How Does A Small Push Lift A Car?

6 minute read Simulation: Hydraulic Lift Quiz at the end

At a car service station, a mechanic pumps a small handle and a one-tonne car rises into the air. Nobody is that strong. So where does the extra force come from?

Start with something you know

Fill a plastic bottle to the very top, close the cap loosely and squeeze the side. The cap pops off. You pushed on the side, but the push turned up at the top. A liquid trapped in a closed space passes a push to every part of it.

Blaise Pascal described this in the 1600s: pressure added to an enclosed liquid reaches every point in the liquid, and every wall of its container, without getting weaker. This is Pascal’s law.

Try it

Hydraulic Lift
Lift a car with a small push. Change the piston sizes.

Try this

  1. Hold the push button and watch both pistons. Which one moves farther?
  2. Lower your push until the car stops rising. How does that minimum change when you make the small piston thinner?
  3. Make both pistons the same size. What does the force multiplier become?

What is happening

Push the small piston with a force F₁. That creates a pressure p = F₁ ÷ A₁ in the oil. The same pressure acts on the big piston, which has a much larger area A₂, so it pushes up with:

F2 = F1 × A2 ÷ A1
F1
your push on the small piston (N)
A1
area of the small piston (m²)
F2
force from the large piston (N)
A2
area of the large piston (m²)

Area grows with the diameter squared. A big piston with 4 times the diameter has 16 times the area, so it multiplies your push by 16.

Nothing comes for free

If force is multiplied, something has to be given up. The oil pushed out of the small cylinder flows into the big one. The big cylinder is much wider, so the same volume lifts it only a little:

d2 = d1 × A1 ÷ A2

You push 16 times less hard but 16 times farther. Work, which is force times distance, is the same on both sides apart from a little friction. That is why a jack needs many pumps to lift a car a few centimetres.

Where you see it

  • Car brakesYour foot presses a small piston in the master cylinder. Brake fluid carries that pressure to bigger pistons at each wheel, which squeeze the brake pads with far more force.
  • ExcavatorsHydraulic cylinders move the arm and bucket of a JCB, with a pump keeping the oil at high pressure.
  • Barber and dentist chairsA few presses of a pedal raise the chair and the person sitting in it.
  • Hydraulic pressesFactories use them to shape car body panels, pressing metal sheets with thousands of tonnes of force.

Easy to mix up

  • The liquid must be almost impossible to squash. Air bubbles in brake lines get squashed instead of passing the pressure on, which is why spongy brakes are dangerous.
  • Pascal’s law multiplies force, not energy or power.

Check your understanding

Hydraulics Quiz

5 questions.

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