How to Calculate Force Based on Pressure

Pressure and force are related, and so you can calculate one if you know the other by using the physics equation, F = P/A. Because pressure is force divided by area, its meter-kilogram-second (MKS) units are newtons per square meter, or N/m2. In the foot-pound-second (FPS) system, the units are pounds per square inch, or psi.

The unit newtons per square meter is so common in physics that it has a special name: the pascal, which equals 1 newton per square meter. The pascal is abbreviated as Pa.

You don’t have to be underwater to experience pressure from a fluid. Air exerts pressure, too, due to the weight of the air above you. Here’s how much pressure the air exerts on you at sea level:

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The air pressure at sea level is a standard pressure that people refer to as 1 atmosphere (abbreviated atm):

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If you convert an atmosphere to pounds per square inch, it’s about 14.7 psi. That means that 14.7 pounds of force are pressing in on every square inch of your body at sea level.

Your body pushes back with 14.7 psi, so you don’t feel any pressure on you at all. But if you suddenly got transported to outer space, the inward pressure of the air pushing on you would be gone, and all that would remain would be the 14.7 pounds per square inch your body exerted outward. You wouldn’t explode, but your lungs could burst if you tried to hold your breath. The change in pressure could also cause the nitrogen in your blood to form bubbles and give you the bends!

Here’s a pressure example problem using water pressure. Say you’re in your neighbor’s pool, waiting near the bottom until your neighbors give up trying to chase you off and go back into the house. You’re near the deep end of the pool, and using the handy pressure gauge you always carry, you measure the pressure on the back of your hand as

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What force does the water exert on the back of your hand? The back of your hand has an area of about

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You reason that if P = F/A, then the following is true:

F = PA

Plugging in the numbers and solving gives you the answer:

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Yikes. A thousand newtons! You whip out your underwater calculator to find that’s about 230 pounds. Forces add up quickly when you’re underwater because water is a heavy liquid. The force you feel is the weight of the water above you.

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