Calculate hydraulic force amplification and mechanical advantage using Pascal's Principle.
Pascal's law states that pressure applied to a confined fluid transmits equally in all directions, which underlies every hydraulic press, brake, jack, and force multiplier. This calculator solves the classic F₁/A₁ = F₂/A₂ relationship for a two-cylinder system, sizing piston areas, force ratios, and stroke ratios to amplify input effort by 5×, 50×, or 500× as required.
Pressure P = F / A is constant throughout a static fluid, so input force F₁ on area A₁ produces output force F₂ = F₁ × (A₂ / A₁) on area A₂. The force multiplier (mechanical advantage) is the area ratio. Conservation of fluid volume means the stroke ratio is inversely proportional: s₂ = s₁ × (A₁ / A₂). A 10× force multiplier requires a 10× longer input stroke for the same output displacement. Working pressure must stay below the lower of the two cylinders' ratings, and seal friction reduces practical output by 5–10%. Pascal's law assumes incompressible, static, and confined fluid — air bubbles or flexing housings reduce real-world output.
A jack designer aiming for a 25× mechanical advantage picks a 12 mm input piston driving a 60 mm output, calculates that 100 N input becomes 2,500 N output, and confirms required input stroke for 50 mm lift is 1,250 mm of pump strokes.
A workshop owner verifying a salvaged 20-ton press measures small-piston diameter 25 mm, large-piston 200 mm, area ratio 64×, then computes that 270 psi on the small piston produces the 20-ton clamping force.
An automotive engineer modelling a brake caliper computes brake-piston force from master-cylinder area ratio and pedal force, then sizes the friction pad to deliver the required wheel torque without lock-up.
It works for any fluid (liquid or gas), but air compressibility reduces practical force multiplication — a hydraulic press is stiffer than a pneumatic one because oil compresses ~0.5%/1000 psi while air compresses much more.
Spongy feel means air is trapped in the system. Pascal's law assumes incompressible fluid; even 5% air content can double pedal travel. Bleed the system from the highest point until firm.
Working pressure (highest pressure the weaker component can hold), cylinder buckling on the long thin input piston, and stroke length practical for the operator. Most jacks limit at 50-200× advantage.