Hydraulic Lift Force Calculator (Pascal's Law)
Calculate the output force of a hydraulic lift using Pascal's law.
Find the force multiplication factor from piston areas.
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.