Air Pressure at Altitude Formula and Calculator

Calculate air pressure at altitude with the barometric formula: for the standard atmosphere in the lower troposphere, use P = P₀(1 − Lh/T₀)^(gM/RL). Enter altitude in metres to estimate pressure in pascals; the calculator also converts the result to kilopascals and standard atmospheres. It assumes standard sea-level conditions, so actual weather and local elevation can change the measured pressure.

Formula

For the International Standard Atmosphere model in the troposphere, pressure is calculated as:

P = P₀ × (1 − Lh/T₀)^(gM/(RL))

• P is estimated air pressure at altitude, in pascals (Pa).
• P₀ is reference pressure at sea level: 101,325 Pa.
• h is altitude above the reference sea-level datum, in metres.
• L is the standard temperature lapse rate, 0.0065 kelvin per metre.
• T₀ is standard sea-level temperature, 288.15 K.
• g is standard gravitational acceleration, 9.80665 m/s².
• M is the molar mass of dry air, 0.0289644 kg/mol.
• R is the universal gas constant, 8.3144598 J/(mol·K).

The calculator’s first output is the pressure in pascals. The other outputs express the same estimate in kilopascals and standard atmospheres; 1 kPa equals 1,000 Pa, and 1 standard atmosphere equals 101,325 Pa. The equation is the constant-lapse-rate form of the barometric equation, derived by combining hydrostatic balance with the ideal-gas relationship.

Worked Example

With the default altitude of 1,000 m, substitute h = 1,000 into the formula:

1. Calculate the temperature factor: 1 − (0.0065 × 1,000 / 288.15) ≈ 0.977442.
2. Calculate the exponent: (9.80665 × 0.0289644) / (8.3144598 × 0.0065) ≈ 5.25588.
3. Raise the temperature factor to that exponent: 0.977442^5.25588 ≈ 0.8870.
4. Multiply by sea-level pressure: 101,325 × 0.8870 ≈ 89,875 Pa.

Rounded as specified by the calculator, the result is 89,875 Pa, or 89.88 kPa and 0.8870 atm. Small differences in the last digits may result from rounding intermediate values in the displayed steps.

How the Estimate Changes with Altitude

Air pressure decreases as altitude increases because there is less air above a location pressing down on it. Pressure does not fall by a fixed number of pascals per metre: the atmosphere is compressible, so the relationship is curved rather than linear. At the same altitude, local pressure can also differ from the standard estimate because temperature and weather affect the density and weight distribution of the air.

The formula’s altitude is measured from sea level, not from the ground where a person happens to be standing. For example, a site 500 m above sea level on a plateau should be entered as 500 m, not as zero merely because the plateau surface is the local starting point.

When to Use This Calculator

This is useful for a quick standard-atmosphere estimate, for understanding why pressure changes with elevation, or for checking the scale of a pressure reading. It is not a substitute for a local barometer or an atmospheric model using current weather data. If you need the pressure at a specific place and time, use a reliable observation or forecast that identifies its pressure reference and elevation.

To enter an altitude expressed in feet, convert it first: 1 ft = 0.3048 m. For example, 3,281 ft is approximately 1,000 m. The calculator accepts altitudes from 0 to 11,000 m because this version uses the standard lower-atmosphere lapse-rate equation within the troposphere. Do not extend its output to higher altitudes by assuming the same formula remains valid.

Common Mistakes and Model Limits

• Mixing units: The input is metres. Entering feet as if they were metres produces a much larger altitude and an incorrect result.
• Confusing absolute and gauge pressure: The formula gives absolute atmospheric pressure. Gauge pressure is measured relative to local atmospheric pressure and can be negative or positive compared with that reference.
• Treating standard pressure as local pressure: 101,325 Pa is a defined standard sea-level reference, not a promise that today’s pressure at every sea-level location equals that value.
• Using elevation above a nearby valley: Use elevation above the sea-level datum, not the height above a nearby town or the ground beneath a mountain summit.
• Overinterpreting precision: A result with many digits does not make the standard-atmosphere assumptions exact for real weather. The calculator rounds pascals to a whole number.

The model assumes dry air with fixed average composition, standard sea-level pressure and temperature, and a specified temperature decrease with height. Real atmospheric temperature profiles vary by location, season, weather system, and time. Above the troposphere, temperature behavior changes by atmospheric layer; a different piecewise model is needed. These limitations matter whenever a precise local value is required.

Pressure Units and Comparisons

Pressure is force per unit area. The SI unit is the pascal: 1 Pa equals 1 newton per square metre. Weather reports commonly use hectopascals (hPa), where 1 hPa = 100 Pa, or millibars, which have the same numerical value as hectopascals. Thus 89,875 Pa is about 898.75 hPa.

Other familiar units include atmospheres and pounds per square inch (psi). One standard atmosphere is 101,325 Pa, while 1 psi is approximately 6,894.76 Pa. These conversions describe units only; converting a standard-model estimate does not make it a measurement of current local conditions.

Frequently Asked Questions

What is the formula for air pressure at altitude?
For the standard troposphere, use P = P₀(1 − Lh/T₀)^(gM/RL), with altitude in metres and the constants shown in the Formula section.

What is air pressure at 1,000 metres?
The standard-atmosphere estimate is about 89,875 Pa, or 89.88 kPa. Actual pressure depends on local weather and atmospheric conditions.

Does air pressure decrease linearly with altitude?
No. It generally decreases nonlinearly because air density changes as pressure and temperature change. A simple fixed pressure drop per metre is only a rough approximation over a limited range.

Is altitude the same as height above the ground?
Not in this formula. Use altitude above sea level. Height above the local ground is relevant only if you first know the ground’s elevation and add the height to it.

Can I use this formula above 11 km?
Not this calculator’s constant-lapse-rate form. Higher layers have different standard temperature behavior, so use a model designed for the relevant altitude range.

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in h | Altitude | m | 1000 | 0 | 11000
out p | Air pressure | Pa | 101325 * (1 - 0.0065 * h / 288.15) ^ (9.80665 * 0.0289644 / (8.3144598 * 0.0065)) | 0
out kpa | Air pressure | kPa | p / 1000 | 2
out atm | Standard atmospheres | atm | p / 101325 | 4