# why is air pressure in force per area instead of volume?

The basic unit of Pascals, (Pa), is one Newton (N) per meter square (area). Why is this, especially for things like air pressure that deal with three dimensional space? Shouldn't something like air pressure (e.g. atmospheric pressure) be in newtons per unit volume? (e.g. N/m^3)

• because for example the total compressive force on an object in a fluid scales with its surface area not its volume, so defining a quantity as force per area is more natural Oct 20, 2015 at 2:46

Air pressure itself doesn't act on a three-dimensional space! It's the pressure on a surface exerted by the air. For example, imagine pressurizing a bike tire. The air inside the tire can only push against the inner surface of the tire, which is two-dimensional.

• Yes but for like compressed air, isn't there force in the air itself? Like the atoms pushing on each other? Oct 20, 2015 at 2:55
• Yep, but each atom can only push against atoms that are close to it. If you divide the air into two 'sections' with a plane, you have the atoms on each side of the plane applying pressure to the plane. But there's no way to divide the air into sections with a 'space' (I can't even imagine that!), so you can't really have three-dimensional pressure. Maybe the pressure you're thinking of is the atoms pushing each other in all three dimensions—which is true, but the important thing is that they push on a plane in all three dimensions.
– eyqs
Oct 20, 2015 at 2:58
• Interesting, I hadn't thought of it that way. So if I have a balloon, the pressure is against the surface of the balloon, measured in area? Oct 20, 2015 at 3:00
• Yep, that's exactly right! The air molecules can't push past the surface, they can only push on what's right in front of them.
– eyqs
Oct 20, 2015 at 3:02
• Maybe one last comment—imagine exerting pressure uniformly against a plane. You can do that, because you can push any point on that plane. But now imagine exerting pressure uniformly against a 'space'. You can push on the part of the 'space' that's closest to you (which is just a plane), but you can't reach into the space to push on every single point!
– eyqs
Oct 20, 2015 at 3:06