This all-in-one online Air Pressure at Altitude Calculator performs calculations using a formula that relates atmospheric pressure (P) at altitude (h) above sea level, air temperature (T), and pressure at sea level (P0).
The formula used is applicable to the atmospheric layers in which the temperature is assumed not to vary with altitude. You can enter the values of any three parameters in the fields of this calculator and find the missing parameter.
P = P0·exp(-Mgh/RT)
What is Atmospheric Pressure?
Atmospheric pressure, or air pressure, is the force exerted by the air in the atmosphere above a given point. At sea level, the standard atmospheric pressure is 101,325 Pascals (Pa), or 29.92 inches of mercury (inHg), equivalent to 1 atmosphere (atm).
This pressure results from the mass of air molecules pulled toward Earth by gravity. The lower the altitude, the more air is stacked above, and the greater the pressure. As altitude increases, air becomes thinner, and pressure decreases.
Temperature directly influences atmospheric pressure through the kinetic energy of air molecules. Warmer air has more energetic molecules that move faster and collide more often with surrounding surfaces, increasing pressure at a given altitude. Conversely, cooler air results in lower molecular activity and less pressure. This relationship is described by the ideal gas law and plays a key role in weather patterns and altitude-related calculations.
How to Calculate Atmospheric Pressure at Altitude
To estimate atmospheric pressure at a given altitude, scientists and engineers use a mathematical model known as the barometric formula. This formula relates atmospheric pressure to altitude based on the assumption of a static atmosphere in hydrostatic equilibrium and an ideal gas behavior for air.
There are two common forms of the barometric formula, depending on whether the temperature is assumed to be constant (isothermal model) or changes with altitude (lapse rate model). The latter is more accurate but the former is more simple and widely used.
When the temperature of the atmosphere is assumed to remain constant with altitude — a reasonable approximation over relatively short vertical distances or in specific atmospheric layers such as the lower stratosphere — the isothermal barometric formula is used. This model simplifies the relationship between pressure and altitude and is expressed as:
$$P = P_{0} \cdot exp\left (-\frac{Mgh}{RT} \right)$$
where:
• \(P\) is the atmospheric pressure at altitude \(h\),
• \(P_0\) is the pressure at the reference level (usually sea level),
• \(M\) is the molar mass of Earth’s air (0.0289644 kg/mol),
• \(g\) is the gravitational acceleration (9.80665 m/s²),
• \(h\) is the height above the reference level (in meters),
• \(R\) is the universal gas constant (8.31432 J/(mol·K)),
• \(T\) is the absolute temperature (in Kelvin), assumed constant.
This exponential model, used in our Air Pressure at Altitude Calculator, captures the essential physics of pressure decreasing with altitude due to the diminishing weight of the air column above. Because it assumes a uniform temperature, the isothermal formula is most accurate over limited altitude ranges or in atmospheric conditions where temperature changes are minimal.
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