Case 1
- Input force F₁
- 100N
- Small piston area A₁
- 5cm²
- Large piston area A₂
- 50cm²
1,000.00N
Open with these valuesPascal's Principle Calculator
1,000.00N
Result: 1,000.00 NThe same pressure acts on both pistons, so the force grows with the area ratio: F₂ = F₁ × A₂ ÷ A₁. A piston ten times larger gives ten times the force. Enter areas, not diameters — with diameters the ratio would be squared and the answer far too large.
The numbers at a glance
Held fixed: Input force F₁ 100.00 N, Small piston area A₁ 5.0000 cm².
| Large piston area A₂ (cm²) | Result (N) |
|---|---|
| 20.0000 | 400.00 |
| 40.0000 | 800.00 |
| 50.0000Your value | 1,000.00 |
| 60.0000 | 1,200.00 |
| 80.0000 | 1,600.00 |
| 100.0000 | 2,000.00 |
Worked examples
Case 2
- Input force F₁
- 50N
- Small piston area A₁
- 2cm²
- Large piston area A₂
- 8cm²
200.00N
Open with these valuesCase 3
- Input force F₁
- 200N
- Small piston area A₁
- 10cm²
- Large piston area A₂
- 25cm²
500.00N
Open with these valuesHow it's calculated
F₂ = F₁ × A₂ ÷ A₁
- StepEnter the force pushing on the small piston.
- StepEnter both piston areas in the same unit — the ratio cancels it out.
- ResultRead the force at the large piston, in the unit of the input force.
Reference table
| F₁, A₁, A₂ | Area ratio | F₂ (N) |
|---|---|---|
| 100, 5, 5 | one to one | 100 |
| 200, 10, 25 | two and a half to one | 500 |
| 50, 2, 8 | four to one | 200 |
| 12.5, 1.25, 6.25 | five to one | 62.5 |
| 100, 5, 50 | ten to one | 1000 |
Questions
How do I calculate the output force?
Multiply the input force by the ratio of the piston areas: F₂ = F₁ × A₂ ÷ A₁. A 100 N force on a 5 cm² piston against a 50 cm² piston gives 1000 N. Keep both areas in the same unit so the ratio stays unitless.
What is Pascal's principle?
Pressure applied to a confined, incompressible fluid is transmitted equally and undiminished in every direction. In a hydraulic press the same pressure therefore acts on both pistons, and the larger one produces a proportionally larger force.
Why does a hydraulic press multiply force?
Because pressure is force divided by area and is identical on both pistons. The output force scales with the area ratio A₂ ÷ A₁, so a piston ten times larger produces ten times the force.
Does a hydraulic press create energy?
No — the large piston gains force but loses distance by the same ratio. To lift it by 1 cm at an area ratio of ten, the small piston has to travel 10 cm. You trade a long, easy stroke for a short, powerful one.
Do I enter areas or diameters?
Areas. If you only know the piston diameters, convert each one first with A = π × (d ÷ 2)². Entering diameters directly would understate the ratio, because area grows with the square of the diameter.
Sources and last check
Information, not professional advice.