Enrichment · STEM Explorations · Engineering

A small push,
a big lift, and
the catch.

Type how hard you push and the size of each piston. The calculator gives the pressure in the fluid, the force on the big piston and how far it moves, so you can design a syringe lift or check a car jack, and see where the extra force comes from.

Work out the forceWhat you get

The hydraulic pressure calculator

The worked example is made up: two water-filled syringes driving a robotics arm. Nothing you type leaves this browser.

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What you get

Enrichment · STEM ExplorationsFree

What you finish with
The fluid pressure, the output force, the force multiplication, the mass it could hold and the distance the large piston moves, with every step. It prints as a summary and downloads as a spreadsheet.
Who it is for
Middle and high school physical science students, robotics and engineering clubs, science teachers and families doing STEM projects.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Metric or US units. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The STEM Explorations space in Caveat Enrichment.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Name the build and choose units.
  2. Type the push on the small piston and both inside diameters.
  3. Add how far you push the small piston, if you want the distances.
  4. Read the output force and the steps, then try a bigger large piston.
  5. Print the summary or download the spreadsheet for your lab notes.

Work out the force

How the force is worked out

Pascal’s principle in four steps.

The worked example: same pressure, bigger area, bigger forceSmall piston area1.767 cm²π × (1.5 ÷ 2)²Pressure113.2 kPa20 N ÷ areaLarge piston area7.069 cm²twice the diameter, 4× the areaForce out80 Npressure × large areaThe worked example: same pressure, bigger area, bigger forceSmall piston area1.767 cm²π × (1.5 ÷ 2)²Pressure113.2 kPa20 N ÷ areaLarge piston area7.069 cm²twice the diameter, 4× the areaForce out80 Npressure × large area
A 20 N push on a 1.5 cm piston makes 113 kPa in the water; that same pressure on a 3 cm piston, four times the area, pushes with 80 N.

Pascal’s principle

Pressure applied to a liquid in a closed system spreads equally through it. Pressure is force divided by area, so the same pressure acting on a larger piston produces a larger force, in proportion to the areas. Area grows with the square of the diameter: a piston twice as wide gives four times the force.

Where the catch is

Liquids barely compress, so the volume pushed out of the small cylinder equals the volume that enters the large one. The large piston therefore moves less, by the same factor the force grew, and force times distance comes out the same on both sides. Real systems lose some to friction, leaks and air bubbles, which compress and waste the push.

Sources

  1. OpenStax. College Physics 2e (2022), section 11.5, Pascal’s Principle (openstax.org).
  2. NASA Glenn Research Center, Beginner’s Guide to Aeronautics: pressure (grc.nasa.gov).
  3. NIST Special Publication 811, Guide for the Use of the International System of Units (2008): the pascal, standard gravity and conversion factors.
  4. Next Generation Science Standards, MS-PS2 Motion and Stability: Forces and Interactions, and HS-ETS1 Engineering Design (nextgenscience.org).

The worked example is made up. The page assumes an ideal system. Your figures stay in this browser. Support: team@caveatacademic.com.