Pressure, Force and Area Calculator (P = F / A)

What is pressure?

Pressure is the force acting perpendicular to a surface divided by the area of that surface:

P = F / A

F is the force (newtons), A the area (square metres) and P the pressure. Its unit is the pascal: 1 Pa = 1 N/m². The pascal is small, so everyday work uses the kilopascal (kPa), the megapascal (MPa) and the bar: 1 bar = 100 kPa.

The same force on a smaller area gives a higher pressure. That is why the sharp edge of a knife cuts, a drawing pin goes into the wall point first and snowshoes do not sink into snow.

Three ways to use it

• Pressure: P = F / A
• Force: F = P × A. This gives the thrust of a piston or cylinder.
• Area: A = F / P. The smallest contact area that keeps the pressure below a limit.

Example

A force of 500 N spread over 25 cm² gives P = 500 / 0.0025 = 200 000 Pa, which is 200 kPa or 2 bar.

With 6 bar acting on a piston 50 mm in diameter, the area is π × 0.05² / 4 = 0.001963 m² and the force is 600 000 × 0.001963 = 1178 N.

If a 60 kg person puts their whole weight on a heel with an area of 1 cm², the pressure is 588 / 0.0001 = 5.9 MPa, more than twenty times the pressure in a car tyre at about 2.5 bar.

Watch the units

The most common mistake is using the area without converting it: 1 cm² = 0.0001 m² and 1 mm² = 0.000001 m². The calculator converts for you. N/mm² and MPa are the same unit.

Limits

The result is an average pressure and assumes the force is perpendicular to the surface. For pressure due to the depth of a liquid, see the hydrostatic pressure tool.