Air Pressure At Altitude Calculator - Barometric pressure by elevation
This air pressure at altitude calculator estimates atmospheric pressure at any elevation using the barometric formula. Enter your altitude, sea-level pressure, and temperature to get results in hPa, atm, mmHg, and psi.
Air Pressure At Altitude Calculator
Results
What Is Air Pressure At Altitude Calculator?
An air pressure at altitude calculator estimates the atmospheric pressure at a chosen height above sea level using the barometric formula. It takes your elevation, the pressure at sea level, and the sea-level temperature, then returns the pressure in hPa, atm, mmHg, and psi. Use it when you need the actual air pressure at a mountain, an airport, or a flight level instead of the standard 1013.25 hPa quoted at sea level.
- • Aviation planning: Pilots convert altimeter settings and field elevations into pressure altitude for performance charts.
- • Mountaineering and hiking: Climbers estimate how thin the air gets at a pass or summit before they go.
- • Physics and earth-science class: Students check the standard-atmosphere pressure profile against textbook tables.
- • Weather and pressure systems: Analysts subtract a storm's low sea-level pressure from the norm to see how much local pressure drops.
Atmospheric pressure is the weight of the air column above you. The higher you climb, the less air sits overhead, so pressure falls. That relationship is not linear, which is why a dedicated calculator beats guessing from a rule of thumb.
This tool follows the U.S. Standard Atmosphere model for the troposphere, where temperature drops about 6.5 C per kilometre of climb. If you want the air density that goes with the pressure, the air density calculator uses the same pressure and temperature inputs.
Pressure and temperature together set the mass of air in a volume, which the air density calculator works out from the same inputs.
How Air Pressure At Altitude Calculator Works
The calculator applies the barometric formula, which comes from balancing the weight of a thin air layer (hydrostatic equilibrium) with the ideal gas law. In the standard atmosphere the temperature is not constant but cools with height, so pressure is raised to a fixed power rather than an exponential.
- P0: Reference pressure at sea level, defaulting to the standard 1013.25 hPa (1 atm).
- h: Height above sea level in metres, positive uphill and negative in basins below sea level.
- T0: Sea-level temperature in kelvin, computed from your Celsius input (T0 = 273.15 + T).
- L: Temperature lapse rate, 0.0065 K per metre in the standard troposphere.
- g, M, R: Gravity 9.80665 m/s2, dry-air molar mass 0.0289644 kg/mol, and the gas constant 8.31447 J/(mol*K).
- Exponent: g*M/(R*L) equals about 5.25578, the fixed power the standard-atmosphere term is raised to.
Because temperature is part of the formula, a cold day at sea level keeps pressure higher aloft than a hot day, and a strong high or low at the surface shifts every value up or down together.
If you want the temperature that pairs with each height, the altitude temperature calculator applies the same 6.5 C/km lapse rate to your sea-level reading.
Sea level, standard conditions
h = 0 m, P0 = 1013.25 hPa, T = 15 C
(1 - 0.0065*0/288.15)^5.25578 = 1, so P = 1013.25 hPa.
1013.25 hPa (1 atm, 760 mmHg, 14.696 psi)
At zero height the result equals the sea-level reference by definition.
5,000 m summit
h = 5000 m, P0 = 1013.25 hPa, T = 15 C
(1 - 0.0065*5000/288.15)^5.25578 = 0.5331, so P = 1013.25 * 0.5331.
540.2 hPa (0.533 atm, 405.2 mmHg, 7.835 psi)
Roughly half of sea-level pressure sits over a 5 km climb, which is why supplemental oxygen matters above 8,000 m.
Cruise altitude, 11,000 m
h = 11000 m, P0 = 1013.25 hPa, T = 15 C
(1 - 0.0065*11000/288.15)^5.25578 = 0.2234, so P = 1013.25 * 0.2234.
226.3 hPa (0.223 atm, 169.8 mmHg, 3.283 psi)
Cabin pressure at jet cruise is held near this level, well under a quarter of sea-level pressure.
According to NOAA / U.S. Standard Atmosphere, sea-level pressure is 1013.25 hPa and the tropospheric lapse rate is 6.5 K per km, the basis for this calculator's barometric formula.
According to Wikipedia - Barometric formula, the standard-atmosphere term is raised to the dimensionless exponent 5.25578, derived from g*M/(R*L).
For the temperature that pairs with each height, the altitude temperature calculator applies the same 6.5 C/km lapse rate to your sea-level reading.
Key Concepts Explained
Four ideas explain why the numbers move the way they do and where the model stops being accurate.
Barometric formula
The core relation linking pressure to height through gravity, air mass, temperature, and the gas constant. It is the equation this calculator solves.
Standard atmosphere lapse rate
In the troposphere temperature falls 6.5 C per km of height. The calculator bakes this cooling into the power term so pressure drops faster than a constant-temperature exponential would.
Pressure altitude vs true altitude
Pressure altitude is the height in the standard atmosphere that has your measured pressure; true altitude is your actual geometric height. They differ whenever the real atmosphere is not at standard temperature or pressure.
Hydrostatic equilibrium
The atmosphere is roughly in balance: the pressure at any level supports the weight of the air above it. The barometric formula is the mathematical form of that balance combined with the ideal gas law.
Pressure altitude is a standard concept in aviation: set your altimeter to 1013.25 hPa and the indicated height is pressure altitude, not your true height above the ground.
All pressures here are absolute atmospheric pressure. If you only need to change between the reported units, the pressure converter handles hPa, atm, mmHg, and psi directly.
The standard atmosphere is a model, not a weather forecast. Real columns of air rarely stay at exactly 15 C and 1013.25 hPa at the surface, so treat the output as the pressure you would find on an average day rather than the reading at a specific place and time.
