Calculator
Provide input force and piston sizes. Choose diameters or areas. Optional efficiency applies to output force. Optional stroke estimates output travel from volume continuity.
Formula used
Pascal’s principle states that pressure in a confined fluid is transmitted equally in all directions.
- Pressure: P = F₁ / A₁
- Output force (ideal): F₂ = P · A₂ = F₁ · (A₂ / A₁)
- Mechanical advantage: MA = F₂ / F₁ = A₂ / A₁
- Stroke relation (optional): s₂ = s₁ · (A₁ / A₂) (volume continuity)
- Efficiency (optional): F₂,actual = F₂,ideal · η, where η is 0–1
How to use this calculator
- Select whether you will enter diameters or areas.
- Enter the input force applied to the small piston.
- Provide the small and large piston sizes in your chosen mode.
- Set an efficiency if you want a loss-adjusted force.
- Choose a pressure unit to display the transmitted pressure.
- Optionally enter an input stroke to estimate output travel.
- Press Calculate. Results appear above the form.
- Use Download CSV or Download PDF for reports.
Example data table
These sample values illustrate scaling with piston area ratio.
| Input force (N) | Small diameter (mm) | Large diameter (mm) | Efficiency (%) | Output force ideal (kN) | Output force with efficiency (kN) | Mechanical advantage |
|---|---|---|---|---|---|---|
| 250 | 20 | 120 | 100 | 9.000 | 9.000 | 36.0 |
| 500 | 25 | 150 | 90 | 18.000 | 16.200 | 36.0 |
| 1000 | 30 | 200 | 85 | 44.444 | 37.778 | 44.4 |
Hydraulic press force guide
1) Principle behind force multiplication
A hydraulic press works because pressure applied to a confined fluid transmits uniformly through the system. When the small piston creates pressure, the large piston experiences the same pressure over a larger area. The result is a higher output force, limited in practice by friction, seal drag, and fluid losses.
2) Key relationship between area ratio and force
The ideal force gain equals the area ratio: F₂/F₁ = A₂/A₁. For circular pistons, area scales with diameter squared, so a 6× diameter increase yields about 36× force gain. This calculator accepts diameters or areas to capture that same ratio directly.
3) Pressure output and unit handling
The calculator reports transmitted pressure using P = F₁/A₁. Pressure is shown in Pa, kPa, MPa, bar, or psi for quick comparison with pump ratings and hose limits. Consistent units matter: small changes in piston size can shift pressure significantly.
4) Efficiency and real‑world output
Real presses rarely achieve ideal output because mechanical and hydraulic losses convert some input energy to heat. Enter an efficiency value to estimate practical force. For example, 90% efficiency reduces a 20 kN ideal output to 18 kN, improving realism for shop planning.
5) Stroke trade‑off and volume continuity
Force multiplication comes with reduced travel. If the input piston moves a stroke s₁, the output stroke is s₂ = s₁·A₁/A₂. A high force ratio means the large piston moves less for the same input stroke, affecting cycle time and tooling setup.
6) Interpreting mechanical advantage
Mechanical advantage (MA) summarizes the press amplification in a single number. Use MA to compare designs: higher MA increases output force but demands higher input stroke and careful alignment. When efficiency is included, MA reflects the usable force gain in the workshop.
7) Design checks and safety considerations
Always compare calculated pressure with component limits such as cylinder ratings, hose burst pressure, and valve settings. Add margins for dynamic loading, imperfect lubrication, and temperature changes. If operating near limits, consult manufacturer data and applicable safety standards before final use.
8) Practical workflow for engineers and technicians
Start with required output force, then choose a feasible pressure level and back‑solve suitable piston sizes. Use the example table to sanity‑check ratios, then refine efficiency to match equipment condition. Export CSV or PDF results to document assumptions for maintenance logs, lab reports, or design reviews.
FAQs
1) What does this calculator compute?
It computes hydraulic pressure from the input force and small piston area, then estimates the output force on the large piston. It also reports mechanical advantage and an optional output stroke estimate.
2) Can I use diameters instead of areas?
Yes. Select “Use diameters” and enter both piston diameters. The calculator converts them to areas using circular geometry, then applies Pascal’s principle to obtain pressure and force.
3) What efficiency should I enter?
Use 100% for an ideal estimate. For real equipment, 80–95% is common depending on seals, fluid condition, and mechanical friction. If unsure, start at 90% and compare with measured performance.
4) Why is output stroke smaller than input stroke?
Fluid volume continuity means the displaced volume must match. A larger output piston area requires less travel to move the same fluid volume, so stroke decreases as force gain increases.
5) Does the calculator include pump flow rate?
No. It focuses on static pressure and force relationships. Flow rate affects speed and cycle time, not the ideal force ratio. Use the stroke estimate with flow data to evaluate motion time separately.
6) Which pressure unit should I choose?
Choose the unit that matches your datasheets. kPa and MPa are common in engineering, bar is frequent in hydraulics, and psi is typical in some industrial systems. The underlying calculation remains the same.
7) Are the results safe to apply directly?
Treat results as estimates. Verify component ratings, apply safety margins, and consider dynamic loads and friction. For critical lifting or forming operations, follow manufacturer guidance and local safety regulations.