Atmospheric Pressure at Altitude Calculator Formula
Understand the math behind the atmospheric pressure at altitude calculator. Each variable explained with a worked example.
Formulas Used
Pressure at Altitude
pressure = surface_pressure * exp(-altitude / scale_height)Pressure (atm)
pressure_atm = surface_pressure * exp(-altitude / scale_height) / 101325Fraction of Sea-Level Pressure
fraction_remaining = exp(-altitude / scale_height)Variables
| Variable | Description | Default |
|---|---|---|
surface_pressure | Surface Pressure (P0)(Pa) | 101325 |
altitude | Altitude (h)(m) | 5000 |
scale_height | Scale Height (H)(m) | 8500 |
How It Works
Barometric Pressure at Altitude
For an isothermal atmosphere the pressure decreases exponentially with height.
Formula
P(h) = P0 * exp(-h / H)
Every scale height of ascent reduces the pressure by a factor of e (about 2.718).
Worked Example
Earth at 5 000 m altitude (P0 = 101 325 Pa, H = 8 500 m).
- 01P = P0 * exp(-h/H)
- 02P = 101325 * exp(-5000/8500)
- 03exp(-0.5882) = 0.5556
- 04P = 101325 * 0.5556 = 56 300 Pa = 0.556 atm
Frequently Asked Questions
Does this work for Mars?
Yes, but with Martian values: P0 is approximately 636 Pa and H is approximately 11 100 m.
Why is the atmosphere assumed isothermal?
The exponential formula is exact for constant temperature. For real atmospheres with lapse rates, it is a good first approximation over limited altitude ranges.
At what altitude is pressure half of sea level?
Solving exp(-h/H) = 0.5 gives h = H * ln(2), approximately 5 900 m on Earth.
Ready to run the numbers?
Open Atmospheric Pressure at Altitude Calculator