# Atmospheric scale height, how is it calculated?

Over on SE.Worldbuilding I found myself stuck on figuring what happens to the scale height of an atmosphere if the composition changes (The specific case involved something breathable in place of the Martian atmosphere.) Google is being quite useless in this regard.

• astro.unl.edu/naap/scaleheight/sh_bg1.html is the 2nd google result for "how to calculate scale height" – Organic Marble Jul 21 '16 at 20:15
• @OrganicMarble Argh! It's labeled as a definition of scale height and somehow I missed the fact that it also showed how to calculate it. – Loren Pechtel Jul 21 '16 at 20:23
• @OrganicMarble If you have time, go ahead and see if you can extract that into an answer. Someone else may have the same Google trouble as Loren. – called2voyage Jul 21 '16 at 20:45

$$H=\frac{kT}{Mg}$$
• $k$ is the Boltzmann constant. ($1.38 \cdot 10^{−23} \frac{J}{K}$)
• $g$ is the acceleration due to gravity.
• $T$ is the absolute temperature.
• $M$ is the average molecular mass.
Of the above factors, only the average molecular mass, $M$, changes if you change the composition. For example, oxygen is lighter than carbon dioxide, giving a larger scale height.
Be aware that changing the composition of the atmosphere also affects things like the green house effect, possibly also changing the absolute temperature, $T$.