Atmospheric Pressure at Altitude Calculator Formula

Understand the math behind the atmospheric pressure at altitude calculator. Each variable explained with a worked example.

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Formulas Used

Pressure at Altitude

pressure = surface_pressure * exp(-altitude / scale_height)

Pressure (atm)

pressure_atm = surface_pressure * exp(-altitude / scale_height) / 101325

Fraction of Sea-Level Pressure

fraction_remaining = exp(-altitude / scale_height)

Variables

VariableDescriptionDefault
surface_pressureSurface Pressure (P0)(Pa)101325
altitudeAltitude (h)(m)5000
scale_heightScale 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)

  • *P0* = surface pressure
  • *h* = altitude above the surface
  • *H* = scale height (about 8.5 km for Earth)

    • 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).

    surface_pressure = 101325altitude = 5000scale_height = 8500
    1. 01P = P0 * exp(-h/H)
    2. 02P = 101325 * exp(-5000/8500)
    3. 03exp(-0.5882) = 0.5556
    4. 04P = 101325 * 0.5556 = 56 300 Pa = 0.556 atm

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