Hydraulic Lift Force Calculator (Pascal's Law)

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” because you trade force for distance. A 100:1 area ratio gives 100× force, but the input must move 100× further than the output. Nothing is created. A bottle jack lifting a car 15 cm on a 50:1 ratio needs 7.5 metres of total handle travel, which is why you pump it dozens of times.

Why the fluid has to be liquid

Hydraulic oil is close enough to incompressible that the pressure appears at the far piston almost instantly. Air is not. A few bubbles trapped in the line simply compress when you push, so the input piston runs through its whole stroke while the output barely lifts, and the pedal or handle feels soft and spongy. That single fact is the reason brakes get bled after any line is opened, and it is the first thing to suspect when a jack holds pressure but will not raise its load.

Seal friction eats into the ideal figures too. A well-maintained cylinder returns perhaps 85 to 95 percent of the theoretical output force, so treat the number above as the ceiling rather than the promise.