Air Pressure at Altitude Calculator
Climb a mountain and the air above you — the ocean of air whose weight is atmospheric pressure — gets shallower. Enter an altitude in metres and this calculator returns the standard-atmosphere pressure there in kilopascals, hectopascals, atmospheres and psi: the single number behind altitude sickness, falling boiling points, barometric altimeters and aircraft performance tables.
The Barometric Formula: Weighing the Sky in Layers
Pressure at any height is the weight of the air still above that height, squeezed by gravity and thinned as it expands into the space available — a self-referential pile-up that calculus resolves into an exponential decay dressed with a temperature correction. The International Standard Atmosphere (ISA) models the lower atmosphere with a constant temperature lapse rate (air cooling 6.5 C per kilometre), which turns the exponential into a power law: P = 101.325 x (1 − 2.25577 x 10^-5 x h)^5.25588 kPa, with h in metres. The constants are the sea-level standard pressure (101.325 kPa, exactly one atmosphere) and the measured structure of real air. Two properties shape everything the formula says: pressure falls fastest near the ground (about 1 kPa per 83 metres at sea level, because the air there is densest — each metre you climb removes a dense metre from the column), and it never quite reaches zero in the formula’s domain, halving roughly every 5.5-6 kilometres instead. The calculator is valid through the troposphere, to 11,000 m — above Everest, above every mountain and most airliners’ cruise.
Worked Examples: A Hill, a Mile-High City, the Roof of the World
The default, 1,000 m: pressure = 89.87 kPa (898.7 hPa, 0.8870 atm, 13.04 psi, 674 mmHg) — a ninth of the sky already beneath you, water boiling at about 96.7 C, and the altitude at which sensitive visitors to highland resorts first notice the thinness at exertion. Denver, 1,609 m (the mile-high city): 83.43 kPa — where baking recipes add their altitude instructions and visiting athletes’ blood oxygen runs a few percent low. Everest’s summit, 8,849 m: 31.4 kPa, barely a third of an atmosphere — the celebrated death-zone figure at which unacclimatised consciousness lasts minutes and even acclimatised climbers stand at the edge of human physiology. And the pressurised cabin of a cruising airliner is held near the 2,400-m value (about 75 kPa), which is why ears pop to a mountain’s pressure while the true air outside sits near 20 kPa. Every one of these is the same power law read at a different height.
What the Falling Pressure Does
The applications queue up quickly once the number exists. Breathing: the oxygen fraction stays 20.9 percent at all these heights, but its partial pressure falls with the total — at Everest, lungs extract oxygen from air at a third of sea-level pressure, the entire physiology of altitude sickness and acclimatisation. Boiling: water boils when its vapour pressure meets the ambient pressure, so boiling points fall about 1 C per 285 m — at 1,000 m water boils at 96.7 C, pasta cooks slower, and pressure cookers exist to buy the pressure back. Aviation: lift, engine power and true airspeed all key off pressure (and its partner, density), and the altimeter is a barometer wearing a height scale — its readings are only as honest as the local pressure setting. Weather: the sea-level pressure maps on forecasts are this same column measured at the ground, its highs and lows the signature of the air’s rearrangement. One formula; physiology, cooking, flight and meteorology all read from it.
Standard Atmosphere Versus the Real Sky
The ISA is a treaty, not a measurement: a fixed reference profile (sea level 101.325 kPa and 15 C, lapse rate 6.5 C/km) agreed so that altimeters, aircraft manuals and engineering tables worldwide speak one language. The real atmosphere at your altitude today deviates — passing weather systems swing sea-level pressure between roughly 98 and 104 kPa, and the whole column rides up or down with them, moving true pressure at 3,000 m by a percent or two either way. Temperature matters too: on a hot day the column expands and pressure at height runs above standard; in deep cold, below it (the source of the cold-weather altimeter error that aviation trains against). Use this calculator for planning, physiology, education and engineering estimates; use a calibrated barometer, corrected to your location, when a decision rides on today’s exact number.
How the Pressure Was First Weighed
The formula’s ancestry is a mountain experiment: in 1648 Blaise Pascal, suspecting that air has weight and thins with height, had his brother-in-law carry a mercury barometer up the Puy de Dome; the column fell by some 8.5 cm over the roughly 1,000-metre ascent — the first demonstration that pressure is altitude’s function, performed with a glass tube on a French volcano. Torricelli’s barometer (1643) had already named the sea-level value this page takes as its constant, and Pascal’s phrase for the experiment remains the best summary of the whole subject: we live at the bottom of an ocean of air, and its depth above us is the pressure. The ISA’s power law is that insight with three centuries of thermometry folded in.
