Hydraulic Lift Force Calculator (Pascal's Law)
Calculate the output force of a hydraulic lift using Pascal's law.
Find the mechanical advantage from input and output piston areas with worked examples.
Pascal’s law states that pressure applied to an enclosed fluid is transmitted equally in all directions. For a hydraulic system:
F₁/A₁ = F₂/A₂ → F₂ = F₁ × (A₂/A₁)
Where:
- F₁ = Input force (on small piston)
- A₁ = Area of small piston (m² or cm²)
- F₂ = Output force (from large piston)
- A₂ = Area of large piston
- Pressure P = F₁/A₁ = F₂/A₂
Mechanical advantage: MA = A₂/A₁ = (D₂/D₁)² (for circular pistons, based on diameter ratio squared)
Conservation of work: In an ideal hydraulic system, work in = work out: F₁ × d₁ = F₂ × d₂ Where d = distance the piston moves. A large output force moves a shorter distance than the input.
Real-world applications:
- Car jacks: A 150 kg person can lift a 1,500 kg car with a 10:1 area ratio
- Hydraulic brakes: Small pedal force creates large braking force at all wheels
- Construction equipment: Excavators, bulldozers, and cranes use hydraulic cylinders
- Aircraft landing gear: Hydraulic pistons retract and extend landing gear
- Industrial presses: Hydraulic presses can deliver thousands of tonnes of force
The hydraulic lever: Hydraulics is called a “hydraulic lever” — you trade force for distance. A 100:1 area ratio gives 100× force, but the input must move 100× further than the output.
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This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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