Math in the Natural Sciences

Math in Meteorology

How much does air pressure decrease with altitude?

It takes mathematics to figure out how much air pressure decreases with altitude. Close to the surface, and due to the pull of gravity, the air pressure exerted by air molecules is greatest (around 1,000 millibars at sea level). From there, it declines quickly with altitude to 500 millibars at around 18,000 feet (5,500 meters). At 40 miles (64.37 kilometers), it will be 1/10,000th of the surface air pressure.

This can also be interpreted another way: For altitudes of less than about 3,000 feet (914.4 meters), the barometric air pressure decreases about 0.01 inches of mercury for each 10 feet (3 meters) of altitude (or a decrease of 1 inch of mercury for each 1,000 foot [304.8 meters] gain in altitude). If millibars are used, it is 1 millibar for every 26.25 foot (8 meter) altitude gain. That means if a person takes a ride in an elevator, hits the button for the 50th floor—and coincidentally has a barometer in his or her pocket—the pressure would fall by approximately 0.5 inch (1.27 centimeters) during the ascent. This also means that higher-altitude cities have major differences in barometric readings. For example, the air pressure in almost mile-high Denver, Colorado, is only 85 percent that of cities that reside at sea level.