Reading Your Own Barometer
A home barometer reads the pressure at your altitude on the day — which is why its raw figure is compared against sea-level-corrected values in forecasts, and why the correction is this page’s formula run backwards from your elevation. Set the instrument by a known local reference (an airport’s reported QNH within a few kilometres serves), and its wanderings thereafter are weather, faithfully recorded: the column above your house, gaining and losing the weight of passing systems, at about a kilopascal per weather event worth noticing.
Related Tools
More from the Physics Calculators hub: the Water Pressure at Depth Calculator — the same idea in a denser fluid — the Hydrostatic Pressure Calculator, and the Distance to Horizon Calculator for the view from the heights this page prices.
Frequently Asked Questions
How much does pressure drop per 1,000 metres?
About 11.4 kPa in the first kilometre (101.325 to 89.87 kPa), and progressively less per kilometre after that, because the air being removed is thinner: the second kilometre costs 10.4 kPa, the drop from 8 to 9 km only about 4.9 kPa. The constant of the climb is proportional, not absolute — pressure halves every 5.5-6 km through this range, which is why “half the atmosphere lies below 5.5 km” is the mountaineer’s favourite summary of the formula.
Why do my ears pop and bags swell on a plane?
Because the cabin is pressurised to only about the 2,400-metre standard (roughly 75 kPa) while the ground outside the airport sat at 101 kPa. Air trapped in your middle ear and sinus cavities — and in crisp packets and water bottles — is still at departure pressure and expands toward the new, lower ambient pressure until membranes and packaging flex enough to equalise. Swallowing and yawning open the Eustachian tubes that let the ear’s share escape; descent reverses the whole transaction, which is why landing pops harder.
What is pressure altitude, and why do pilots care?
Pressure altitude is the height in the standard atmosphere at which the measured pressure occurs — what an altimeter reads when set to the standard 1013.25 hPa. Aircraft performance (takeoff roll, climb, engine output) is governed by the air’s actual density, which standard-atmosphere pressure altitude summarises when combined with temperature into density altitude. On a hot day at a high airport, density altitude can exceed the field’s true elevation by over a kilometre — the invisible mountain that performance charts, and this calculator’s formula, exist to reveal.
How low does pressure get at Everest, and can humans survive it?
About 31-33 kPa on the summit (the standard figure here is 31.4 kPa; direct measurement in 1981 read near 33.7 kPa on the day, weather riding above standard). It is just survivable by fully acclimatised climbers for short exposures — the blood’s oxygen saturation there sits near the edge of consciousness, supplemental oxygen restores the equivalent of a few thousand metres of descent, and no human can live at that pressure permanently. The formula’s cold output is, in this case, a physiological boundary condition.
Why do climbers and pilots talk about oxygen if the percentage never changes?
Because lungs run on partial pressure, not percentage: oxygen is 20.9 percent of the air at every altitude this page covers, but 20.9 percent of a third of an atmosphere delivers a third of the pressure driving oxygen across the lung membrane — the quantity physiology actually meters. Acclimatisation answers with more red cells and deeper breathing; supplemental oxygen answers by raising the percentage delivered at altitude pressure until the product matches a survivable altitude. Pilots use the same arithmetic in reverse to set cabin altitudes and oxygen rules — the formula’s output, multiplied by 0.209, is the number the whole high-altitude world is organised around.
What is QNH, and why do altimeters need setting?
QNH is the local sea-level pressure, measured at the airfield and corrected through this page’s very formula, broadcast so pilots can set their barometric altimeters to read true height above sea level at that place and hour. Because weather moves the column’s weight daily, yesterday’s setting can misread by hundreds of feet today — the standard ritual of dialling in the current QNH before descent exists because the altimeter is a pressure gauge trusting the ISA to translate, and the translation is only as good as the constant it is handed.
Does the formula work below sea level?
Yes, modestly: the Dead Sea shore at −430 m gives about 106.6 kPa by the same power law, and mines and below-sea basins read correspondingly above one atmosphere. This page’s input range starts at 0 for tidiness, but the mathematics extends a few hundred metres downward without complaint — the exponent never notices the sign.