Pressure Calculator

How the pressure calculation works

Pressure is force distributed over area:

P = F ÷ A

The SI unit is the pascal (1 Pa = 1 N/m²). Practical engineering uses kilopascals, bar and psi: 1 bar = 100 000 Pa ≈ atmospheric pressure at sea level, and 1 psi = 6 894.76 Pa. In imperial mode the calculator converts lbf and ft² internally before reporting all four units.

The area term is where most errors hide. A hydraulic cylinder's effective area is the piston area minus the rod area on the rod side; a tyre's contact patch shrinks as pressure rises, which is exactly why higher inflation means lower rolling resistance. For circular contacts, A = π d² / 4 — a 63 mm cylinder bore is about 31.2 cm² (0.00312 m²), the default example here.

Worked example

A 5000 N load spread over a 0.00314 m² piston face: P = 5000 ÷ 0.00314 ≈ 1 592 000 Pa ≈ 15.9 bar ≈ 231 psi. Same load on a 4× larger area drops pressure to a quarter — the principle behind snowshoes, foundation footings and crane outrigger pads.

Gauge vs absolute

Calculated P = F/A is gauge pressure — relative to atmosphere. Add 101 325 Pa (1.013 bar) for absolute pressure, which matters in gas-law work and vacuum systems.

Frequently asked questions

1. What is the formula for pressure?

P = F ÷ A: pressure equals force divided by the area over which it acts. In SI units, newtons per square metre give pascals.

2. How do you convert psi to bar?

Multiply psi by 0.0689476. So 100 psi ≈ 6.89 bar. To convert bar to psi, multiply by 14.5038.

3. Is calculated pressure gauge or absolute?

P = F/A gives gauge pressure relative to the surrounding atmosphere. Add 101 325 Pa for absolute pressure — required for gas-law and vacuum calculations.

4. Why does spreading the same force over more area reduce pressure?

Pressure divides by area, so doubling contact area halves it. Snowshoes, crane pads and building foundations all use this: same weight, bigger footprint, lower ground pressure.