This calculator applies ideal Pascal-law force ratio and incompressible volume continuity to two circular piston bores. It does not rate a jack or establish a safe lifted load.
Hydrostatic Jack Interactive Calculator
Explore ideal force multiplication, reciprocal displacement and input-piston pressure for two connected circular areas.
Equation Used
- Entered force acts directly and axially on the small pump piston.
- Two circular full-bore piston areas share uniform ideal pressure.
- Incompressible no-leak fluid and equal displaced volume for the stroke relation.
- No lever, check valves, reservoir refill, friction, seal drag, opposing pressure, compressibility, hose expansion, cylinder/frame strength, stability, load holding, overload relief or safety model.
The entered force acts directly on the pump piston; handle leverage is not included. Friction and opposing pressure affect delivered force, while leakage affects displaced volume. Safe capacity depends on component and structural ratings.
Ideal force and displacement reciprocity
Equal ideal pressure gives F1/A1=F2/A2, while equal displaced volume gives A1s1=A2s2. Thus force rises by A2/A1 while output travel falls by the reciprocal ratio.
The animation is a qualitative two-piston diagram. Its piston widths and travel are not drawn to the entered dimensions; use the calculated values for comparisons. It does not show a complete jack or pump cycle.
Use as a Pascal-law check
The identities can verify ideal force, travel and direct-piston pressure arithmetic. They cannot determine handle effort, pumping cycles, speed, capacity or safe support load.
Ideal work consistency
For circular bores, A2/A1=(d2/d1)². Ideal F2/F1=A2/A1 and s2/s1=A1/A2, so F1s1=F2s2. Pressure is F1/A1; with N and mm² this is MPa.
Worked force-and-travel example
For 10 mm pump bore, 50 mm ram bore, 200 N direct piston force and 25 mm pump stroke, area ratio is 25:1, ideal output is 5,000 N, output travel is 1.00 mm and ideal pressure is about 2.546 MPa.
Scope and limitations
A real jack requires handle/pivot geometry, pump/check/release valves, reservoir and refill, seals/friction/leakage, fluid compressibility and trapped air, cylinder wall/end-cap and ram strength, buckling and side load, base and load stability, mechanical load holding, overload protection, stroke stops, guarding, inspection and applicable lifting rules. Never work beneath a load supported only hydraulically.
Frequently asked questions
Is entered force the handle force?
No. It acts directly on the pump piston; handle leverage is absent.
Is output force a safe capacity?
No. Strength, stability and load holding are not checked.
Why does ram travel change with bore ratio?
Equal displaced volume requires A₁s₁ = A₂s₂. A larger ram area gives less output travel; if the entered ram area is smaller than the pump area, the ideal output travel is greater.
Calculation basis
Two ideal pistons at equal fluid pressure have a force ratio equal to their area ratio. For circular bores this is (d₂/d₁)². Incompressible fluid with no leakage gives the reciprocal travel ratio.
Pressure is the direct pump-piston force divided by its area. With force in newtons and area in square millimetres, the result is in MPa. The equations exclude handle leverage, pumping valves, losses and structural capacity.
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