How Heavy Is the Air?

Figuring out the mass of Earth’s atmosphere via the back of an envelope

May the force be with you

Let’s start with the relationship between mass and weight: something with a mass m has a weight mg. In everyday conversation we use the terms mass and weight interchangeably, and we use units of mass when we talk about weight (e.g., a kilogram is a unit of mass and, if you’re still using old money, a pound is defined as a unit of mass rather than of weight). Weight is a force and you may remember F=ma as the classical equation relating force to mass and acceleration. This is Newton’s second law of motion.

Under pressure

Pressure is something that is reported on weather apps and news sources. The only stumbling block to being able to apply what you can recall is the units. If you recall pressure as a manometric measurement, i.e., height of fluid in a manometer, you’ll need to know how to get from that to a measurement in SI units. Knowing that standard atmospheric pressure at sea level (1 atm) corresponds to 760 mm Hg (millimetres of mercury) is not immediately helpful when what we need here is a measurement in pascals (1 pascal = 1 Pa = 1 newton per square metre = 1 Nm⁻²).

Area surveillance

Force relates to pressure as F=PA, where P is the pressure and A is the area over which the pressure applies. For an area of 1 m² we have F and, recalling that F=mg, dividing by g we have m. Multiply that by the surface area of the Earth and we have the mass of the atmosphere.

Mass effect

We calculated the mass per square metre earlier as 10 000 kg, which gives the total mass of the atmosphere as 5×10¹⁴×10⁴ kg = 5×10¹⁸ kg.



consultant · father · husband · itinerant · programmer · speaker · trainer · writer

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
Kevlin Henney

consultant · father · husband · itinerant · programmer · speaker · trainer · writer