Altitude and Pressure Calculator: Barometric Formula

The barometric formula (also called the hypsometric formula) describes how atmospheric pressure decreases with increasing altitude. In the troposphere (below about 11,000 m), the standard form is P = P0 × (1 - L × h / T0)^(g × M / (R × L)), where P0 = 101,325 Pa is sea-level pressure, L = 0.0065 K/m is the temperature lapse rate, T0 = 288.15 K is sea-level temperature, g = 9.80665 m/s² is gravitational acceleration, M = 0.0289644 kg/mol is the molar mass of dry air, R = 8.31446 J/(mol·K) is the universal gas constant, and h is altitude in metres. The formula is derived from the ideal gas law combined with the hydrostatic equation.

Atmospheric pressure at any point equals the weight of the air column above that point per unit area. As altitude increases, there is less air above, so the weight decreases and pressure falls. The relationship is roughly exponential: pressure halves for every increase of about 5,500 m (18,000 ft). Temperature also decreases with altitude in the troposphere (at the standard lapse rate of 6.5°C per 1,000 m), which causes the pressure drop to follow a power law rather than a pure exponential.

The International Standard Atmosphere is a model of how atmospheric pressure, temperature, and density vary with altitude, defined by ICAO in document Doc 7488. It provides a globally agreed reference for aviation, instrument calibration, and engineering design. ISA assumes sea-level conditions of 15°C (288.15 K) and 1013.25 hPa (101,325 Pa), a constant temperature lapse rate of 6.5°C per 1,000 m up to the tropopause at 11,000 m, and an isothermal layer (constant -56.5°C) from 11,000 m to 20,000 m. Actual conditions differ from ISA and are accounted for using ISA deviations.

Water boils when its vapour pressure equals atmospheric pressure. As altitude increases, atmospheric pressure falls, so water boils at a lower temperature. At sea level (1013.25 hPa), water boils at 100°C. At 2,000 m (about 795 hPa), the boiling point drops to roughly 93°C. On Mount Everest (about 315 hPa at the summit), water boils at approximately 70°C. This is why high-altitude cooking instructions specify longer times: food cooks in water that is significantly cooler than at sea level.

The summit of Mount Everest is at approximately 8,849 m above sea level. Using the ISA barometric formula, the pressure at that altitude is approximately 315 hPa (31,500 Pa), about 31% of sea-level pressure. The corresponding ISA temperature is approximately -42.6°C. In practice, conditions on Everest vary significantly with weather systems, but the ISA value provides a standard reference. This pressure is equivalent to about 236 mmHg or 9.3 inHg.