Why You Float in Water but Sink in Air

Step off the edge of a pool and you bob back up. Step off the edge of a cliff and you do not. Both times you are surrounded by a fluid — water in one case, air in the other — and in both cases that fluid pushes up on you. So why does one push hold you up and the other does not?

The push has a name: buoyancy. Any fluid you are sitting in squeezes you from every direction. The squeeze from below is a little stronger than the squeeze from above, because pressure in a fluid grows as you go deeper. That tiny mismatch adds up to a net upward shove. This is the buoyant force.

Here is the part that surprises people. The size of the buoyant force does not depend on what you are made of. It depends on the fluid you pushed out of the way. If your body takes up 70 liters of space, then jumping into a pool shoves 70 liters of water aside, and the water shoves back with a force equal to the weight of that displaced water. Jumping off a cliff shoves 70 liters of air aside, and the air shoves back with a force equal to the weight of that displaced air. Same volume, very different weights.

Seventy liters of water weighs about 70 kilograms — roughly what a person weighs. Seventy liters of air weighs less than a tenth of a kilogram. So in the pool, the upward shove from the water nearly matches your weight, and you float. In the air, the upward shove is almost nothing compared to your weight, and you fall.

The cleanest way to say this uses density, which is how much mass is packed into a given volume. Water is about 800 times denser than air. A fluid can only hold you up if its density is close to or greater than yours. Your body's density is just barely under water's, which is why you float low in the pool with only your face above the surface. Your density is hundreds of times greater than air's, so air cannot come close to supporting you.

This also explains things that look strange at first. A steel ship floats because its hull encloses a huge volume of air, dropping the ship's average density below water's. A hot-air balloon rises because heating the air inside makes that air less dense than the cool air outside — so the balloon, taken as a whole, is lighter than the air it pushes aside, and the air's buoyant force wins. A helium balloon does the same trick without needing a flame, because helium is already much less dense than air.

So the question "will it float?" is really the question "is this thing less dense than the fluid around it?" Floating and sinking are not opposites of swimming and falling. They are the same physics, run with different numbers. You float in water and sink in air for the same reason a rock sinks in water: the fluid you are in is either dense enough to hold you up, or it isn't.