Princípio de Pascal (prensa hidráulica)

F₁/A₁ = F₂/A₂.
Created by
Renato Passos, Eng. de Software
Reviewed by
Renato Passos, Eng. de Software

Last updated: Apr 18, 2026

F₂
1.000,00 N

Formula

F₂ = F₁·A₂/A₁

About this calculator

This calculator applies Pascal's Principle to determine the force exerted by a hydraulic press. Pascal's law states that pressure applied to a confined fluid is transmitted equally in all directions. In practice, a small force applied over a small area can generate a much larger force over a larger area, provided the fluid is incompressible. The formula used is F₂ = F₁ · A₂ / A₁, where F₁ is the input force, A₁ is the input piston area, A₂ is the output piston area, and F₂ is the resulting force.

To use the tool, enter values for F₁, A₁, and A₂. The calculation automatically returns the force F₂. For example, if you apply 100 N on a piston of 0.01 m² and the output piston has 0.1 m², the output force will be 1000 N, multiplying the force by 10. This shows how the hydraulic press amplifies force, useful in jacks, brakes, and hydraulic lifts.

Common use cases include sizing hydraulic systems in auto shops, designing vehicle lifts, and industrial pressing equipment. The calculator helps predict the force needed to lift a weight or the force a hydraulic cylinder can exert. Remember that areas must be in the same unit (m², cm², etc.) and that real efficiency may be lower due to friction and leaks.

Important precautions: ensure area units are consistent; always use the same system (m² with m², cm² with cm²). The formula assumes incompressible fluid and no losses; in practice, consider a safety factor. Do not confuse diameter with area: piston area is π·r². For accurate calculations, measure cylinder diameter and calculate the area correctly.

Frequently asked questions

Can I use any unit for the areas?

Yes, as long as all areas are in the same unit, such as m², cm², or mm². The resulting force will have the same unit as the input force.

What happens if area A₂ is smaller than A₁?

In that case, the output force F₂ will be smaller than the input force F₁. The hydraulic press does not amplify force but can be used to increase displacement.

Does this calculator account for friction losses?

No. The formula assumes an ideal system without losses. In practice, consider a safety factor of 10 to 20% to compensate for friction and leaks.

What is the difference between piston diameter and area?

Diameter is a linear measurement from one edge to the other. Area is calculated as π·(diameter/2)². Always use area, not diameter, in the formula.

Can I use this calculator for systems with multiple pistons?

Yes, as long as pressure is the same everywhere. For series systems, force accumulates; for parallel, total area is the sum of individual areas.

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