Math in the Natural Sciences

Math in Meteorology

How is air density related to air pressure?

The expression “thin air” is actually a reference to the atmosphere’s density— or how “thick” the air molecules are near the Earth’s surface. In chemistry terms, density is merely the mass of anything (including air) divided by the volume the mass occupies. For example, the density of dry air at sea level is high, mainly due to the pull of gravity. In metric system terms, sea level density is about 1.2929 kilograms/meter3, or about 1/800th the density of water. But as altitude increases, the density drops dramatically. Mathematically speaking, the density of air is proportional to the air pressure and inversely proportional to temperature. Thus, the higher up one is in the atmosphere, the lower the air pressure and the lower the air density.

There is somewhat of an athletic advantage to higher elevations—at least for players of such sports as football and baseball. Because the air density is lower, a ball thrown in high-elevation places like Denver, Colorado, will travel even farther than a ball thrown in a close-to-sea-level city, such as Miami, Florida. In fact, the air at the Denver stadium allows balls to travel almost 10 percent farther.


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