × h) / T₀)^(g × M / (R × |L|)), where P₀ is the surface pressure, T₀ is the surface temperature in Kelvin, L is the lapse rate (−0.0065 K/m), h is the altitude in metres, g = 9.80665 m/s², M = 0.0289644 kg/mol, and R = 8.31446 J/(mol·K).
The temperature at altitude is computed as T(h) = T₀ + L × h. This linear decrease holds throughout the troposphere. In the stratosphere (above ~11 km), temperature remains roughly constant at −56.5 °C before rising again in the mesosphere, but most practical aviation and mountaineering applications stay within the tropospheric range.
Air density at altitude is derived from the ideal gas law for dry air: ρ = P / (R_specific × T), where R_specific = 287.058 J/(kg·K) for dry air. Humidity reduces air density slightly because water vapour (molecular mass 18 g/mol) is lighter than dry air (29 g/mol). The calculator uses the virtual temperature correction to account for humidity when computing density.
Density altitude is the altitude in the International Standard Atmosphere at which the air density would equal the actual density. It is widely used in aviation: an aircraft engine or wing generates less lift and thrust at high density altitude, even if the actual altitude is low. Density altitude increases on hot, humid days and at high elevations, which is why high-altitude airports on warm days demand careful performance calculations.
Common applications of this calculator include aviation performance planning, weather balloon trajectory prediction, meteorological station calibration, mountaineering oxygen requirement estimates, HVAC system design for high-altitude buildings, and ballistic trajectory adjustments for firearms and projectiles. Understanding how pressure and density change with altitude is fundamental to fluid dynamics, thermodynamics, and atmospheric science.
Air pressure at altitude examples
Realistic scenarios showing pressure, temperature, and density at different altitudes.
| Scenario | Pressure at Altitude | Notes |
|---|---|---|
| Commercial aircraft cruise: 35,000 ft altitude, 15 °C surface temperature, 1013.25 hPa | ≈ 238 hPa | At typical jet cruise altitude the pressure is roughly 23% of sea-level pressure, requiring a pressurised cabin. |
| Mount Everest summit: 8,848 m altitude, 15 °C surface temperature, 1013.25 hPa | ≈ 314 hPa | Pressure at the summit is about 31% of sea-level. Supplemental oxygen is needed above 8,000 m. |
| Mountain weather station: 1,000 m altitude, 15 °C surface temperature, 1013.25 hPa | ≈ 899 hPa | A moderate elevation reduces pressure by roughly 11%, a standard correction in weather forecasting. |
| High-altitude airport: 3,500 m altitude, 15 °C surface temperature, 1013.25 hPa | ≈ 658 hPa | Airports like La Paz (3,600 m) have density altitudes near 4,500 m, significantly reducing aircraft performance. |
How to use the air pressure at altitude calculator
- Enter the altitude you want to analyse and select the unit (metres or feet).
- Enter the surface (sea-level) temperature and choose the unit (°C, °F, or K). Default is 15 °C (ISA standard).
- Enter the surface pressure and select the unit (hPa, Pa, atm, or psi). Default is 1013.25 hPa (ISA standard).
- Enter the relative humidity percentage (0–100). This affects air density but has only a minor effect on pressure.
- Click Calculate to see pressure, temperature, air density, and density altitude at the specified elevation.
Air pressure at altitude FAQ
Why does air pressure decrease with altitude?
Atmospheric pressure at any point equals the weight of the air column above it. As altitude increases, less air mass sits above you, so the pressure falls. The rate of decrease is fastest near sea level where air is densest, and slows at higher altitudes.
What is the International Standard Atmosphere?
The ISA is a mathematical model of the atmosphere adopted by the International Civil Aviation Organization (ICAO). It defines standard values for temperature, pressure, and density at sea level (15 °C, 1013.25 hPa, 1.225 kg/m³) and a standard temperature lapse rate of 6.5 K/km in the troposphere. It is used as a reference for aircraft performance and altimeter calibration.
What is density altitude and why does it matter for aviation?
Density altitude is the pressure altitude corrected for non-standard temperature. It represents the altitude in the standard atmosphere at which the air would have the same density as the actual conditions. High density altitude means thin air — aircraft engines produce less power, wings generate less lift, and propellers are less efficient, all reducing takeoff and climb performance.
How much does pressure drop per 1,000 feet?
Near sea level, pressure drops approximately 1 inch of mercury (about 34 hPa) per 1,000 feet of altitude. This rule of thumb is useful for quick estimates but becomes less accurate at higher altitudes where the rate of decrease slows due to the decreasing air density.
Does humidity affect atmospheric pressure?
Moist air is actually slightly lighter than dry air at the same temperature and pressure, because water vapour (molecular mass 18) is lighter than diatomic nitrogen and oxygen (28 and 32). This means humid air has a lower density and a slightly higher density altitude. The pressure effect is small — less than 1% — but the density effect is measurable and important for aviation.
Can I use this calculator for scuba diving or underwater pressure?
No. This calculator uses the barometric formula for atmospheric air pressure, which only applies to gases. Underwater pressure increases by approximately 1 atmosphere (101.325 kPa) for every 10 metres of water depth, governed by the hydrostatic equation with liquid water density rather than compressible gas density.