If Clouds Are Made of Water, How Do They Stay in the Air?

By Rhett Allain

Everyone loves clouds. Although they are gigantic and beyond our reach, they inspire us with their wide variety of shapes. I mean, who hasn't played the game of guessing what a cloud looks like?

Of course, cloud watching can lead to some more scientific questions. If clouds contain water, shouldn't they be heavier than the air around them? And if so, why do they float?

Answering those questions takes a few steps, so let's get to it.

Why Do Things Float?

If you take a helium-filled balloon from a party and let it go, it doesn't fall. It will likely rise up in the air—although it's possible that it’s so perfectly weighted that it neither rises nor falls, but simply hovers. We often call this floating. But how does it work?

The simplest way to understand it is to consider air floating in air. (Yes, air floats.) Imagine you have a block of air that is 1 cubic meter. Air has mass, so there is a downward-pulling gravitational force on this air. If it's near the surface of the Earth, this force has a magnitude equal to the product of the mass of air (m) and the gravitational field (g = 9.8 newtons per kilogram). If there’s no wind, and the block of air just stays in place, then the total force on it must be equal to zero newtons. There has to be an upward-pushing force that's equal to the gravitational force. We call this upward-pushing force the buoyancy force.

The buoyancy force is actually the result of the air around the cube pushing against it in all directions. Since the density of air increases as you get closer to the ground, the force from the air pushing up from the bottom of the cube is greater than the force from the air pushing down on the top. The result is a net upward-pushing force.

If I know the density of air (ρ = 1.2 kg/m3), then I can calculate the magnitude of this buoyancy force. (Remember that m = ρV, where V is the volume.) I'm going to write the density as ρair so that we don't confuse it with other things later.

Illustration: Rhett Allain