Interesting fact: If you could gather all the air around Earth into one colossal pile, it would still form only a thin shell compared with the planet's size.
The answer: Earth's air weighs about 5.15 x 10^18 kilograms in total, which is the same order of magnitude as the mass of the atmosphere as a whole. It is an enormous number, even though the atmosphere looks thin from space.
This question is basically a planetary version of asking how much the atmosphere weighs. The challenge is that Earth's air is spread unevenly, compresses under gravity, and gradually thins with altitude. Knowing its total mass matters in climate science, weather prediction, atmospheric chemistry, and understanding how life survives beneath a stable blanket of gases.



