Calculate atmospheric pressure at any altitude using the barometric formula. Convert between pressure units and estimate air density and boiling point changes.
The Barometric Formula Calculator computes atmospheric pressure at any altitude using the International Standard Atmosphere (ISA) model. This fundamental relationship between altitude and pressure is essential for aviation, meteorology, engineering, and outdoor activities.
Atmospheric pressure decreases roughly exponentially with altitude. At sea level, standard pressure is 101,325 Pa (14.696 psi, 29.92 inHg). By 5,500 meters (18,000 ft), pressure drops to approximately half. This calculator uses the hypsometric equation with temperature lapse rate to give accurate results from sea level through the stratosphere.
Enter altitude and optional temperature to calculate pressure, air density, boiling point, and oxygen partial pressure. Compare multiple altitudes side by side and explore how conditions change with elevation for cooking, aviation, and physiological applications. It is a quick way to translate elevation into a real-world pressure number. That makes it easier to compare mountain, flight, and weather conditions at a glance. It also helps when you want a fast check before looking at a full atmosphere table.
Use this calculator when you need a quick pressure-at-altitude estimate without paging through ISA tables. It is useful for aviation planning, altitude-aware engineering checks, cooking adjustments, and general comparisons of how air conditions change with elevation. The output gives a practical reference point instead of forcing a manual lookup. That is enough for fast comparisons without digging into a full atmosphere chart.
P = P₀ × (1 - L×h/T₀)^(g×M/(R×L)). Where: P₀ = sea level pressure (101325 Pa), L = temperature lapse rate (0.0065 K/m), h = altitude (m), T₀ = sea level temperature (288.15 K), g = 9.80665 m/s², M = molar mass of air (0.0289644 kg/mol), R = gas constant (8.31447 J/(mol·K)).
Result: 70,121 Pa (10.17 psi)
P = 101325 × (1 - 0.0065×3000/288.15)^5.2559 = 70,121 Pa. Temperature at 3000m = 288.15 - 0.0065×3000 = 268.65 K (−4.5°C). Air density drops to about 0.91 kg/m³ from 1.225 at sea level.
The barometric formula describes how atmospheric pressure varies with altitude in a gravitational field. For the troposphere (0-11 km), temperature decreases linearly with altitude at the lapse rate of 6.5°C/km. This makes the pressure-altitude relationship a power law rather than a simple exponential.
Above the tropopause (11 km), temperature remains roughly constant at -56.5°C through much of the stratosphere. In this isothermal region, pressure decreases as a true exponential function. The transition between these two regimes is handled by switching formulas at the tropopause boundary.
As altitude increases, reduced atmospheric pressure means fewer oxygen molecules per breath. At sea level, oxygen partial pressure is about 21.2 kPa. At 3,000m it drops to 14.3 kPa, and supplemental oxygen is recommended above 4,000m for unacclimatized individuals. Commercial aviation regulations require supplemental oxygen for crew above 12,500 ft.
The barometric formula is used in altimeters, weather station corrections (reducing observed pressure to sea level), HVAC system design at altitude, combustion engine derating, and aerospace vehicle design. Pressure altitude is a primary parameter in aircraft performance calculations, affecting lift, engine power, and true airspeed.
Roughly 12 hPa (0.35 inHg) per 100 meters near sea level. The rate decreases at higher altitudes because the atmosphere becomes less dense. As a rule of thumb, pressure halves every 5,500m (18,000 ft).
The International Standard Atmosphere defines reference conditions: sea level at 15°C (59°F), 101,325 Pa, with temperature decreasing at 6.5°C per 1,000m up to 11,000m (tropopause), then constant at -56.5°C through the stratosphere. It provides a common baseline for aviation and engineering calculations.
Water's boiling point drops about 1°C (1.8°F) for every 300m (1,000 ft) of altitude gain. At 2,000m (6,500 ft) it boils at about 93°C. At the summit of Everest (8,849m), water boils at roughly 70°C (158°F).
Commercial aircraft typically pressurize to an equivalent altitude of 6,000-8,000 ft (1,800-2,400m), which is about 75-79 kPa. The Boeing 787 maintains a lower cabin altitude of 6,000 ft for improved comfort.
Lower boiling point means food takes longer to cook. At 5,000 ft: add 25% to boiling times. Baking adjustments needed above 3,000 ft: reduce leavening, increase liquid, increase oven temperature slightly.
Density altitude is the altitude in the standard atmosphere that corresponds to the actual air density. Hot days and low pressure increase density altitude, reducing aircraft performance and engine power.