The air pressure at altitude calculator above does not use a single exponential decay curve. It implements the three lowest layers of the International Standard Atmosphere separately, because the atmosphere does not have one temperature profile and a single formula is only ever right in one of them. Below 11,000 m the temperature falls steadily and the pressure follows a power law. From 11,000 to 20,000 m the temperature is constant and the decay really is exponential. Above 20,000 m the temperature starts rising again and the power law returns with the opposite sign.
Arb Digital publishes this because the single-formula versions elsewhere quietly go wrong exactly where people need them — around the tropopause, where airliners cruise and weather balloons spend most of their flight. This page also runs in reverse, turning a measured pressure back into the altitude an altimeter would display, and states plainly where the model stops being valid rather than extrapolating past it.
What This Air Pressure at Altitude Calculator Does
In the forward direction you give it a height in metres or feet and it returns the atmospheric pressure there. In reverse it takes a pressure and returns the height the standard atmosphere assigns to it. Both directions use the same layered model, so they are exact inverses of each other rather than two independent approximations.
The supporting grid adds four things. The pressure in inches of mercury is there because aviation, American weather reporting and a lot of older instrumentation still use it. The share of sea-level pressure is the fraction of the atmosphere still above you, which is the intuitive form — at the top of Everest it is about a third. The standard temperature is what the model puts at that height, which you need if you are going on to compute density. The boiling point of water is the most tangible consequence of the whole calculation and the reason cooking times change in the mountains.
The sea-level pressure and temperature boxes generalise the model. Leave them at 1013.25 hPa and 15 °C for the textbook standard atmosphere, or enter today's actual values to get a column that matches real conditions rather than a reference day.
How to Use It
- Pick the direction first. Altitude to pressure reads the altitude box; pressure to altitude reads the known-pressure box and ignores the altitude entirely.
- Set the altitude unit before typing. The dropdown changes how the number is interpreted, so switching it after entering a value reinterprets that value rather than converting it.
- Use absolute pressure in reverse mode. An altimeter setting or a sea-level-corrected barometer reading is not the pressure at your location, and feeding one in will report a height near zero regardless of where you are.
- Adjust the sea-level values for real conditions. A cold, high-pressure winter day and a hot low-pressure summer day can differ by more than 50 hPa at the surface, which propagates all the way up the column.
- Watch the model-range warning. Above 32,000 m the tool stops rather than extrapolating, because the next layer has a different lapse rate and the equation would silently produce a wrong answer.
The Formula: How Pressure at Altitude Is Calculated
Two equations do all the work, selected by whether the layer you are in has a temperature gradient. In a layer with a constant lapse rate L, hydrostatic balance and the ideal gas law combine to give p = pb × (T ÷ Tb)k/L, where T = Tb − L(h − hb) and the subscript b marks the base of the layer. In a layer with no gradient the same derivation gives the pure exponential p = pb × exp(−k(h − hb) ÷ Tb). The constant k is gM ÷ R = 9.80665 × 0.0289644 ÷ 8.314462618 = 0.0341632 K/m, built from standard gravity, the molar mass of dry air and the molar gas constant.
The three layers this tool implements are the troposphere from the surface to 11,000 m with a lapse rate of 6.5 K per kilometre, the lower stratosphere from 11,000 to 20,000 m at a constant 216.65 K, and the layer from 20,000 to 32,000 m with a lapse rate of −1 K per kilometre, meaning the temperature rises with height. NASA Glenn Research Center's Earth Atmosphere Model in metric units sets out the same three-zone division with the same boundaries.
Work through the default. At 1,500 m the standard temperature is 288.15 − 0.0065 × 1500 = 278.4 K, which is 5.25 °C. The exponent is 0.0341632 ÷ 0.0065 = 5.25588. So the pressure is 1013.25 × (278.4 ÷ 288.15)5.25588 = 1013.25 × 0.83450 = 845.6 hPa, about 83.5 % of sea level. Water there boils at 94.9 °C rather than 100 °C.
Which Standard Atmosphere This Uses, and Where It Stops Being Valid
The model is the International Standard Atmosphere as defined by ISO 2533, which is numerically identical to the US Standard Atmosphere 1976 over the whole range this tool covers. The two differ only above about 32 km, which is exactly where this calculator stops.
There are three separate limits worth naming. The first is the upper boundary: at 32,000 m the lapse rate changes again to −2.8 K per kilometre and this tool refuses to extrapolate rather than returning a plausible-looking wrong number. The second is that the ISA is a reference atmosphere, not a weather forecast. It describes an average mid-latitude day, and real profiles depart from it substantially — a strong temperature inversion near the surface breaks the constant-lapse-rate assumption outright. The third is that the ISA assumes dry air of fixed composition. Humidity changes the effective molar mass slightly, which matters for density work but is negligible for pressure at the precision anyone actually needs.
The reverse direction carries an extra caveat that trips people up constantly. Pressure altitude is not geometric altitude. When you feed a measured pressure into this tool you get the height at which the standard atmosphere would have that pressure, which is what a pressure altimeter displays. On a cold day the real air column is denser, pressure falls faster with height, and the indicated altitude reads higher than your true height above the ground. The National Weather Service pressure altitude calculator from the El Paso office performs the same conversion for meteorological use.
Why Pressure Falls Exponentially and Not Linearly
The pressure at any height is the weight of all the air above that height, spread over a unit area. That framing explains the shape of the curve immediately. Air is compressible, so the air near the surface is squeezed by everything above it and is therefore dense; the air high up has almost nothing on top of it and is thin. Each successive slice of height contains less mass than the one below, so each contributes less pressure drop.
