Pneumatic Cylinder Force Calculator
Push and pull force, load ratio, recommended bore and air consumption.
Calculate the extend (push) and retract (pull) force of a double-acting pneumatic cylinder from bore, rod diameter and supply pressure, including seal friction losses.
- Live results
- Full step-by-step working
- PASS / FAIL checks
- Free PDF report
Results
Step-by-step calculation (6 steps)
- 1Piston areasFormulaA₁ = π·D²/4, A₂ = π·(D² − d²)/4SolutionA₁ = π × 50²/4, A₂ = π × (50² − 20²)/4ResultA₁ = 1963 mm², A₂ = 1649 mm²
- 2Theoretical forcesFormulaF = p·A (p in N/mm² = bar × 0.1)SolutionFext = 0.6 × 1963, Fret = 0.6 × 1649ResultFext,th = 1178 N, Fret,th = 989.6 N
- 3Effective forces (after friction)FormulaFeff = η·FSolutionFext = 0.9 × 1178, Fret = 0.9 × 989.6ResultFext = 1060 N, Fret = 890.6 N
- 4Load ratioFormulaLR = Fload / Ftheoretical ≤ 0.7SolutionLR = 600 / 1178ResultLR = 0.509 ≤ 0.7PASS
- 5Minimum bore for this loadFormulaDmin = √(4·F / (π·p·LR))SolutionDmin = √(4 × 600 / (π × 0.6 × 0.7))ResultDmin = 42.65 mm → standard bore 50 mm
- 6Free air consumptionFormulaV = (A₁ + A₂)·s·(p + 1.013)/1.013, Q = V·nSolutionV = (1963 + 1649) × 200 × (6 + 1.013)/1.013 × 10⁻⁶ResultV = 5.002 NL/cycle, Q = 50.02 NL/min
Engineering takeaways
- Size cylinders with a load ratio of 0.5 to 0.7 so the cylinder still moves at the required speed when the supply pressure drops.
- Add 20 to 30% to air consumption for tubing and dead volumes when sizing the compressor.
- Long strokes under side load need a guided cylinder or external guides. Check rod buckling for strokes over about 10 × rod diameter.
The PDF report contains every input, formula, substitution and check shown above, in LTM calculation-sheet format.
Worked Example
Enter the load to check the load ratio and get the minimum standard ISO bore for normal, fast or slow motion. The calculator also gives free air consumption per cycle and per minute for compressor sizing.
The calculator above opens with this example. Change any input to run your own case.
Inputs
| Bore diameter D | 50 mm |
|---|---|
| Rod diameter d | 20 mm |
| Supply pressure p (gauge) | 6 bar |
| Force efficiency η (seal friction) | 0.9 |
| Required load force (0 = skip check) | 600 N |
| Load acts during | Extend (push) |
| Load ratio limit | 0.7 normal motion |
| Stroke | 200 mm |
| Cycles per minute | 10 cpm |
Results
| Extend force | 1060 N |
|---|---|
| Retract force | 890.6 N |
| Recommended bore | 50 mm PASS |
| Air consumption | 50.02 NL/min |
Pneumatic Cylinder Formulas Used
Piston areas
- Dbore
- drod diameter
Cylinder force
- pgauge pressure (1 bar = 0.1 N/mm²)
- ηforce efficiency, 0.85 to 0.95
Load ratio
Air consumption
- sstroke
- ncycles per minute
Basis: ISO 15552 / ISO 6432 standard bores; load ratio sizing method. Results are for preliminary design and should be confirmed against supplier data and the governing standard.
Pneumatic Cylinder Calculator FAQ
How do I calculate pneumatic cylinder force?
Multiply pressure by piston area. At 6 bar (0.6 N/mm²) a 50 mm bore has 1963 mm² of area, giving 1178 N theoretical push force, or about 1060 N after 10% seal friction.
What load ratio should I use?
Keep the load at 50% of theoretical force for fast, dynamic motion, up to 70% for normal motion, and up to 85% for slow motion or clamping at the end of stroke. A lower ratio gives more consistent speed.
Why is retract force lower?
The rod takes up part of the piston area on the rod side, so the same pressure acts on a smaller area when retracting.
How much air does a cylinder use?
Each double stroke fills both chambers at working pressure. Convert to free air by multiplying by (p + 1.013)/1.013. Add 20 to 30% for tubing and valve dead volumes.
Which bore sizes are standard?
ISO 15552 bores are 32, 40, 50, 63, 80, 100, 125, 160, 200 and 250 mm. ISO 6432 mini cylinders cover 8 to 25 mm.
Related Calculators
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