Atmospheric Pressure by Elevation: Formula and Calculator

Calculate atmospheric pressure from elevation by entering altitude above sea level; the calculator estimates pressure using the standard-atmosphere barometric formula. It returns pressure in kilopascals (kPa), with standard sea-level pressure as its reference.

Formula

For elevations in the troposphere, the calculator uses the standard-atmosphere pressure equation:

p = p₀ × (1 − Lh/T₀)^gM/(RL)

• p is estimated atmospheric pressure at elevation h, in kilopascals (kPa).
• p₀ is standard pressure at sea level: 101.325 kPa.
• h is elevation above standard sea level, in metres (m).
• L is the standard temperature lapse rate, 0.0065 K/m.
• T₀ is standard sea-level temperature, 288.15 K.
• g is standard gravitational acceleration, approximately 9.80665 m/s².
• M is the molar mass of dry air, approximately 0.0289644 kg/mol; R is the universal gas constant, approximately 8.31446 J/(mol·K).

Combining the constants gives the calculator’s exponent, approximately 5.25588. Its expression uses the equivalent constants directly: p = 101.325 × (1 − 0.0065h/288.15)^5.25588. The psi and atm outputs are conversions of the result, not separate atmospheric models.

Worked Example

With the default elevation h = 1,000 m:

1. Calculate the temperature factor: 1 − (0.0065 × 1,000 ÷ 288.15) ≈ 0.977442.
2. Raise it to the standard exponent: 0.977442^5.25588 ≈ 0.8870.
3. Multiply by sea-level pressure: 101.325 × 0.8870 ≈ 89.87 kPa.
4. Convert units: 89.87 × 0.1450377 ≈ 13.04 psi; 89.87 ÷ 101.325 ≈ 0.8870 atm.

These are approximate values rounded to the displayed precision. The first result, 89.87 kPa, is the calculator’s main answer for the default elevation.

What Elevation Does to Pressure

Atmospheric pressure is the force per unit area exerted by the air above a location. Near sea level, the standard reference is 101.325 kPa, equivalent to 1 atmosphere or about 14.696 pounds per square inch (psi). As elevation increases, less air lies overhead, so pressure generally decreases. Because air compresses under its own weight, pressure does not fall by a fixed amount for every metre climbed; it declines nonlinearly.

For a sense of scale, the standard-atmosphere estimate is about 89.9 kPa at 1,000 m, 79.5 kPa at 2,000 m, and 54.0 kPa at 5,000 m. These are model estimates, not guaranteed local readings. Pressure at a given altitude changes with weather and atmospheric conditions.

How to Enter Elevation Correctly

Enter elevation above mean sea level, not height above the ground at a nearby point, unless that ground reference is itself at sea level. The calculator accepts metres from 0 to 11,000 m, the approximate upper boundary of the standard tropospheric layer used by this simplified formula. For elevations in feet, convert before entering: metres = feet × 0.3048. For example, 5,000 ft is 1,524 m.

Elevation and altitude are often used interchangeably in everyday questions, but their precise meanings can differ by field. Elevation commonly describes a fixed point’s height above sea level; altitude may describe an aircraft or object’s height above a reference surface. For this calculation, the key requirement is height above the sea-level reference—not height above local terrain.

• Use a positive elevation above sea level. Do not enter a negative number for a location below sea level; this calculator’s input range begins at zero.
• Convert feet to metres before using the input. Entering 5,000 as metres when you mean 5,000 feet greatly overstates the elevation.
• Use the location’s elevation, rather than an uncorrected GPS altitude or a device’s pressure-derived altitude if its reference is unclear.

Reading the Pressure Result

The primary result is absolute atmospheric pressure in kPa. The extra results express the same pressure in psi and atmospheres: 1 kPa is approximately 0.145038 psi, and 1 atm is defined as 101.325 kPa. These conversions make comparisons easier, but they do not represent different kinds of pressure.

In weather reports, pressure may be adjusted to sea level so that readings from places at different elevations can be compared. That sea-level-adjusted value is not the same as the actual pressure at the elevated location. Likewise, a gauge-pressure reading is pressure relative to surrounding air; atmospheric pressure itself is an absolute-pressure quantity. Check what a sensor or report is displaying before comparing its number with this calculator.

Limits and Common Sources of Error

The calculation assumes a standard atmosphere: a defined temperature profile and representative dry-air properties. Real air is affected by temperature, humidity, weather systems, and changing conditions with height. Consequently, the formula is useful for a quick estimate, but a calibrated local barometer is preferable when an accurate current pressure measurement is needed.

The displayed precision is not a promise of real-world accuracy. Two decimal places in kPa communicate the calculation’s rounded output; they do not account for local weather or uncertainty in the elevation. For aircraft, scientific work, or other applications where pressure accuracy matters, use the relevant measured data or a more detailed atmospheric model.

• Wrong reference: confusing height above local ground with elevation above sea level.
• Wrong units: entering feet into a metre input, or comparing kPa with a value reported in hPa. One kPa equals 10 hPa.
• Wrong pressure type: treating sea-level-adjusted weather pressure or gauge pressure as actual local absolute pressure.
• Over-interpreting the estimate: assuming a standard model captures today’s local weather.

Frequently Asked Questions

What is atmospheric pressure at sea level?
Standard atmospheric pressure at sea level is 101.325 kPa, equal to 1 atm or approximately 14.696 psi. Actual measured pressure varies with weather.

How much does pressure drop per 1,000 metres?
There is no fixed drop per 1,000 m because pressure decreases nonlinearly. In the standard-atmosphere model, pressure is about 89.9 kPa at 1,000 m and 79.5 kPa at 2,000 m.

How do I calculate pressure at altitude in feet?
Convert the altitude to metres using metres = feet × 0.3048, then enter that value. For instance, 10,000 ft is 3,048 m.

Is elevation the same as altitude?
They can mean different things in technical contexts, but either can be used here if the number is height above sea level. Height above nearby ground alone is not enough unless the ground’s elevation is known.

Why is my barometer reading different?
The calculator uses standard atmospheric conditions, while a barometer measures local conditions that change with weather and temperature. Also check whether the displayed value is local absolute pressure, gauge pressure, or pressure adjusted to sea level.

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in h | Elevation | m | 1000 | 0 | 11000
out p | Atmospheric pressure | kPa | 101.325 * (1 - 0.0065 * h / 288.15) ^ 5.25588 | 2
out psi | Atmospheric pressure | psi | p * 0.1450377 | 2
out atm | Atmospheric pressure | atm | p / 101.325 | 4