Pressure (Physics): Definition, Units, Formula & Examples

Pressure is one of the most important concepts in physics. While you’ll undoubtedly have some idea of what pressure is from things like atmospheric pressure readings given in weather reports or water pressure in your home’s heating system, when you’re studying physics, the details really matter. Learning the precise definition of pressure helps you understand key concepts related to gases, thermodynamics, buoyancy and much more.

Definition of Pressure

Pressure is simply defined as the ​amount of force per unit area​. The key point when you’re trying to understand pressure is to think about what happens on the atomic level in a liquid or gas at high pressure. The constituent molecules are constantly moving around, and this means they’re bumping into the walls of the container all the time. The more they move (due to higher temperatures), the more they bump into the walls of the container and the higher the pressure.

The definition, then, simply turns this general picture into a clear, physical definition. Every time a molecule strikes the side of a container, it imparts a force onto it, and the sum of these forces for a small section of the interior is the total pressure. The most convenient way to do this is to choose an area that is one “unit” squared in your chosen measurement system, which is what “per unit area” means in the definition.

Mathematically, you can define pressure as:

P = \frac{F}{A}

Where ​P​ is pressure, ​F​ is the force on the surface and ​A​ is area.

Pressure Units

The SI unit of pressure is the ​Pascal (Pa)​, where 1 Pa = 1 N/m2, i.e. one Newton per square meter. The Newton is the unit of force, so it’s easy to see that the Pascal meets the requirements for a unit of pressure. However, the Pascal is quite a small unit for things like atmospheric pressure, so there are quite a large number of alternatives also in use. One of the simplest ways to do this is to simply use kPa (i.e. kilopascals, or thousands of pascals), but there are other options too.

The most well-known alternative unit is ​pounds per square inch (psi)​, which is used in the U.S. for things like water pressure. For atmospheric pressure, the appropriately-named unit “atmospheres” (atm) is often used, because 1 atm corresponds to atmospheric pressure at sea level. The torr is an alternative unit used for atmospheric pressures, which is defined as 1/760 of an atmosphere, or 133.3 Pa. In meteorology, millibars are often used, where 1 bar = 100,000 Pa and 1 millibar = 100 Pa.

Finally, there are some even more unusual units for pressure, including millimeters of mercury (mmHg), which is defined based on the pressure exerted by a 1 mm tall column of mercury and is often used for blood pressure.

This was originally the intention of the torr, and so it shouldn’t come as much of a surprise that the two are essentially the same: 1 mmHg = 133.322 Pa. Finally, in some cases pressure is measured as a value in dyne per square centimeter. Here, the dyne is a unit of force with 1 dyne = 0.00001 Newtons, and so 1 dyne per square centimeter equals 0.1 Pa.

Atmospheric Pressure

Atmospheric pressure at sea level is equal to 1 atmosphere, or around 101,325 Pa. This is a ​huge​ value – it’s more than the force of gravity on 10,000 kg of matter, pushing down on you ​all the time​. The pressure is essentially just this, but the matter is actually the air: Pressure is literally caused by the weight of the air pushing down over the surface of the Earth.

This might seem strange because you never ​notice​ atmospheric pressure, even though it’s so massive, but you’ve evolved in this environment, and so you don’t notice it. There is a measure of pressure that takes this into account, too, called ​gauge pressure​. This is the pressure difference between the absolute pressure (i.e. the total pressure) and atmospheric pressure.

For example, if you have a completely flat tire on your car, when you connected a gauge it would read zero. However, there is ​air​ inside the tire that’s at atmospheric pressure; it’s just that this information isn’t really relevant when you’re interested in whether something like a car tire is appropriately pressurized. There is still absolute pressure, but in this case (and many others) the gauge pressure is really what you need to know.

Water Pressure

Water pressure is one of the most familiar forms of pressure in day-to-day life, but in a hydrostatic situation (one where the water isn’t flowing), the pressure works differently to the way it does in your water heating system. However, this is an interesting situation to look at when you’re first learning about pressure because the pressure in a situation like this depends on depth.

The pressure (​P​) at any depth (​d​) is given by the equation:

P = ρgd

Where ​ρ​ (“rho”) is the density of the liquid and ​g​ is the acceleration due to gravity (on Earth, ​g​ = 9.81 m/s2). The density of water at 20 °C is ​ρ​ = 998 kg/m3, but generally the calculations are greatly simplified if you assume a temperature of 4 °C, where ​ρ​ = 1000 kg/m3 or 1 g/cm3. So if you’re calculating the water pressure at a depth of 25 m, the equation shows:

\begin{aligned} P &= ρgd \\ &= 1000 \text{ kg/m}^3 × 9.81 \text{ m/s}^2 × 25 \text{ m} \\ &=245250 \text{ Pa} = 245.3 \text{ kPa} \\ \end{aligned}

How a Barometer Works

A barometer is a device for measuring atmospheric pressure (sometimes called barometric pressure) that works by using a column of mercury. A tube containing mercury – open at one end – is inverted and placed in a reservoir that also contains mercury. When it’s set up, the reservoir is open to the atmosphere, but the mercury in the tube is only in contact with the reservoir, and the process of inverting the tube creates a vacuum in the top.

The barometer measures pressure because the force due to atmospheric pressure (basically the weight of the air) pushes down on the mercury in the reservoir and thereby pushes the mercury in the tube up.

If the column of mercury creates an equally large force directed downwards (the water pressure equation from the previous section describes the origin of this force), there will be no change, but if the air pressure is higher, the level of mercury in the tube will have to increase by a corresponding amount to balance the forces. After calibrating the scale, this simple system can be used to measure the air pressure.

Other Examples

There are other examples of pressure you’ll be familiar with from everyday life too, including blood pressure. This is the (gauge) pressure created by your heart pumping blood around your body, and this is measure in mmHg (millimeters of mercury), and you have two readings: systolic for the pressure when your heart pushes out and diastolic for the pressure between beats. Of course, the pressure during beats is the higher number of the two, and between 90/60 mmHg and 120/80 mmHg is considered ideal.

Air pressure is also a crucial concept in meteorology, which maps the positions and movements of high pressure and low pressure systems to predict changes in the weather. Through the relationship between atmospheric pressure and temperature, and what happens when a low pressure system meets a high pressure system, meteorologists predict the temperatures and things such as wind in different regions.

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