Hydraulics rest on one line: F = P · A. Pressure pushing on an area produces a force. And by Pascal's principle, pressure applied to a confined fluid is the same everywhere in it — so a small piston and a large piston connected by fluid feel the same pressure but produce different forces. The bigger piston wins, in proportion to its area. That's a hydraulic press, a jack, a digger arm.
A pump makes 100 bar (10 MPa). Push it against a 50 mm bore piston — area 19.6 cm² — and you get 19.6 kN of force, about 2 tonnes. Feed the same pressure to a 150 mm piston (9× the area) and it pushes 9× harder: ~177 kN.
The catch is stroke: the big piston moves 9× less for the same fluid. Force up, distance down — energy is conserved, exactly like a lever.
A circle's area is π/4·d². Double the bore and you quadruple the area — and the force. It's
why a small increase in cylinder diameter buys a big jump in capacity.
1 bar ≈ 14.5 psi ≈ 0.1 MPa ≈ 100 kPa. Hydraulic systems often run 100–350 bar (roughly 1,500–5,000 psi). The tool converts as you switch units.
No. The output piston moves less in exact proportion to the force gain, so the work (force × distance) is the same on both sides, minus real-world losses. Hydraulics trade distance for force, like any machine.
On a cylinder's retract stroke, the rod takes up part of the piston, so the effective area — and the force — are smaller. This tool models the full-bore (extend) area; subtract the rod area for retract.