Atmospheric Pressure from Elevation and Temperature

This calculator estimates the air pressure at a given elevation from the air temperature and the sea-level pressure. It uses the isothermal barometric formula and gives the pressure in kilopascals, inches of mercury and psi.

Formula

Barometric formula for a layer of air at constant temperature: P = P0 × e^(−g M h ÷ (R T)).

P0: sea-level pressure (standard 101.325 kPa)
g = 9.80665 m/s², M = 0.0289644 kg/mol (molar mass of dry air), R = 8.3144598 J/(mol·K)
h: elevation in metres (feet × 0.3048)
T: air temperature in kelvin (°C + 273.15)

Worked Example

1,500 m, 15 °C, standard sea-level pressure.

T = 15 + 273.15 = 288.15 K
g M h = 9.80665 × 0.0289644 × 1500 = 426.07; R T = 8.3144598 × 288.15 = 2395.81
Exponent = −426.07 ÷ 2395.81 = −0.177838; e^(−0.177838) = 0.83708
P = 101.325 × 0.83708 = 84.82 kPa
84.82 ÷ 3.386389 = 25.05 inHg; 84.82 ÷ 6.894757 = 12.30 psi; 83.7% of sea level

Limits and common mistakes

Real air cools with height, so this one-temperature formula is an estimate; at 1,500 m the standard-atmosphere value is 84.56 kPa, close to this.
Weather changes pressure by a few kPa from day to day; a barometer reading beats any formula.
Feet to metres: multiply by 0.3048 (5,000 ft = 1,524 m).

Formula used

in h | Elevation above sea level | m | 1500 | -500 | 11000
in tc | Air temperature | °C | 15 | -90 | 60
in p0 | Sea-level pressure | kPa | 101.325 | 80 | 110
out p | Pressure at elevation | kPa | p0 * exp(-9.80665 * 0.0289644 * h / (8.3144598 * (tc + 273.15))) | 2
out inhg | Pressure | inHg | p / 3.386389 | 2
out psi | Pressure | psi | p / 6.894757293168361 | 2
out pct | Share of sea-level pressure | % | p / p0 * 100 | 1

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Photo collage: a mountain ridge above the clouds and a brass barometer with a blank dial. — Save this card: a 1000 × 1500 image of Atmospheric Pressure from Elevation and Temperature.

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.

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