# Pressure Calculator

Created by Davide Borchia
Last updated: Jul 23, 2022

"Pressure pushing down on me, pressing down on you, no man ask for": can we help David Bowie and Freddy Mercury calculate that pressure?

• What is pressure;
• Why we don't get crushed by the weight of the atmosphere above us;
• How to calculate pressure;
• The most important measurement units of pressure;
• Some examples of the pressure formula in action.

## What is pressure?

For physicists, pressure is the amount of perpendicular force applied to a unit area. Pressure is a macroscopic quantity. When we are talking about the pressure of our feet over the floor, we can easily identify the force (our weight) that determines the pressure. However, when we are dealing with atmospheric pressure (aerostatic pressure), we are witnessing a property arising from the microscopic behavior of molecules: the pressure of a gas is the effect of the huge number of collisions between the gas molecules and the walls of its container.

The higher you go, the lower the pressure: learn why with our air pressure at altitude calculator!

The pressure of a gas doesn't act only on the walls of the container but also on every object exposed to it. Every human is surrounded by the pressure of the air column above them, and trust us, it's not little: over a square meter at sea level, there are more than $10$ tons of atmosphere.

So how is it possible we don't get crushed like a can?

First thing: as said, the pressure of a gas is equal over every exposed surface. Second, our bodies are made of solid and liquids (mainly) that are uncompressible: they "answer" to an applied pressure with the same force (think of Newton's third law). So no crushing.

For the gases inside our bodies, the story is a bit different. We are engineered by evolution to live at sea level (or slightly above it), so the gases inside us are at that pressure. If we experience an impromptu change of external pressure, our bodies will react: that's what happens when your ears "pop" during a flight!

## How do we calculate pressure in physics?

We can write a very general formula for the pressure that holds for every situation. From the definition above, the pressure equation is nothing but the ratio between force and surface:

$p = \frac{F}{A}$

Where:

• $p$ is the pressure (you can use either lowercase or uppercase "p");
• $F$ is the perpendicular force; and
• $A$ is the area where the force is applied.

To calculate pressure, remember to consider the perpendicular component of the incident force! The component parallel to the surface never contributes to the value of $p$.

Pressure is measured with various units, usually depending on the context. The more general one is the pascal, symbol $\text{Pa}$. We define this unit as:

$1\ \text{Pa} = \frac{1\ \text{N}}{1\ \text{m}^2}$

From this definition, we can list the other measurement units for pressure, starting from the more common ones::

• The $\text{PSI}$, (pound per square inch, $\text{lbf}/\text{in}^2$) for the US customary units;
• The $\text{bar}$, which equals $100,000\ \text{Pa}$ and roughly correspond to the atmospheric pressure at sea level;
• The $\text{atm}$, which at $101,325\ \text{Pa}$ equals the **average atmospheric pressure at sea level.

However, these are just a few examples: pressure is notoriously defined with a wide array of units, which often makes pressure conversion a difficult task!

## How do I measure pressure?

We measure pressure with a type of instrument called a barometer, from the Latin word for weight.

Barometers come in all shapes and types, but they all behave in similar ways. However, we can obtain a different reading by setting different zero-points.

If we take a measurement against a vacuum, we are measuring the absolute pressure. When you are flying at cruising altitude, the cabin of your plane is pressurized at $0.8\ \text{atm}$: this is the absolute pressure.

If we take as a reference the atmospheric pressure, we are dealing with the gauge pressure. Following the plane example, the gauge pressure would be $-0.2\ \text{atm}$.

If we are taking any other reference value, then we are measuring the differential pressure.

## Some examples of pressure: the pressure equation in real life

A submarine can withstand extreme pressures during its operation. The Soviet submarine K-278 Kosmolet reached a depth of $1,020\ \text{m}$ in the Norwegian Sea. At that depth, the pressure is $101.9\ \text{atm}$, or $10,325,018\ \text{Pa}$. If you plug this value in the pressure equation, you'll find a weight corresponding to a mass of water of more than $1,000\ \text{t}$, for each square meter! Imagine an Amtrack train with ten carriages. On every single square meter!

And this is nothing. The deepest known point of our planet, the Challenger Deep at the Mariana trench, lies $10,920\ \text{m}$ below the ocean's surface. At that depth, the pressure is a staggering $1,081.1\ \text{atm}$. Insert the value in the correct field of the calculator for the pressure formula: you will find a force in newtons. Use our force calculator to find the mass of $11,000$ tons on each square meter of surface. This makes it one, if not the, hardest points to reach on Earth.

We calculated both these values with the hydrostatic pressure calculator: if you are interested in learning how the formula to calculate the pressure in a fluid, visit our tool!

Do you want more? The diamond anvil cell is an instrument used in physics and geology to study extremely high pressure. The properties of diamond (virtual incompressibility, purity, etc.) make it the best choice for the role. The instrument is designed to reduce the surface of contact to the minimum, allowing us to attain the required pressures. The highest pressure on record is $770\ \text{GPa}$, more than twice the pressure at the center of Earth.

Davide Borchia
Force
N
Area
ft²
Pressure
psi
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