Pressure Calculator

Pressure is the intensity with which a force acts on a particular area. When a force is spread over a larger surface area, pressure decreases while a force concentrated on a very small surface area leads to a dramatic increase in pressure. This calculator computes pressure from force and contact area and also allows calculations in reverse. If one of the three fields is left blank, the value for that field will be computed.

What is pressure?

Pressure is defined as the force acting perpendicular to a surface divided by the area of that surface. Since pressure is a scalar quantity it has no particular direction, only a magnitude. At any point within a fluid, the pressure acts equally in all directions.

This concept can explain various everyday phenomena. A sharp knife is able to cut because its thin blade concentrates a small force over a very tiny area, creating high pressure. Snowshoes, on the other hand, spread out weight over a large surface area, keeping the pressure exerted on the snow low enough to prevent sinking.

Formula for pressure:

Pressure is defined as force divided by area.

Here P stands for pressure, F for the force acting on a surface and A for the area over which the force is distributed. In the SI unit system, dividing the force in newtons by the area in square metres results in a pressure value in pascals. One pascal corresponds to one newton per square metre.

Since this equation contains three quantities, it can be rearranged to calculate a missing quantity.

Example calculation:

Assume that a force of 600 newtons acts on a plate with an area of 1.5 square metres. The pressure is then:

However, if the contact area is reduced to that of a very thin high heel, which would be about 2 square centimeters, then for the same force this becomes 0.0002 square meters. The pressure increases to three million pascals, which is about thirty times atmospheric pressure. Although the force remains the same, a much smaller area results in a completely different outcome.

Rearranging the equation.

This table shows the same relationships expressed in three different forms corresponding to each of the three possible missing quantities.

Pressure units:

The pascal is the SI unit, but depending on your field of study, pressure will often be expressed in other units. In meteorology and industry, bar and kilopascals are common, while pounds per square inch is used in American engineering. Millimeters of mercury and torr are used for blood pressure measurements and vacuum work. This calculator allows you to select the appropriate units for each field and read off the values.

Manometric pressure, absolute pressure, differential pressure:

The value of a pressure is meaningful only when it is known what reference was used. Absolute pressure refers to a complete vacuum. Gauge pressure refers to the ambient air and is the absolute pressure minus the local barometric pressure. Differential pressure refers to a separately selected pressure, such as on both sides of a filter.

This distinction is important in practice. A tire pressure gauge that reads 220 kPa is reading the gauge pressure. The actual absolute pressure of the air inside the tire is about 321 kPa, because atmospheric pressure itself is about 101 kPa. If you open up the levels for gauge and absolute pressures, you can convert between both values using your own reference pressure.

Normal atmospheric pressure

Normal atmospheric pressure is defined as 101,325 pascals which is equivalent to 101.325 kilopascals, about 1.013 bar, or about 14.7 pounds per square inch or 760 millimeters of mercury column. This represents the weight of the air column above a given area at sea level.

Many everyday pressure values fall in this range. A car tire has a pressure of about 220 kilopascals or 32 pounds per square inch, while a bicycle tire with sufficient air will have a much higher value. A deep vacuum in the laboratory, on the other hand, has much lower values. The results can be compared to some of these pressure values using this calculator's default settings.

Using the calculation tool

Enter the force and area of contact, select the unit if necessary then check the pressure in the results section. Switching between kPa, psi, bar, atm or mmHg in the pressure field will show the results in the desired units. If you open the layer for common units, you can display multiple units at once.

To calculate a different size just leave the appropriate field blank. If you enter pressure and area then the calculator will return the force. If you enter force and pressure then the calculator will return the required area to withstand that pressure. No mode selection is needed as leaving fields blank tells the calculator which size to calculate.

Fields of application for pressure calculation

Engineers design hydraulic pistons based on force and area to ensure that foundations do not sink into the ground and materials are chosen which will not collapse under load. In medicine pressure is used to explain blood flow and settings of ventilators.

In everyday life the same formula determines the correct tyre pressure and explains why snowshoes or wide tyres float on soft ground. It can also explain why extremely sharp blades require only very little force. As long as a force acts on a surface, the pressure is the decisive factor.

Assumptions and limitations

Basic calculations assume that the force is applied evenly and perpendicularly to a flat surface so that pressure at every point of contact is equal. In reality, contact is almost never this uniform. Where screw heads, tires or foundations experience higher pressures in some places, peak values can be significantly greater than average values given by this formula.

This tool treats pressure as force divided by area, just like it is treated in mechanics. The pressure due to the weight of a fluid at rest depends on depth and density, while the pressure of a gas follows the Gas Laws. These calculations are related but not identical.