Pascal's Principle Calculator (Hydraulic Press)
See how a hydraulic press multiplies force between two pistons, and how far the output piston moves, using Pascal’s principle.
How it works
F₂ = F₁ · (A₂ ÷ A₁) · A = π·(d ÷ 2)² · output travel = input travel ÷ (A₂ ÷ A₁)
Pascal's principle says pressure applied to a confined fluid is transmitted equally everywhere. Because pressure is the same at both pistons, the larger piston feels a force scaled up by its area ratio — and area grows with the square of diameter, so a 5× wider piston multiplies force 25×. Energy is conserved: the big piston moves proportionally less than the small one, so you trade distance for force just like a lever.
Worked example
Push with 100 N on a 2 cm piston (area = π×0.01² = 3.14×10⁻⁴ m²) connected to a 10 cm piston (area = π×0.05² = 7.85×10⁻³ m²). The area ratio is 25, so the output force is 100 × 25 = 2,500 N. If you push the small piston 100 mm, the large one rises only 100/25 = 4 mm.
Sources: Pascal's law — Wikipedia
Frequently asked questions
Why does a hydraulic jack multiply force so much?
Force multiplication equals the ratio of piston areas, and area depends on diameter squared. A modest difference in diameter produces a large force gain — that is how a car jack lifts a tonne with a light hand pump.
Does the hydraulic press give free energy?
No. The output piston moves less in exact proportion to the force gained, so work in equals work out (ignoring friction). You cannot get more energy than you put in.
What if I use piston areas instead of diameters?
You can use areas directly in F₂ = F₁·(A₂/A₁). This calculator converts diameters to areas with A = π·(d/2)² for you.
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This calculator is for educational purposes. Double-check important results before acting on them.