Pascal Press Calculator (Hydraulic Jack Force Multiplication)
Force on the large piston of a hydraulic press or jack from the force on the small piston and the two piston diameters, with the fluid pressure and the stroke.
Results
The dashed line marks the value you entered.
What this tool does
Pascal's principle says pressure applied to a confined fluid is transmitted equally everywhere, so the same pressure acts on a large piston over a larger area and gives a larger force: F₂ = F₁ × A₂ ÷ A₁. Because area goes with the square of the diameter, a piston 5 times wider gives 25 times the force. Nothing is free — the fluid volume is conserved, so the large piston moves only by the inverse of the force ratio, and work in equals work out. Friction and seal drag make real machines deliver somewhat less than the ideal figure.
Formula
p = F₁ ÷ A₁ · F₂ = F₁ × A₂ ÷ A₁ = F₁ × (d₂ ÷ d₁)² · s₂ = s₁ × (d₁ ÷ d₂)²
Variables
| Symbol | Meaning | Unit |
|---|---|---|
f1 | Force on the small piston | N |
d1 | Diameter of the small piston | mm |
d2 | Diameter of the large piston | mm |
s1 | Stroke of the small piston | mm |
F2 | Force on the large piston | N |
RT | Force multiplication | — |
PR | Pressure in the fluid | bar |
S2 | Movement of the large piston | mm |
Worked example
- Force on the small piston200 N
- Diameter of the small piston20 mm
- Diameter of the large piston100 mm
- Stroke of the small piston100 mm
- Force on the large piston5000 N
- Force multiplication25.00
- Pressure in the fluid6.4 bar
- Movement of the large piston4.0 mm
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.