Rule of thumb · MechanicalNº 52 / 167

Double the piston diameter, quadruple the force

In a hydraulic cylinder, force scales with the piston diameter squared, not the diameter itself.

Why it works

Force = pressure × area, and area = π(d/2)² — a 2:1 diameter ratio between two pistons gives a 4:1 force ratio at the same pressure, exactly how a hydraulic jack multiplies a small hand force into tonnes.

When it fails

On the extend stroke. Retracting, the rod area is subtracted from the piston, so a cylinder with a 2:1 rod pulls only about half as hard as it pushes at the same pressure — which is why a press returns faster than it advances, and why pulling loads need the bore sized on the annulus.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

Open Hydraulic Force Calculator →

More in Mechanical

← PreviousDouble the wire, sixteen times the spring rate Next →The groove, not the ring, usually fails first

How does cylinder bore affect hydraulic force?

In a hydraulic cylinder, force scales with the piston diameter squared, not the diameter itself. Force = pressure × area, and area = π(d/2)² — a 2:1 diameter ratio between two pistons gives a 4:1 force ratio at the same pressure, exactly how a hydraulic jack multiplies a small hand force into tonnes.

Browse all 167 rules of thumb →