Example data table
| # | Bore (mm) | Rod (mm) | Pressure (bar) | Direction | Cylinders | Efficiency | Safe force (N) |
|---|---|---|---|---|---|---|---|
| 1 | 20 | 8 | 5 | Extension | 1 | 85% | 107 |
| 2 | 20 | 8 | 5 | Retraction | 1 | 85% | 90 |
| 3 | 32 | 12 | 6 | Extension | 1 | 90% | 347 |
| 4 | 32 | 12 | 6 | Retraction | 1 | 90% | 299 |
| 5 | 40 | 14 | 6 | Extension | 1 | 90% | 543 |
| 6 | 50 | 20 | 7 | Extension | 2 | 88% | 1,935 |
| 7 | 50 | 20 | 7 | Retraction | 2 | 88% | 1,626 |
| 8 | 63 | 25 | 6 | Extension | 1 | 92% | 1,377 |
| 9 | 80 | 32 | 8 | Retraction | 1 | 90% | 2,432 |
| 10 | 100 | 32 | 7.5 | Extension | 1 | 92% | 4,335 |
1) Pressure basics and gauge versus absolute
Most pneumatic systems report gauge pressure (above atmosphere). Using gauge pressure matches common readings such as 6–8 bar or 90–120 psi. Absolute pressure would add about 1 bar (14.7 psi) and can overstate force. Enter the same pressure type you measure at the regulator.
2) Bore area and extension force
Extension force is based on the full bore area: A = πD²/4. A 50 mm bore has an area near 1,963 mm². At 6 bar, the ideal push force is about 1,178 N. If you need lbf, divide newtons by 4.448. Larger bores scale quickly because area grows with the square of diameter.
3) Retraction force and rod diameter
Retraction uses the annulus area where the rod occupies part of the piston face: A = π(D² − d²)/4. With a 50 mm bore and 20 mm rod, the effective retract area drops to about 1,649 mm², so retract force is lower at the same pressure. Rod diameter also affects stiffness and buckling capacity. This matters for clamps, lifts, and return strokes.
4) Multiple cylinders, efficiency, and friction
If cylinders share the same supply, total force is multiplied by the cylinder count. Real force is reduced by seal friction, side loading, port losses, and flow limits; an efficiency of 0.85–0.95 is common for planning. At higher speeds, pressure at the cylinder can sag below the regulator setting.
5) Unit conversions and sanity checks
Quick rules help verify results: 1 bar ≈ 100,000 Pa and 1 N ≈ 0.225 lbf. A practical shortcut is Force(N) ≈ Pressure(bar) × Area(mm²) / 10 (ideal, single cylinder). If your answer is far off, re-check diameter units (mm vs inches) and whether you selected extend or retract.
6) Safety factor and real-world load limits
Use a safety factor when sizing: 1.25–2.0 is typical depending on risk and variability. Account for gravity, payload inertia, misalignment, and tooling friction. Also verify maximum rated pressure for the cylinder body. For vertical lifting, consider holding strategy (check valves, mechanical locks) because air compressibility can allow drift even when force seems sufficient.
FAQs
1) Should I use gauge pressure or absolute pressure?
Use gauge pressure for most pneumatic sizing because regulators and gauges read above atmosphere. Only use absolute pressure if your data source is absolute and you adjust consistently across all calculations.
2) Why is retract force smaller than extend force?
On retract, the rod blocks part of the piston area. The effective area becomes π(D² − d²)/4, so the same pressure produces less force. A thicker rod reduces retract force further.
3) What efficiency value should I enter?
For clean, well-aligned cylinders, 0.90 is a practical starting point. Use 0.85 if side loads, fast cycling, or long hoses are expected. Measure actual force if the application is safety-critical.
4) How do I estimate force in pounds?
Calculate force in newtons, then convert using 1 N ≈ 0.22481 lbf (or lbf = N ÷ 4.448). This helps compare your result with datasheets that list force in pounds.
5) Does air flow affect the calculated force?
Yes. At higher speeds, pressure at the cylinder can drop due to valve flow limits, small tubing, or long lines. The static formula assumes the chosen pressure is present at the cylinder.
6) Why include a safety factor?
Loads vary, friction changes, and air compressibility adds uncertainty. A safety factor (often 1.25–2.0) helps ensure the cylinder can start motion reliably and still perform when conditions are not ideal.
Formula used
- Abore = πD² / 4
- Arod = πd² / 4
- Aannulus = Abore − Arod
- Ftheoretical = P × A × n
- Feffective = Ftheoretical × η
- Fsafe = Feffective ÷ SF
Use bore area for extension. Use annulus area for retraction. Results assume steady pressure at the cylinder port.
How to use this calculator
- Select a calculation mode that matches your goal.
- Choose acting type and the force direction.
- Enter bore size, and rod size for retraction.
- Enter supply pressure, efficiency, and safety factor.
- For sizing, enter the desired force and calculate.
- Download CSV or PDF to store your results.