How to Calculate the Mass of the Earth's Atmosphere

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We live at the bottom of an ocean of air, even if we're not always aware of this. Earth's atmosphere, like all other physical things and your aunt's cooking, has mass, a great deal of mass, in fact. Like other physical properties, mass can be measured, even the mass of something as seemingly daunting to calculate as this planet's atmosphere. You won't need a giant trash bag or a really big set of scales to measure the mass of the Earth's atmosphere, just some commonsense applications of the laws of physics and a few tools.

Things You'll Need

  • Barometer
  • Pen and paper
  • Calculator
  • Measure atmospheric pressure at sea level, using the barometer. Take multiple readings, on different days and in different spots, then average them out. The average level at sea level, according to the University of Illinois, is 29.92 inches of mercury, or 1,013.25 millibars, or 1 atmosphere (atm). That's 14.7 lbs. of pressure on every square inch of the Earth, or your body, notes Physlink.com, or about 1 kg of atmospheric mass for every square centimeter.

  • Calculate the surface area of the Earth. Think of the Earth as a ball whose radius, the distance from the center to the surface, is about 4,000 miles or 6,300 km. Apply the formula for determining the size of the surface of a sphere, 4 times pi (which we'll round off to 3.14) times the square of the radius. Write down the result, 498,506,400 square km.

  • Convert square kilometers to square centimeters; there are 10 billion square cm in each square km, or a 1 followed by 10 zeroes. Following that formula in our example yields 4,985,064,000,000,000,000 square cm. Since each square centimeter of the Earth's surface has a kilogram of mass over it, and there are 1,000 kg in a metric ton, the total atmospheric mass works out to about 5 times 10 to the 15th power metric tons, or 5 quadrillion metric tons.

Tips & Warnings

  • These numbers are all estimates, of course. The Earth isn't a perfect sphere, and the atmosphere isn't a perfect wrap, either. Whether the air is dry or wet can have a big effect on the numbers, too; researchers Kevin Trenberth and Lesley Smith point out that atmospheric mass, depending on the water vapor in the air, can range by 1.5 quadrillion tons.
  • Big as those numbers sound, remember that the Earth itself is a million times more massive than its atmosphere, says the Santa Cruz Institute for Particle Physics.
  • Don't confuse "mass" with "weight," even though both are measured in pounds or kilograms. Mass measures the amount of matter. The weight of that matter depends on the force of gravity; mass doesn't. An astronaut with a mass of 200 lbs. on Earth will have the same mass while floating in weightless space.

References

  • Photo Credit Hemera Technologies/Photos.com/Getty Images
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