Atmospheric Pressure at Altitude: Calculate It

Calculate atmospheric pressure at altitude with the barometric formula: enter the altitude above sea level in metres, and the calculator estimates pressure in kilopascals using the standard atmosphere model. It also converts the result to hectopascals and atmospheres for easy comparison.

Formula

For altitudes within the lower part of the atmosphere, the calculator uses the standard-atmosphere pressure equation:

p = p₀ × (1 − Lh / T₀)^5.25588

• p is estimated atmospheric pressure at altitude, in kilopascals (kPa).
• p₀ is standard sea-level pressure, 101.325 kPa.
• L is the standard temperature lapse rate in the model, 0.0065 K per metre.
• h is altitude above mean sea level, in metres (m).
• T₀ is standard sea-level temperature, 288.15 K.

The exponent 5.25588 follows from the standard model’s temperature gradient and the properties of air. The calculator’s first result is pressure in kPa; 1 kPa equals 10 hPa, and standard sea-level pressure is 1 atmosphere (atm), or 101.325 kPa.

Worked Example

Using the default altitude of 1,000 m:

1. Calculate the temperature factor: 1 − (0.0065 × 1,000 / 288.15) = 0.97744, approximately.
2. Raise it to the model exponent: 0.97744^5.25588 ≈ 0.88699.
3. Multiply by standard sea-level pressure: 101.325 × 0.88699 ≈ 89.87 kPa.

The corresponding outputs are 898.7 hPa and 0.8869 atm. Small differences in the last displayed digit can result from rounding intermediate steps; the calculator evaluates the expression before rounding its outputs.

How Pressure Changes with Altitude

Air has weight, so the air above a location presses down on the air below it. As altitude increases, there is less atmosphere overhead and pressure decreases. The relationship is not a fixed subtraction for every kilometre: air compresses under the weight above it, making the atmosphere denser nearer the surface and thinner higher up.

At sea level, the standard atmosphere assigns a pressure of 101.325 kPa, or 1,013.25 hPa. At 1,000 m, this model gives about 89.87 kPa. At roughly 5,000 m, it gives about 54.0 kPa. These are reference estimates, not promises about the pressure on a particular day or at a particular location.

Pressure can also be expressed in pascals (Pa), millibars (mbar), inches of mercury (inHg), or pounds per square inch (psi). A hectopascal is numerically equal to a millibar; 1 kPa is 1,000 Pa. For US customary comparisons, 1 psi is approximately 6.895 kPa. Check which unit a device or data source uses before comparing readings.

When to Use This Estimate

This calculation is useful when you need a quick reference pressure from an elevation, such as for understanding weather observations, comparing elevations, or checking the expected order of magnitude for an atmospheric model. Use altitude above sea level, not height above the ground at your current location.

Altitude may be given in feet. Convert it to metres before using the calculator: multiply feet by 0.3048. For example, 3,280.84 ft is approximately 1,000 m. The input accepts 0 to 20,000 m because the equation here is intended for the lower atmosphere; do not extrapolate it to high-altitude conditions beyond its stated range.

If you need pressure at a known location and time, a local observation or a suitable weather source is generally more relevant than this standard-atmosphere estimate. Actual pressure varies with weather, temperature, latitude, and the real vertical temperature profile. Elevation itself may also be uncertain, especially when reported by a phone or map.

Standard Pressure Versus Actual Pressure

The formula assumes a simplified reference atmosphere: sea-level temperature of 15 °C, a prescribed decrease of temperature with altitude, and standard physical properties of air. Real air does not follow those assumptions exactly. A warm air column, a cold air column, and changing weather systems can all produce different pressure at the same elevation.

Weather reports often give sea-level pressure: a measured station pressure adjusted mathematically to a common reference elevation so readings from different elevations can be compared. Station pressure is the pressure actually measured at the station. These are different quantities. If comparing your calculation to a weather report, confirm whether the report shows station pressure or sea-level pressure and use matching units.

Standard sea-level pressure is a reference value, not the pressure on every day at sea level. Consequently, a calculator based on 101.325 kPa will not reproduce every local barometer reading, even if the altitude is entered correctly.

Common Calculation Mistakes and Limits

• Mixing feet and metres: the calculator expects metres. Entering a number in feet without converting it overstates the altitude and produces an incorrect estimate.
• Confusing elevation with height: a building’s height above its surroundings is not necessarily its altitude above sea level. Add the ground elevation if you need the building’s approximate altitude.
• Comparing unlike pressure readings: station pressure and sea-level-adjusted pressure are not interchangeable.
• Expecting a weather forecast: altitude alone cannot account for current weather or local atmospheric conditions.
• Using the model outside its range: this calculator covers 0–20,000 m. The atmosphere has different temperature layers, so a single lower-atmosphere equation should not be extended indefinitely.

Rounding is another source of apparent disagreement. Keep full precision through the calculation and round only the final result. For many general comparisons, two decimal places in kPa are more than adequate, but a displayed estimate should not be mistaken for a precision measurement.

Frequently Asked Questions

What is atmospheric pressure at 1,000 metres?
Under the standard-atmosphere formula used here, it is about 89.87 kPa, or 898.7 hPa. Actual pressure can differ with weather and local atmospheric conditions.

How do I calculate pressure at altitude in feet?
Convert feet to metres by multiplying by 0.3048, then use the resulting altitude in the formula. For instance, 5,000 ft is 1,524 m, approximately.

Does pressure decrease linearly with altitude?
No. Pressure decreases nonlinearly because air density changes with height. The standard-atmosphere equation accounts for that through a power relationship rather than a constant pressure drop per metre.

Why is my barometer reading different from this result?
The calculator uses standard temperature and atmospheric assumptions. Weather, temperature structure, and whether the barometer reports station or sea-level pressure can all explain a difference.

What is the standard atmospheric pressure at sea level?
The reference value is 101.325 kPa, equal to 1,013.25 hPa, 1 atm, or about 14.696 psi. A real sea-level reading varies with weather.

Can this formula calculate pressure in the upper atmosphere?
Not reliably. This calculator is limited to 20,000 m and uses a lower-atmosphere model. Higher altitudes require a model that accounts for the atmosphere’s changing temperature layers.

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in h | Altitude above sea level | m | 1000 | 0 | 20000
out p | Atmospheric pressure | kPa | 101.325 * (1 - 0.0065 * h / 288.15) ^ 5.25588 | 2
out hp | Atmospheric pressure | hPa | p * 10 | 1
out atm | Atmospheric pressure | atm | p / 101.325 | 4