Hydraulic Press Calculator
Pascal’s principle for a hydraulic press or jack — output force from input force and piston diameters, mechanical advantage, pressure, and how far the load rises per stroke.
How it works
P = F₁/A₁ = F₂/A₂ → F₂ = F₁ × (d₂/d₁)²; d₂ = d₁ × (A₁/A₂) (distance); work in = work out (ideal)
Pascal’s principle says pressure applied to an enclosed fluid is transmitted undiminished, so a small force on a small piston produces a large force on a large one in proportion to the areas — and, since area goes as diameter squared, a 10:1 diameter ratio gives 100:1 force. Energy is conserved: the big piston moves 100 times less, which is why a car jack needs many pump strokes. Seals and fluid friction cost a few percent.
Worked example
150 N on a 20 mm piston is 4.8 bar; on a 200 mm piston that pressure yields 15,000 N ideally, 13,500 N at 90% efficiency — enough to lift 1.4 tonnes — while a 100 mm pump stroke raises the load just 1 mm.
Frequently asked questions
Is the pressure the same everywhere?
Yes, apart from the small hydrostatic difference due to height, which is negligible against working pressures of tens of bar.
Why do hydraulic presses use oil, not air?
Liquids are nearly incompressible, so force transmits immediately and stiffly; compressed air stores energy and springs back.
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This calculator is for educational purposes. Double-check important results before acting on them.