Last updated: 2026-06-15

Pressure

Pressure measures how concentrated a force is. The same push feels very different depending on the area it acts over: a finger pressed against your palm is harmless, but the same force behind a needle breaks the skin. Pressure captures this with a simple ratio — force divided by area, $P = F / A$. This calculator finds the pressure from a force and a contact area, and can rearrange the formula to solve instead for the force or the area.

How pressure works

Only the part of the force that pushes perpendicular to a surface — the normal force — creates pressure on it. Spread that force over a wide area and the pressure is low; squeeze it onto a tiny area and the pressure soars, even though the force itself has not changed. This is the principle behind sharp blades, drawing pins and stiletto heels, and equally behind snowshoes, wide tyres and broad foundations that avoid high pressure by spreading a load.

Formula

In SI units, a force in newtons divided by an area in square metres gives a pressure in pascals: $1\ \text{Pa} = 1\ \text{N/m}^2$. The pascal is small, so kilopascals (kPa), bar and atmospheres are often handier — $1\ \text{bar} = 100\ \text{kPa}$ and $1\ \text{atm} = 101.325\ \text{kPa}$.

Worked example

A box presses down with a force of 500 N through a base measuring 0.01 m² (a 10 cm × 10 cm footprint). The pressure on the floor is:

If the same box rested on a base half as large, 0.005 m², the pressure would double to 100 kPa, because the force is now squeezed through half the area.

Units of pressure

Pressure is quoted in many units depending on the field. The pascal (Pa) is the SI unit; weather reports use hectopascals (hPa) or millibars; tyre gauges use psi or bar; and chemistry often uses atmospheres. The conversions are fixed: $1\ \text{bar} = 100\,000\ \text{Pa}$, $1\ \text{atm} = 101\,325\ \text{Pa} \approx 14.7\ \text{psi}$, and $1\ \text{psi} \approx 6895\ \text{Pa}$. This calculator lets you enter and read each quantity in whichever unit suits the problem.

Limitations

This calculator treats the force as acting uniformly and perpendicular to a flat area. For a force applied at an angle, use only its normal component. It also assumes the pressure is the same everywhere over the area; real contact patches often carry an uneven pressure distribution, in which case the result is the average pressure. For pressure inside a fluid that rises with depth, use a hydrostatic pressure calculator instead.