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

INSTRUCTIONS: Choose units and enter the following:

• (h)  Height (altitude) above sea level.

Barometric Pressure at Altitude (p): The barometric pressure is returned in pascals.  However, this can be automatically converted to other pressure units (e.g. atmospheres) via the pull-down menu.

The Math / Science

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 latitudes¹.

The Exponental Atomosphere formula (aka Isothermal Atmosphere" formula²) 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:

• p - atmospheric pressure at altitude
• p₀  - sea level standard atmospheric pressure (101325 Pa)
• L  - temperature lapse rate, = g/cp for dry air (0.0065 K/m)
• c_p -  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) )

History

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

Usage

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)

1. ^ http://en.wikipedia.org/wiki/Atmospheric_pressure
2. ^ http://en.wikipedia.org/wiki/Atmospheric_pressure
3. ^ http://www.physics.oregonstate.edu/~tgiebult/COURSES/ph441/pdf/43.pdf