# Is it possible to calculate atmospheric pressure if given temperature (F) and elevation?

I am working on a report at work and need to determine the atmospheric pressure for small intervals over a 24 hour period. Searching Google, I've found charts which give a base pressure of 14.65 psia at sea level. This is at 68F. That changes to 13.17 psia at 3000ft above sea level.

What I am looking to do is create a spreadsheet where I enter the elevation as a constant, then provide the temperature (F), then have it calculate the atmospheric pressure. Knowing it is 13/17 psia at 68F is useful only if the temperature is 68F for the entire 24 hour period, but it isn't. Currently it ranges from 30F to 75F but could move either direction substantially depending on time of year.

Is this possible to determine?

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There is a standard model of the atmosphere
It's also built into matlab, I don't know of any spreadsheets but some googling should find one.

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That built into matlab function you quote is in the Aerospace toolbox, a toolbox far from all Matlab users have access to. –  gerrit Feb 20 '13 at 8:48
Sorry - don't use matlab, it just came up in a search for an excel file –  Martin Beckett Feb 20 '13 at 14:48

It depends on the precision you need.

A common and good approximation is the Hypsometric equation, that relates pressure and elevation in the standard Earth atmosphere (source Wikipedia):

$\ h = z_2 - z_1 = \frac{R \cdot T}{g} \cdot \ln \left [ \frac{P_1}{P_2} \right ]$

• $h$ = thickness of the layer [m]
• $z$ = geopotential height [m]
• $R$ = specific gas constant for dry air
• $T$ = average temperature throughout the layer in kelvin [K]
• $g$ = gravitational acceleration [m/s$^2$]
• $P$ = pressure [Pa]

You can also write it as:

$( z_2 - z_1 ) = \frac{R \cdot Ta}{g} \ln \left( \frac{P_1}{P_2} \right)$

There exist other approximations, for example based on a climatology of lat/lon what parametrise for $g$ and $R$.

A very simple approximation for a typical temperature and pressure for a standard tropical atmosphere, you can use,

$z = 16 \cdot 10^3 \cdot 5 - \log_{10}(P_1))$

where $P_1$ is the pressure you're interested in in Pa.

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