Barometric Formula (Troposphere)

vCalc Reviewed
Equation / Last modified by KurtHeckman on 2016/10/24 14:32
Barometric Formula (Troposphere)
Variable Instructions Datatype
Altitude Above Sea Level Enter the altitude in your chosen units Decimal (m)
1 variables
vCalc.Barometric Formula (Troposphere)

The Barometric Pressure at Altitude calculator computes the normal barometric pressure based on the altitude (h) using the Exponential Atmosphere formula (aka Isothermal Atmosphere" formula1).

Atmospheric pressure generally decreases as altitude within the troposphere increases.  Although weather and climate may influence exact atmospheric pressure in any given region, an approximation of pressure within the troposphere can be made with knowledge of altitude alone.

Atmospheric pressure is the force per unit area exerted on a surface by the weight of air above in the atmosphere of Earth.  The troposphere is the lowest layer of Earth's atmosphere, extending about 17km (11 miles) from the Earth's surface in middle latitudes2.


The formula relates pressure, p, to and altitude, h, as
                      `p = p_0 * ( 1 - (g * h)/(c_p * T_0) ) ^ ((c_p * M) / R) `

with the following parameters

Parameter Value
p0  - sea level standard atmospheric pressure 101325 Pa
L  - temperature lapse rate, = g/cp for dry air 0.0065 K/m
cp -  constant pressure specific heat 1007 J/(kg•K)
T0  - sea level standard temperature 288.15 K
g  - Earth-surface gravitational acceleration 9.80665 m/s2
M  -  molar mass of dry air 0.0289644 kg/mol
R  -  universal gas constant 8.31447 J/(mol•K)


Empirical knowledge of the effects of barometric pressure has existed for centuries, as the construction of effective pumps demonstrates.  However, the first documented theoretical explanation of barometric pressure accompanied an experiment performed by Evangelista Torricelli in 1643 or 1644, which became known at the time as "The Experiment from Italy."3


This formula is applicable only to altitudes up to about 44,000 meters.  Additionally, local weather and climate effects also affect the exact barometric pressure at any given point.

See also

Ideal gas law (pressure)