Hydraulic Press Calculator
The output force of a hydraulic press or jack from the input force and the two piston sizes, with the system pressure, the mechanical advantage and how far each piston moves.
Pascal’s principle: pressure applied to a confined fluid is the same everywhere in it.
How the hydraulic press calculator works
Pascal’s principle: pressure applied to a confined fluid is the same everywhere in it. A small piston pressed with a small force makes a pressure F₁ ÷ A₁ that acts on the whole area of the large piston, so the output force scales with the ratio of the areas — the square of the ratio of diameters. Nothing is free: the small piston travels further in the same proportion.
Formula: F₂ = F₁ × (d₂ ÷ d₁)²; p = F₁ ÷ A₁; x₁ = x₂ × (d₂ ÷ d₁)²
Worked examples
| Inputs | Output force (N) | Note |
|---|---|---|
| 100 N on 20 mm, output on 200 mm | 10,000 | 10,000 N (×100) |
| A bottle jack: 300 N, 12 mm pump, 40 mm ram | 3,333.3 | 3,333 N — lifts 340 kg |
| Equal pistons | 50 | 50 N — no advantage |
FAQFrequently asked questions
Where does the extra force come from?
From the area ratio — pressure is the same on both pistons, and force is pressure times area. Energy is conserved because the small piston moves as many times further as the force is multiplied: work in equals work out.
Why do car jacks pump so many times?
A jack with a 100:1 area ratio lifts a tonne with a few hundred newtons, but the handle must push 100 mm of fluid for every 1 mm of lift — hence the pumping.
What pressure can the system take?
Typical hydraulic systems run at 7–35 MPa (70–350 bar); hoses, seals and cylinders are rated for it. The pressure row shows what the input force alone produces.
Does the fluid matter?
It must be effectively incompressible and must not leak past the seals; hydraulic oil also lubricates and resists corrosion. Air will not do — it compresses, which is why pneumatic systems behave differently.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Measurement Institute — Australia's measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.