What is Pascal's principle?

Pascal's principle states that a pressure change applied to an enclosed fluid is transmitted equally throughout the fluid. In a hydraulic system this gives F₁/A₁ = F₂/A₂, meaning a small force on a small piston produces a proportionally larger force on a larger piston.

What is mechanical advantage in a hydraulic system?

Mechanical advantage equals A₂/A₁ (or equivalently F₂/F₁). A ratio greater than 1 means the system amplifies force; less than 1 means it amplifies speed or displacement instead.

Does Pascal's principle conserve energy?

Yes. While force is amplified, the displacement is reduced by the same ratio, so work (force × distance) remains constant, minus real-world friction losses.

What units should I use?

Any consistent set works. This calculator lets you mix Newton/lbf for force and cm²/m²/in² for area — all values are converted to SI (N and m²) before solving, then converted back for display.

Can I solve for an area instead of a force?

Yes. Use the "Solve for" dropdown to pick any of the four variables (F1, A1, F2, A2). Enter the other three values and the calculator solves for the selected unknown.

Pascal Principle Calculator

Name: Pascal Principle Calculator
Availability: InStock
Author: Nham Vu

Calculate the output force, input force, or piston area in a hydraulic system using Pascal's principle.

Hydraulic System Inputs

Solve for

Force unit

N lbf

Area unit

cm² m² in²

F1 — Input Force

A1 — Input Piston Area

A2 — Output Piston Area

F2 — Output Force

Result

Fill in the inputs and click Calculate.

Output Force (F2)

—

Applied formula

Variable	Value	SI equivalent

Mechanical Advantage (A2 / A1) —

Pascal's Law — How it works

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Summary

Calculate the output force, input force, or piston area in a hydraulic system using Pascal's principle.

How it works

Select what you want to calculate: output force, input force, input area, or output area.
Enter the known values in the three remaining input fields.
Choose units for force (N or lbf) and area (cm², m², or in²).
Click "Calculate" to see the result with the derived formula.
Use "Reset" to clear all fields and start a new calculation.

Use cases

Design hydraulic press systems and determine required piston sizes.
Verify mechanical advantage calculations for hydraulic jacks.
Solve textbook physics problems involving Pascal's law.
Estimate cylinder force output given supply pressure and bore area.
Compare small-to-large piston configurations for force amplification.

Frequently Asked Questions

Last updated: 2026-07-01 · Reviewed by Nham Vu