Pascal's Principle Calculator
Enter the input force and the two piston areas to get the output force of a hydraulic press — and see how a small piston pushing a confined fluid multiplies your force.
Force multiplied by area ratio
Enter the input force and the small and large piston areas and the calculator returns the output force F2 = F1 × A2 / A1 in newtons.
Use the same area unit
Both piston areas must be in the same unit — here square centimetres — so the A2 / A1 ratio is unitless and the output force stays in newtons.
What is Pascal's principle?
Pressure transmitted through a fluid
The Pascal's principle calculator turns a small input force into the much larger output force of a hydraulic press. Pascal's principle states that pressure applied to a confined, incompressible fluid is transmitted equally and undiminished in every direction. Because pressure is force divided by area, the same pressure acting on a larger piston produces a larger force. Enter the force on the small piston and the areas of both pistons, and the calculator returns the output force in newtons. It is the physics behind car brakes, hydraulic jacks, lifts, and the press that shapes steel.
Enter the input force in newtons and the two piston areas in square centimetres to get the output force of the hydraulic press instantly.
The output force is the input force multiplied by the ratio of the large piston area to the small piston area.
F2 = F1 × A2 / A1The pressure is the same on both pistons, so the force scales exactly with the area. A piston ten times larger produces ten times the force. Because both areas appear as a ratio, any consistent area unit works — square centimetres here — and the output force comes back in the same unit as the input force, newtons.
Suppose you push a small piston of 5 cm² with a force of 100 N, and the large piston has an area of 50 cm².
Divide the areas
50 cm² ÷ 5 cm² = 10 — the area ratio, which is the force-multiplication factor.
Multiply by the input force
100 N × 10 = 1,000 N — the input force scaled by the area ratio.
Read the output force
The large piston pushes with 1,000 N — ten times the input force, exactly the area ratio.
The output force tells you how much the hydraulic press can lift or push, and it is always the input force times the area ratio — never more energy than you put in. Force multiplication equals the area ratio: a large piston fifty times the area of the small one multiplies the force fifty-fold. But there is no free lunch, because energy is conserved. The trade is distance: the large piston moves a shorter distance than the small one by exactly the same ratio. To raise the large piston by 1 cm in the example above, the small piston must travel 10 cm. That is why a car jack needs many short pumps to lift a wheel a few centimetres — you are exchanging a long, easy stroke for a short, powerful one. Pressure stays equal everywhere in the fluid; only the force and the distance change, in opposite proportions.
The formula is exact for an ideal system, but real presses fall a little short of it.
Ideal incompressible fluid, friction ignored
This calculator assumes a perfectly incompressible fluid and a sealed system, so the full pressure reaches the large piston. It ignores friction in the seals and cylinders, the weight of the fluid, and any air trapped in the line — all of which reduce the real output force slightly. Keep both piston areas in the same unit so the A2 / A1 ratio is unitless; the output force then shares the unit of the input force, newtons.