Elevation to Pressure Converter
Convert elevation pressure between units instantly. Includes conversion tables, common equivalents, and calculation formulas.
Elevation to Pressure Converter
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Formula: P = P0 x (1 - L*h/T0)^(g*M/(R*L))
Worked example โ At 1,609 m: 83,844 Pa (0.828 atm, 24.76 inHg)
Formula
P = P0 x (1 - L*h/T0)^(g*M/(R*L))
The barometric formula models pressure decrease with altitude. P0 is sea-level pressure (101,325 Pa), L is the lapse rate (0.0065 K/m), h is altitude, T0 is temperature in Kelvin, g is gravity (9.80665 m/s2), M is molar mass of air (0.0289644 kg/mol), and R is the molar gas constant (8.314462618 J/mol/K, exact since the 2019 SI redefinition).
Worked Examples
Example 1: Denver, Colorado
Problem:Calculate atmospheric pressure at Denver (elevation 1,609 m) at 15 degrees C.
Solution:P = 101325 x (1 - 0.0065 x 1609 / 288.15)^5.2559 P = 101325 x (1 - 0.03629)^5.2559 P = 101325 x 0.8274 P = 83,844 Pa = 838.44 hPa
Result:At 1,609 m: 83,844 Pa (0.828 atm, 24.76 inHg)
Example 2: Commercial Aircraft Cabin
Problem:Aircraft cabins are pressurized to about 6,000 feet (1,829 m). What is the cabin pressure?
Solution:Convert 6,000 ft = 1,828.8 m P = 101325 x (1 - 0.0065 x 1828.8 / 288.15)^5.2559 P = 101325 x 0.8106 P = 82,139 Pa
Result:At 6,000 ft: 82,139 Pa (0.811 atm, 11.91 psi)
Frequently Asked Questions
How does elevation affect atmospheric pressure?
Atmospheric pressure decreases with increasing elevation because there is less air above you to exert downward force. The relationship follows an exponential decay described by the barometric formula. At sea level, standard pressure is 101,325 Pa (1 atm). At 1,500 meters (about 5,000 feet), pressure drops to roughly 84,600 Pa. At the summit of Mount Everest (8,849 m), pressure is only about 33,700 Pa, roughly one-third of sea level pressure.
What is the barometric formula?
The barometric formula calculates atmospheric pressure as a function of altitude, temperature, and physical constants. The standard formula is P = P0 x (1 - Lh/T0)^(gM/RL), where P0 is sea-level pressure, L is the temperature lapse rate (0.0065 K/m), h is altitude in meters, T0 is the base temperature in Kelvin, g is gravitational acceleration, M is molar mass of air, and R is the universal gas constant. This formula assumes a linear temperature decrease with altitude, which is accurate in the troposphere up to about 11 km.
Why does water boil at lower temperatures at higher elevations?
Water boils when its vapor pressure equals the surrounding atmospheric pressure. At higher elevations, atmospheric pressure is lower, so water reaches the boiling point at a lower temperature. At sea level water boils at 100 degrees C, but at Denver (1,600 m) it boils at about 95 degrees C, and at the top of Mount Everest it boils at approximately 70 degrees C. This is why cooking times increase at altitude and why pressure cookers are especially useful in mountainous regions.
How does altitude affect human physiology?
As altitude increases and pressure decreases, the partial pressure of oxygen drops proportionally. At 2,500 meters, oxygen availability is about 74% of sea level, which can cause mild altitude sickness in unacclimatized individuals. At 5,500 meters, it drops to about 50%, making sustained activity very difficult without acclimatization. Above 8,000 meters (the death zone on Everest), oxygen is so scarce that the human body deteriorates rapidly and supplemental oxygen is typically required for survival.
What is the difference between station pressure and sea-level pressure?
Station pressure is the actual atmospheric pressure measured by a barometer at its own elevation, and it is what this calculation returns. Sea-level pressure is that reading mathematically reduced to what it would be at sea level, so that readings from stations at different elevations can be compared on a weather chart. Without the reduction, elevation would dominate the map and hide the pressure systems, because a few hundred metres of altitude outweighs the pressure difference across an entire weather front.
How does the temperature lapse rate affect the result?
The barometric formula assumes air temperature falls linearly with height at the standard lapse rate of 0.0065 kelvin per metre. A colder air column is denser, so pressure falls faster with height than the standard model predicts, while a warmer column makes pressure fall more slowly. Temperature inversions, where air warms with height, violate the linear assumption entirely. This is why the temperature input matters and why altimeters need a temperature correction for accurate work in extreme conditions.
What are pressure altitude and density altitude in aviation?
Pressure altitude is the altitude in the standard atmosphere at which the observed pressure would occur, obtained by setting the altimeter to the standard datum of 1013.25 hectopascals. Density altitude corrects pressure altitude for the actual temperature, giving the altitude at which the standard atmosphere would have the current air density. Density altitude is what governs aircraft performance, because lift, propeller thrust and naturally aspirated engine power all scale with air density rather than with pressure alone.
How does air density change with elevation?
Air density follows the ideal gas law, equalling pressure divided by the specific gas constant of dry air, 287.058 joules per kilogram-kelvin, times absolute temperature. Because pressure falls with height while temperature falls more slowly, density declines steadily with elevation from the sea-level standard of 1.225 kilograms per cubic metre. Reduced density lowers aerodynamic drag but also cuts the oxygen mass drawn into an engine per stroke and reduces convective cooling at a given airspeed.
Up to what altitude is this barometric formula valid?
The linear lapse rate form used here models the troposphere, which extends to roughly 11 kilometres in the standard atmosphere. Above that, in the lower stratosphere, temperature stops falling and becomes approximately constant, so pressure decays exponentially with height rather than following the power law. Applying the troposphere formula above the tropopause introduces growing error, and the standard atmosphere handles it by switching to an isothermal expression for that layer.
Why are there so many different pressure units in use?
Each unit survives from a different measurement tradition, and all are fixed multiples of the same quantity: one standard atmosphere equals 101,325 pascals, 1013.25 hectopascals, 760 millimetres of mercury, about 29.92 inches of mercury and about 14.696 pounds per square inch. Meteorology outside the United States uses hectopascals, US aviation altimeters use inches of mercury, clinical medicine uses millimetres of mercury, and industrial and tyre gauges use psi or bar. Converting between them is exact arithmetic.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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