Pressure Calculator

How to use this calculator

Enter a force and the area it acts on. For round pistons, pipes or pads, enter the diameter instead of the area and the area is worked out for you. Units can be mixed freely — for example, force in newtons and area in in² — and the pressure can be displayed in Pa, kPa, MPa, bar, atm, psi, mmHg or Torr.

Turn it around to size hardware: enter the pressure available (say 3,000 psi from a hydraulic pump) and the force you need, and the calculator returns the piston area and diameter.

The formula

P = F / A

A = π D² / 4

P: pressure
F: force (perpendicular)
A: area
D: diameter (for a circular area)

Worked example

A 100 lbf load is applied to a hydraulic piston 2 inches in diameter. What pressure does it create in the fluid?

Piston area A = π × 2² / 4 = 3.14 in².
Pressure P = F / A = 100 / 3.1416 = 31.8 psi.
In SI: 31.8 psi = 219 kPa = 2.19 bar.

The fluid pressure is about 32 psi. A second piston of 6 in diameter (9× the area) would push with 900 lbf.

Everyday pressures

Situation	Pressure
Standard atmosphere	101.325 kPa = 14.70 psi
Car tire (gauge)	30–35 psi ≈ 210–240 kPa
Road bike tire (gauge)	80–100 psi
Household water supply	40–80 psi
Garden-variety hydraulic jack	up to ~10,000 psi

Assumptions and limits

The force is perpendicular to the surface and evenly distributed. A tilted force contributes only its normal component.
Values are whatever reference the force implies; tire and pipe gauges read gauge pressure (above atmospheric).

Frequently asked questions

How do I convert psi to kPa?

Multiply by 6.894757. 30 psi is 206.8 kPa; 1 bar is 14.504 psi.

Why does a smaller area give a higher pressure?

The same force divided over less area means more force on each square inch. That is why a stiletto heel can exert more pressure than an elephant’s foot.

What is the difference between gauge and absolute pressure?

Absolute pressure is measured from vacuum; gauge pressure is measured from atmospheric pressure. Absolute = gauge + 101.325 kPa (14.7 psi) at sea level.

Pressure Calculator (P = F/A)