What is Pascal’s principle?

Pressure applied to a fluid in a closed container is transmitted undiminished to every part of the fluid and the walls of the container. That is why pressing on a small piston produces the same pressure under a large piston.

How do you calculate the output force of a hydraulic press?

Find the pressure on the input piston (force ÷ area), then multiply by the output piston’s area. With 50 lb on a 2 in² piston (25 psi) and a 20 in² output piston, the output force is 25 × 20 = 500 lb.

If a hydraulic press multiplies force, why doesn’t it create energy?

The large piston moves a shorter distance. The same volume of fluid leaves the small cylinder and enters the large one, so if the output area is 10 times larger, the output piston moves one tenth as far. Force × distance, the work, is the same on both sides.

Free tool · OAR Mechanical Comprehension

Hydraulic press calculator

Pressure on a confined fluid is passed on undiminished. Enter the input force and both piston areas to get the output force, the pressure and how far each piston moves.

Result

Output force: 500 lb
Fluid pressure: 25 psi
Mechanical advantage: 10 : 1
Output piston travel: 1 in

The output piston pushes 10 times harder but moves 10 times less: the work in equals the work out.

How the calculation works

Pressure = input force ÷ input area
Output force = pressure × output area, which is the same as F₂ = F₁ × A₂ ÷ A₁
Mechanical advantage = output area ÷ input area
Output travel = input travel × input area ÷ output area (the same volume of fluid moves on both sides)

Example: 50 lb on a 2 in² piston makes 25 psi. On a 20 in² output piston that becomes 500 lb, a mechanical advantage of 10 : 1. Push the small piston 10 in and the large one rises only 1 in.

Where you see it

Car brakes, floor jacks, barber chairs and aircraft control systems all use the same idea: a small force on a small piston becomes a large force on a large one. Practice questions sometimes give piston diameters instead of areas; if you get a diameter, remember that area grows with the square of the diameter, so doubling the diameter quadruples the force.

Test yourself: an OAR-style question

A hydraulic lift’s small piston has an area of 5 in² and has 20 lb of force applied to it. The large piston has an area of 50 in². How much output force does the large piston generate?

190 lb
220 lb
200 lb
180 lb

Show answer

C. 200 lb

The pressure is 20 ÷ 5 = 4 psi, and Pascal’s principle passes it unchanged to the large piston: 4 × 50 = 200 lb.

Questions like this come up on the Mechanical Comprehension section of the OAR. The 2,604 questions in the app each come with a written explanation.

FAQ

What is Pascal’s principle?: Pressure applied to a fluid in a closed container is transmitted undiminished to every part of the fluid and the walls of the container. That is why pressing on a small piston produces the same pressure under a large piston.
How do you calculate the output force of a hydraulic press?: Find the pressure on the input piston (force ÷ area), then multiply by the output piston’s area. With 50 lb on a 2 in² piston (25 psi) and a 20 in² output piston, the output force is 25 × 20 = 500 lb.
If a hydraulic press multiplies force, why doesn’t it create energy?: The large piston moves a shorter distance. The same volume of fluid leaves the small cylinder and enters the large one, so if the output area is 10 times larger, the output piston moves one tenth as far. Force × distance, the work, is the same on both sides.

Sources

OpenStax. College Physics 2e, 11.5 Pascal’s Principle

Checked against this source on October 24, 2026. Ideal hydraulic system: incompressible fluid, no leaks or friction, pistons at the same height. For OAR preparation only; not affiliated with or endorsed by the U.S. Navy. Calculations run in your browser.