How to Calculate PSI

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Pounds per square inch (psi) is a unit of pressure most commonly associated with tire pressure for an automobile or bike tire. However, because pressure gauges are attached to most tire pumps, there's often very little need to calculate psi in this context. People working with hydraulics also use psi, often to determine the amount of force that potable water or waste water is exerting on a vessel or system.

Determining the force of water is also important in hydrostatics, for example, to see how much pressure the walls of a submarine are capable of withstanding. The military also uses pressure calculations when developing the anti-submarine measures known as depth charges, which explode when a certain water pressure flips on a spring-loaded detonator. Determining the amount of pressure a column of water exerts on a surface requires solving a simple equation.

Determining Water Pressure

    Use the formula pressure P = 0.43h where h is the water column in feet. We use the constant 0.43 (lb/in2)/ft because this is the amount of pressure 1 foot of water places on a surface below it regardless of the volume of water.

    Perform the calculation. For example, if a submarine is operating at a depth of 2,000 feet below the surface of the water, or in other words, in water with a 2,000-foot height, then

    P=0.43\frac{\text{ lb/in}^2}{\text{ft}}\times 2000\text{ ft}=860\frac{\text{lb}}{\text{in}^2}

    meaning 860 psi of force is being exerted on the submarine.

    Psi can also be converted into any number of other popular units, such as mmHg (multiply the psi value by 51.715), kiloPascals (multiply by 6.895) and millibars (multiply by 68.948). So in our example, the submarine is experiencing 44,474.79 mmHg, 5,929.7 kiloPascals (kPa) or 59,295.28 millibars of pressure.


    • The depth of 2,000 feet given in the example is probably too much for the typical military submarine to handle. On April 10, 1963, the nuclear attack submarine USS Thresher accidentally descended to its maximum test depth of around 1,300 feet off the coast of Cape Cod, killing everyone on board. Some research submarines are built to go to much greater depths. According to Rutgers physics professor Dick Plano, a submarine at the Woods Hole Oceanographic Institution can drop down nearly 15,000 feet.


    • Always use caution when working with any kind of pressurized system.



About the Author

Brett Smith is a science journalist based in Buffalo, N.Y. A graduate of the State University of New York - Buffalo, he has more than seven years of experience working in a professional laboratory setting.