By Zencalcy Editorial TeamLast reviewed About us
A hydraulic press transmits pressure through an enclosed fluid. Because pressure is the same everywhere, applying a small force to a small piston creates the same pressure on a larger piston, which then exerts a proportionally larger force. The trade-off is that the large piston moves a shorter distance.
Force multiplication from two piston diameters.
F₂ = F₁ (d₂ / d₁)² P = F₁ / A₁
For circular pistons the area ratio is the square of the diameter ratio. The ideal result assumes an incompressible fluid and no friction or seal losses, so real presses deliver somewhat less.
| Symbol | Meaning |
|---|---|
| F₁, F₂ | Input and output forces, in newtons. |
| d₁, d₂ | Input and output piston diameters. |
| P | Pressure in the hydraulic fluid, in pascals. |
The diameter ratio is 4, so the area ratio is 16 and the output force is 1,600 N. The fluid pressure is 100 / (π × 0.025²) = 50.9 kPa.
Continue with the Hydrostatic Pressure Calculator, Pressure Calculator, or the Seesaw Balance Calculator — or browse more statics tools and all physics calculators.
No. Force is multiplied but the large piston moves a proportionally shorter distance, so work in equals work out in an ideal press. Energy conservation is preserved.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026