Calculation of the relationship between atmospheric pressure and altitude for dry air

parameters and units:

z [m] = altitude

p₀ [hPa] = pressure at the ground

p [hPa] = pressure at altitude z

R* = 287 J kg^-1 K^-1 = gas constant for dry air

R* = R / M_a

R = gas constant = 8.314 J K^-1 mol^-1

M_a = molecular weight of air = 28.96 g mol^-1

g = gravity accelaration constant
= 9.81 m s^-2

T_m [K] = mid temperature between the the temperature at the ground T₀ and the temperature in altitude z T_z

T_m = (T₀ + T_z) / 2

g / R* = 0.034 K m^-1

1 J = 1 N m

1 N = 1 kg m s^-2

The formula is only valid for dry air. For humid air the molecular weight changes.
For the plotted graph the following reasonable assumptions have been made:

Temperature at the ground: 20°C
Temperature decrease rate: - 1°C / 200 m
Temperature at 10000 m: - 30°C

Pressure at the ground: 1000 hPa

It can be seen from the calculated pressures in higher altitudes, that the pressure in 5,500 m is about 500 hPa in 11,000 m about 250 hPa.

about this page:

author: Dr. Elmar Uherek - Max Planck Institute, Mainz
last published: 2004-04-20