What is Pascal's principle?
Press a brake pedal gently and a tonne of squeeze grips the wheel. Pump a jack with one hand and a car rises. Play with the idea Pascal worked out in the 1650s, then find it in brakes, rooftop tanks, blood-pressure cuffs and your own popping ears.
▶ Play with it · Read the 60-second explainer · Watch the 40-second video
- Pressure spreads everywhere. Push on a trapped liquid and the extra pressure, P = F ÷ A, reaches every part of it equally and presses on every wall. Three gauges on a hydraulic lift all read the same, wherever you put them.
- Small piston, big force. The same pressure on a bigger area gives a bigger force: F₂ = F₁ × A₂ ÷ A₁. Car brakes, motorcycle and bicycle disc brakes and bottle jacks all multiply your push this way.
- Nothing is free. The liquid barely squashes, so the big piston moves much less than the small one. Force × distance, the work, is the same on both sides: hydraulics trade distance for force and never create energy.
- Depth is pressure. A liquid's own weight adds P = ρ g h, depending only on depth, not on the container's shape. About 0.1 bar per metre of water sets your tap's pressure under a rooftop tank, and a blood-pressure reading changes with your arm's height.
- Where it surprises. A thin tube of water a few metres tall can burst a barrel, because height, not weight, sets the pressure. And gases squash: a bubble of air in a brake line makes the pedal spongy.
| Term | Meaning |
|---|---|
| Pressure | Force on each unit of area, P = F ÷ A, measured in pascals (N/m²). |
| Pascal's principle | A change of pressure anywhere in a confined fluid is passed on undiminished to every part of it. |
| Pascal (Pa) | The SI unit of pressure, one newton per square metre; 100,000 Pa is 1 bar. |
| Hydraulic press | Two pistons of different areas joined by a liquid, multiplying force by the ratio of their areas. |
| Mechanical advantage | How many times a machine multiplies force; for a hydraulic press, A₂ ÷ A₁. |
| Hydrostatic pressure | Pressure from a liquid's own weight at depth h: P = ρ g h. |
| Hydrostatic paradox | The force on the bottom of a vessel depends on the liquid's depth, not on its amount or the vessel's shape. |
| Compressibility | How much a fluid shrinks under pressure; tiny for liquids, large for gases. |
From Archimedes' floating bodies to the brakes in every car, how people learned that a push on a trapped fluid goes everywhere.
- 1586 · The hydrostatic paradox (Simon Stevin, Leiden, Dutch Republic)
- 1648 · Carrying a barometer up a volcano (Florin Périer, for Blaise Pascal, Puy de Dôme, near Clermont)
- 1654 · A machine for multiplying forces (Blaise Pascal, Paris)
- 1795 · The hydraulic press (Joseph Bramah, London, England)
- 1894 · Lifting Tower Bridge (Sir W. G. Armstrong, Mitchell and Co., London, England)
- 1917 · Hydraulic brakes (Malcolm Loughead (later Lockheed), California)
- 1971 · The pascal becomes a unit (14th General Conference on Weights and Measures, Sèvres, near Paris)
The full story, with 20 moments, charts, people and 33 sources: glassbox.how/e/pascalclear/history. The data lives in history.json.
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