About the Hydraulic Press Calculator
This hydraulic press calculator applies Pascal’s principle: pressure applied to a confined fluid is transmitted equally in every direction, so a small force on a small piston produces a large force on a big piston. Enter the force you apply and the size of each piston — as diameters or areas — and it returns the output force, the mechanical advantage, the fluid pressure inside the system and how far the large piston moves for a given stroke of the small one.
It is useful for physics homework on Pascal’s law, for sizing a workshop press, car lift, log splitter or hydraulic jack, and for understanding why the large piston moves so little. You can also work backwards: enter the load you need to lift and the calculator tells you how hard you must push.
The results are ideal values for an incompressible fluid with no friction or leakage and pistons at the same height. Real presses lose a few percent to seal friction, and the pressure figure should always be checked against the rated working pressure of the cylinder, hoses and pump.
How to use the hydraulic press calculator
- 1Choose whether to find the output force or the input force you need.
- 2Enter the force you apply or the load to be lifted, in newtons.
- 3Enter both piston sizes as diameters or areas.
- 4Optionally enter how far you push the small piston to see the large piston’s travel.
- 5Read the force, mechanical advantage and system pressure.
Formula and method
Pascal’s principle says the pressure in a confined, incompressible fluid is the same everywhere (ignoring height differences). Pressure is force divided by area, so F₁/A₁ = F₂/A₂ and the output force is the input force multiplied by the area ratio A₂/A₁ — the mechanical advantage. When pistons are given as diameters, each area is π × d² ÷ 4, so the advantage equals the square of the diameter ratio: doubling the large piston’s diameter quadruples the force.
Energy is conserved, so the force gain is paid for in distance. The fluid volume pushed out of the small cylinder (A₁ × s₁) equals the volume entering the large one (A₂ × s₂), so the large piston moves s₁ × A₁ / A₂. The pressure shown is the fluid pressure the cylinder, seals and hoses must withstand. All values are ideal: real systems lose some force to friction.
- F₁, F₂
- Force on the small (input) and large (output) piston
- A₁, A₂
- Piston areas
- P
- Fluid pressure (same throughout)
- d
- Piston diameter (A = π d² / 4)
- s₁, s₂
- Distance each piston travels
Worked examples
200 N on a 2 cm piston driving a 10 cm piston
The diameter ratio is 5, so the area ratio is 25. A 200 N push becomes 5,000 N — enough to hold about 510 kg. The fluid pressure is 200 N ÷ 3.1416 cm² ≈ 636.6 kPa, and a 10 cm stroke moves the big piston only 0.4 cm.
Force needed to lift 15,000 N with a 3 cm and 30 cm piston
A 10× diameter ratio gives a 100× area ratio, so lifting a 15,000 N load (about 1.5 tonnes) needs only 150 N on the small piston. The fluid pressure is 15,000 N ÷ 706.86 cm² ≈ 212 kPa.
Pistons given by area: 5 cm² and 250 cm²
The area ratio is 250 ÷ 5 = 50, so 100 N in gives 5,000 N out. The pressure is 100 N ÷ 0.0005 m² = 200,000 Pa, or 200 kPa (about 29 psi).
Frequently asked questions
What is Pascal’s law?+
Pascal’s law states that a pressure change applied to an enclosed incompressible fluid is transmitted undiminished to every part of the fluid and the walls of its container. That is why a hydraulic press multiplies force.
How do you calculate the force of a hydraulic press?+
Multiply the input force by the ratio of the piston areas: F₂ = F₁ × A₂/A₁. With circular pistons this is F₁ × (D₂/D₁)², so a piston 4 times wider gives 16 times the force.
Does a hydraulic press create energy?+
No. The force gain is matched by a loss in distance: the large piston moves A₁/A₂ as far as the small one, so work in equals work out in the ideal case, and friction makes the real output slightly smaller.
How do I convert tonnes of press force to newtons?+
A metric tonne-force is 1,000 kg × 9.80665 m/s² ≈ 9,807 N. A “20-ton” shop press rated in short tons is about 20 × 8,896 N ≈ 178,000 N.
What pressure does a hydraulic system run at?+
Pressure is the input force divided by the small piston’s area. Hand jacks and shop presses often reach tens of megapascals (several thousand psi), so every component must be rated above the calculated pressure.