Atmospheric Pressure from Elevation and Angle

Atmospheric pressure from elevation can be estimated with the barometric formula; angle alone cannot determine it. Enter elevation above sea level and atmospheric temperature to calculate an approximate pressure, with the result shown in kilopascals and standard atmospheres.

Formula

This calculator uses the isothermal barometric formula, a simplified form of the hydrostatic pressure relation:

p = p₀ × exp(−g h / (R T))

• p is estimated pressure at the specified elevation, in kilopascals (kPa).
• p₀ is reference sea-level pressure, set here to 101.325 kPa.
• h is elevation above sea level, in metres (m).
• g is gravitational acceleration, taken as 9.80665 m/s².
• R is the specific gas constant for dry air, 287.05 J/(kg·K).
• T is the entered air temperature converted to kelvins: °C + 273.15.
• exp means the exponential function e raised to the expression in parentheses.

The second output converts kilopascals to atmospheres by dividing by 101.325 kPa per atmosphere. The equation assumes temperature is constant over the height interval and treats air as a dry ideal gas. Its temperature input must be above absolute zero; a broad upper bound simply prevents unreasonable entries, not a claim that the model is accurate in all conditions.

Worked Example

With the defaults, elevation is 1,000 m and temperature is 15°C. Convert temperature to kelvins: 15 + 273.15 = 288.15 K.

Calculate the exponent: −9.80665 × 1,000 ÷ (287.05 × 288.15) ≈ −0.1186.

Then p = 101.325 × exp(−0.1186) ≈ 90.00 kPa. In atmospheres, 90.00 ÷ 101.325 ≈ 0.8883 atm. Values are rounded to the precision shown by each calculator output.

What Elevation and Angle Tell You

Elevation matters because air pressure is caused by the weight of the air above a location. As altitude increases, there is generally less air overhead, so pressure falls. The drop is not a fixed number of kilopascals per kilometre: air density changes with altitude, and temperature changes the relationship between height and pressure.

An angle, by itself, gives no additional information about atmospheric pressure. A slope angle may help determine vertical height if you also know a distance along the slope. For a straight slope of length L and angle θ measured from the horizontal, the vertical rise is L × sin(θ). If the known distance is horizontal instead, the rise is horizontal distance × tan(θ). Use that vertical rise to update elevation; do not substitute the slope length directly as the elevation change.

For example, a 100 m slope at 30° above horizontal rises 50 m, because 100 × sin(30°) = 50. You would add 50 m to the starting elevation before estimating pressure. Without a distance, the angle does not reveal the rise.

How to Use and Interpret the Estimate

Enter the location’s elevation relative to mean sea level, not its height above a nearby valley or building. Enter a representative air temperature in degrees Celsius. The result is a model estimate for that elevation and temperature, rather than a reading from a local instrument.

• kPa is a common metric pressure unit; 1 kPa equals 1,000 pascals.
• Atmospheres compare the result with the standard reference pressure of 101.325 kPa.
• For US customary reporting, 1 kPa is approximately 0.1450 pounds per square inch (psi), and 1 standard atmosphere is approximately 14.696 psi.
• Elevation may be supplied in feet after converting it to metres: 1 ft = 0.3048 m.

At sea level, this model returns 101.325 kPa regardless of temperature because the reference pressure is fixed there. At positive elevations it returns a lower value. Actual sea-level pressure is not always the standard reference value, so the fixed baseline is useful for an estimate, not a substitute for local weather data.

Accuracy, Alternatives, and Common Errors

The atmosphere is layered and its temperature varies with altitude. A constant-temperature model is therefore a convenient approximation, especially across modest height differences, not a complete weather or atmospheric model. More detailed calculations use measured temperature profiles, humidity, and current pressure observations. For a precise local value, use a calibrated barometer or a reputable weather observation that reports station pressure at the site.

Common errors include confusing gauge pressure with absolute pressure, entering feet as though they were metres, and using a slope angle without its associated distance. This calculator estimates absolute atmospheric pressure. Gauge pressure is pressure relative to the surrounding atmosphere; a gauge at the local ambient pressure reads zero even though atmospheric pressure is not zero.

Another common misconception is that temperature alone determines the pressure at a place. Temperature affects the vertical pressure profile, but the actual pressure also depends on the mass of air above the location and changing weather systems. Likewise, pressure does not fall in a perfectly linear way with altitude. Avoid extending this simplified formula far beyond its stated 0–11,000 m elevation range or treating its rounded result as an observation.

Frequently Asked Questions

Can I calculate atmospheric pressure from elevation alone?
Yes, approximately, if you choose a standard atmosphere model and its assumptions. This calculator also asks for temperature because the isothermal formula uses temperature to estimate how quickly pressure changes with height.

Can an angle calculate pressure?
No. An angle has no pressure information on its own. If it describes a slope, combine it with a known slope or horizontal distance to find vertical elevation change, then use the resulting elevation in a pressure model.

What is standard atmospheric pressure at sea level?
The standard reference is 101.325 kPa, equal to 1 atmosphere or about 14.696 psi. Actual pressure at a sea-level location can differ with weather and other atmospheric conditions.

How do I convert elevation in feet to metres?
Multiply feet by 0.3048. For example, 3,280.84 ft is approximately 1,000 m. Convert before entering the value so the calculator’s units stay consistent.

Why does a barometer disagree with this result?
The formula fixes sea-level reference pressure and simplifies the temperature profile. Real weather, local temperature layers, humidity, and measurement conditions can shift observed pressure from the estimate.

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• Atmospheric Pressure from Elevation and Temperature

in h | Elevation | m | 1000 | 0 | 11000
in t | Atmospheric temperature | °C | 15 | -273.15 | 100
out p | Atmospheric pressure | kPa | 101.325 * exp(-9.80665 * (h / 1000) / (287.05 * (t + 273.15))) | 2
out a | Pressure | atm | p / 101.325 | 4