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Hydraulic Press Calculator (Pascal's Law)

Find the output force and piston travel of a two-piston hydraulic press or jack from Pascal's law, F2 = F1 × (d2/d1)².

Mechanical advantage
25×
Output force
2,500 N
Output force (pounds-force)
562.02 lbf
Piston 2 travel distance (cm)
0.2

How it works

A hydraulic press or jack has two pistons connected by a sealed, incompressible fluid. Pascal's law says pressure transmitted through that fluid is the same everywhere, so the pressure under each piston is equal: F1/A1 = F2/A2. Since circular piston area is proportional to diameter squared, this reduces to a pure ratio of diameters: F2 = F1 × (d2/d1)² — a bigger output piston multiplies the input force by the square of how many times wider it is.

That force multiplication isn't free: the fluid displaced by the small piston has to go somewhere, so the large piston moves a proportionally smaller distance — specifically d2 = d1 ÷ (d2/d1)². Multiplying the two relations together shows output work (force × distance) always equals input work, confirming the press trades force for distance rather than creating energy.

FAQ

Why does the output piston move less than the input piston?

Because the fluid is conserved — the volume the small piston pushes out has to exactly fill the space the large piston's movement opens up. Since the large piston has more area, the same volume of fluid only moves it a shorter distance. This is the same force-for-distance trade-off as any lever or gear train, just done with fluid pressure instead of rigid parts.

Does piston diameter have to be in any particular unit?

No — only the ratio between the two diameters matters for the force multiplication, so as long as both piston diameters are entered in the same unit (which this calculator's metric/imperial toggle enforces automatically), the result is correct regardless of which unit system you pick.

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