Pascal's Law Calculator (Hydraulic Press)
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
Pascal's law gives F2 = F1 × (A2 ÷ A1): a force of 100 N applied to a 0.001 m² piston, transmitted to a 0.05 m² piston, produces a force of 5,000 N — the hydraulic press multiplies the force by 50.
Explanation
Pascal's law states that pressure applied at one point of a confined incompressible fluid (like the oil in a hydraulic circuit) is transmitted fully and instantly in every direction, with no loss. This is the principle that lets a hydraulic press multiply a force: by applying a modest force on a small piston, the pressure created in the fluid is found unchanged on a larger piston, where it produces a much greater force, proportional to the ratio of the two piston areas. It's the same physical principle that lets a simple push on a car's brake pedal (small area, low force) generate a much greater braking force on the pads (large area), through the incompressible brake fluid in the circuit. This force gain isn't free, though: Pascal's law also implies that the small piston must travel a much greater distance than the large piston for the same volume of fluid displaced — the hydraulic press multiplies force but divides displacement in the same proportion, consistent with the conservation of energy (no machine creates energy out of nothing).
Example: a force of 100 N, from a 0.001 m² piston to a 0.05 m² piston
Inputs
Applied force: 100 N. Small piston area: 0.001 m². Large piston area: 0.05 m².
Calculation
Pressure = 100 ÷ 0.001 = 100,000 Pa. Force obtained = 100 × (0.05 ÷ 0.001) = 100 × 50 = 5,000 N.
Result
This hydraulic press multiplies the initial force by 50, taking it from 100 N to 5,000 N.
Frequently asked questions
Does a hydraulic press create extra energy?
No: if the force is multiplied by 50, the distance traveled by the large piston is 50 times smaller than that traveled by the small piston, for the same volume of fluid displaced. The work (force × distance) input and recovered stays equal on both sides — the hydraulic press converts a small force over a long distance into a large force over a short distance, without creating energy.
Why does the fluid need to be incompressible?
Because Pascal's law assumes pressure is transmitted instantly and without loss throughout the fluid. A compressible fluid (like air) would absorb part of the applied force by compressing itself, instead of transmitting it fully to the second piston — which is why hydraulic circuits use liquids (oil, water) rather than gases.
Does this principle apply to a car's hydraulic brakes?
Yes, exactly the same principle: the brake pedal applies a force to a small piston (the master cylinder), transmitted by the brake fluid to larger pistons at each wheel, which press the pads against the discs with a force far greater than the one exerted on the pedal.