All pressures here are absolute; if you only need to change between the reported units, the pressure converter handles hPa, atm, mmHg, and psi directly.
How to Use This Calculator
Three inputs and one click on this air pressure at altitude calculator give you the pressure at your elevation.
- 1 Enter your altitude: Type the elevation in metres above sea level. Use a negative number for locations below sea level such as Death Valley.
- 2 Set sea-level pressure: Leave the default 1013.25 hPa for standard conditions, or enter the current station pressure from a weather report or altimeter setting.
- 3 Enter sea-level temperature: Type the temperature at sea level in Celsius; the standard atmosphere assumes 15 C, but a real reading improves accuracy.
- 4 Read the results: The output shows atmospheric pressure in hPa, atm, mmHg, and psi, updating as you change any input.
- 5 Compare elevations: Change the altitude to see how pressure changes between a trailhead and a summit, or between sea level and a cruise level.
A pilot at a 1,600 m field with a 1018 hPa altimeter setting and 18 C at sea level gets about 824 hPa. Entering 1013.25 hPa instead shows the standard 822 hPa pressure altitude, a small but chart-relevant gap.
Change the altitude to compare elevations, then the density altitude calculator shows how temperature shifts that pressure into an effective density altitude.
Benefits of Using This Calculator
The tool turns a textbook equation into numbers you can use for decisions.
- • Fast, unit-complete answers: Get hPa, atm, mmHg, and psi at once instead of converting by hand for a lab or a chart.
- • Better mountain planning: Estimate how thin the air is at a pass or summit to judge pacing, acclimatisation, and oxygen needs.
- • Clean aviation math: Pilots separate pressure altitude from true altitude and see the effect of a non-standard altimeter setting.
- • Teaching and verification: Students confirm standard-atmosphere tables and check how temperature shifts the whole profile.
Because the model is deterministic, the same inputs always return the same pressure, which makes it useful for grading or for repeating a planning scenario.
The boiling point at altitude calculator takes the pressure this tool returns to show why water boils sooner on a peak.
The boiling point at altitude calculator takes the pressure this tool returns to show why water boils sooner on a peak.
Factors That Affect Your Results
Three inputs drive the result; a couple of limitations explain where the model drifts from reality.
Altitude
The dominant factor. Pressure falls from 1013 hPa at sea level to about 540 hPa at 5,000 m and roughly 226 hPa at 11,000 m.
Sea-level pressure
A 30 hPa high or low at the surface shifts pressure at every altitude up or down by about the same amount proportionally.
Sea-level temperature
A colder column holds pressure higher aloft; a hotter column lets it drop faster. The effect grows with height.
Lapse rate
The 6.5 C/km standard rate is an average; inversions or very dry air change the real cooling and the real pressure.
- • The formula assumes a dry, standard troposphere below 11 km. Above that the temperature stops falling and a different layer equation applies.
- • Real humidity, local weather, and deviations from the 6.5 C/km lapse rate mean measured pressure can differ by several hPa from the estimate, especially near storms.
Near the ground pressure drops about 12 hPa per 100 m, but the rate slows with height because the air gets thinner, so a fixed 'per 1,000 feet' rule only works over short spans.
The same thinning also explains why aircraft cabins are pressurised: at 11 km the outside pressure is under a quarter of sea level, far too low to breathe without supplemental oxygen or a sealed cabin.
If you need a component gas such as oxygen, the partial pressure calculator scales the total pressure by the gas fraction.
According to Wikipedia - Atmospheric pressure, pressure falls roughly exponentially with height because it balances the weight of the air column through hydrostatic equilibrium.
For a component gas such as oxygen, the partial pressure calculator scales the total pressure by the gas fraction.
Frequently Asked Questions
Q: How much does air pressure drop per 1,000 feet of altitude?
A: Near sea level pressure falls about 1.2 hPa per 100 m, or roughly 3.6 hPa per 1,000 feet, under standard conditions. The drop slows as you climb because the air column gets thinner, so the same 1,000 feet removes a smaller share of the remaining air higher up. Above a few kilometres a fixed per-thousand-feet rule overstates the loss.
Q: What is the air pressure at the top of Mount Everest?
A: Using the standard atmosphere at 8,848 m, the calculator returns about 314 hPa, or 0.31 atm, roughly 31 percent of sea-level pressure. Measured summit pressure varies with weather and is often a bit lower, which is why climbers rely on bottled oxygen above 8,000 m.
Q: Why does air pressure decrease as you go higher?
A: Pressure is the weight of the air above you. Climbing reduces the height and mass of that overhead column, so there is less weight pressing down. Combined with the ideal gas law and gravity, that decline follows the barometric formula rather than a straight line.
Q: How do temperature and humidity change the pressure at altitude?
A: A colder sea-level temperature keeps pressure higher at a given height because the air column is denser; a hotter temperature lets it fall faster. Humidity has a smaller effect: water vapour is lighter than dry air, so moist air slightly lowers the effective molar mass and the pressure. This calculator uses dry standard-atmosphere values.
Q: What is pressure altitude versus true altitude?
A: True altitude is your actual geometric height above sea level, while pressure altitude is the height in the standard atmosphere that matches your measured pressure. Set an altimeter to 1013.25 hPa and its reading is pressure altitude. They diverge whenever the real atmosphere differs from the 15 C, 1013.25 hPa standard.
Q: Can I use this for aviation flight planning?
A: Yes, for the standard-atmosphere part of planning. Enter your field elevation, the current altimeter setting as sea-level pressure with a standard 15 C, and read pressure altitude for performance charts. Treat the result as an estimate; always cross-check against official charts and the live altimeter setting before flight.