The result is a roughly constant fractional decrease per unit height, which is the definition of exponential decay. Near the surface the scale height is about 8,400 m, meaning pressure falls by a factor of e every 8,400 m, and halves roughly every 5,500 m. That is why sea level to 5,500 m leaves you with half the atmosphere but 5,500 m to 11,000 m only takes another quarter, and why the pressure at airliner cruise altitude is around a quarter of sea level rather than the tenth a linear intuition would suggest.
Temperature complicates this because the scale height itself depends on temperature — colder air has a shorter scale height and falls off faster. That is precisely why the constant-lapse-rate power law is used inside the troposphere rather than a fixed exponential, and why the exponential form only becomes exact in the isothermal layer above 11,000 m.
What the Boiling Point Figure Tells You
Water boils when its saturation vapour pressure equals the surrounding air pressure, so the boiling point is a direct readout of altitude. This tool inverts the Clausius–Clapeyron relation with a latent heat of vaporisation of 40,660 J/mol, which is accurate to within a few tenths of a degree across the range that matters.
The practical consequences are larger than they look. At 2,000 m water boils near 93 °C, which is a seven-degree reduction in the maximum temperature a pot of boiling water can reach. Reaction rates roughly double for every ten degrees, so food genuinely does take longer, and the effect compounds for anything relying on sustained heat — hard-boiled eggs, dried beans, rice. At Everest's summit the boiling point is around 69 °C, cool enough to put a finger in, and far too cool to cook most things at all.
Where This Sits Next to Our Other Pressure Tools
Four pages on this site say the word pressure and they do genuinely different jobs. This one derives atmospheric pressure from a height using a layered atmospheric model. The pressure calculator solves the definition, pressure equals force over area, for any of the three quantities. The hydrostatic pressure calculator handles a column of liquid, where density is essentially constant and the pressure therefore rises linearly with depth — the exact opposite of the compressible-gas case here. The pressure converter rescales a pressure between hectopascals, inches of mercury, psi, bar and atmospheres without changing what it describes.
Downstream, the pressure this page produces is the main input to the air density calculator, which combines it with temperature and humidity to get the density of the air, and to the density altitude calculator for the aviation form of that result. The temperature converter handles scale changes on the way in. Everything is listed on the free online tools hub.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Assuming pressure drops linearly with height — it decays exponentially, halving roughly every 5,500 m near the surface. Linear interpolation between two known heights is badly wrong over any large gap.
- Using one formula through the tropopause — the troposphere power law and the stratosphere exponential give different answers above 11,000 m, and only one of them is right up there.
- Feeding an altimeter setting into reverse mode — altimeter settings are already corrected to sea level. The reverse calculation needs the raw absolute pressure at your location.
- Confusing pressure altitude with true altitude — on a cold day a pressure altimeter reads higher than your real height above ground, because the real column is denser than the standard one.
- Extrapolating past 32,000 m — the lapse rate changes there. This tool stops instead of returning a confident wrong number.
Related Free Tools From Arb Digital
Feed the result into the air density calculator to turn pressure and temperature into a density, or into the density altitude calculator for the aviation restatement. For the definitional side of pressure, use the pressure calculator; for liquid columns, the hydrostatic pressure calculator; for unit changes, the pressure converter. The temperature converter handles Celsius, Fahrenheit and kelvin. Everything Arb Digital publishes is indexed on the free online tools hub.
Frequently Asked Questions
About 697 hectopascals, or 20.6 inches of mercury, in the standard atmosphere. That is roughly 69 per cent of sea-level pressure. The exact figure moves with the sea-level pressure and temperature of the day, which is why this tool lets you change both.
The International Standard Atmosphere defined by ISO 2533, which matches the US Standard Atmosphere 1976 over this range. It implements three layers separately: a 6.5 kelvin per kilometre lapse rate to 11,000 metres, a constant 216.65 kelvin from 11,000 to 20,000 metres, and a minus 1 kelvin per kilometre lapse rate from 20,000 to 32,000 metres.
At 32,000 metres, where the lapse rate changes again. The tool refuses to calculate above that rather than extrapolating. It is also a reference atmosphere rather than a forecast, so real profiles with inversions or unusual weather will differ from it at any height.
Because air is compressible. The pressure at any height is the weight of the air above it, and that air is densest near the surface where it is most compressed. Each successive slice of height holds less mass, so each contributes a smaller pressure drop, which produces a constant fractional decrease per unit height.
No. Pressure altitude is the height at which the standard atmosphere would have your measured pressure. On a cold day the real air column is denser and pressure falls faster with height, so a pressure altimeter reads higher than your actual height above the ground.
The boiling point falls with pressure, so it drops roughly one degree Celsius for every 300 metres of elevation near sea level. At 2,000 metres water boils near 93 degrees Celsius and at the summit of Everest around 69 degrees. This calculator reports the figure directly from the pressure it computes.
The pressure converter rescales a pressure you already have between hectopascals, psi, bar and inches of mercury. This page derives a pressure that was never entered, from a height and an atmospheric model, and can also run the derivation backwards.
This tool is provided for educational and general reference use. It implements a reference atmosphere rather than actual weather, and does not account for humidity, inversions or local conditions, so treat its output as a physics result rather than a substitute for a calibrated instrument reading.
