Pneumatic Cylinder Force Calculator
Pneumatic cylinder theoretical output (extend and retract, N and kgf) from bore, rod and pressure, and the SMC bore for a required force and load factor.
Formulas
- Theoretical output F = P × A (N = MPa × mm²)
- Extend A1 = π × D² ÷ 4, retract A2 = π × (D² − d²) ÷ 4
- To deliver a force: F = η × A × P → A = F ÷ (η × P)
- 1 kgf = 9.806 65 N, 1 MPa = 10 bar ≈ 10.2 kgf/cm² ≈ 145 psi
Load factor η (SMC guideline)
| Use | Load factor |
|---|---|
| Static — clamping, low-speed press fitting | 0.7 or less |
| Dynamic — moving the load vertically or horizontally | 0.5 or less (lower to 0.4, 0.3, 0.2 for high speed) |
| Dynamic — horizontal movement on a guide | 1 or less |
The load factor is the margin for forces the theoretical output ignores, such as seal and bearing friction and back pressure on the exhaust side while moving. SMC also says to set the regulator to about 85 % of the supply pressure.
Double-acting cylinder theoretical output (SMC Data 3 table, ø20–ø100)
| Bore / rod (mm) | Extend area mm² | Retract area mm² | 0.5 MPa extend N | 0.5 MPa retract N | 0.7 MPa extend N |
|---|---|---|---|---|---|
| ø20 / 8 | 314 | 264 | 157 | 132 | 220 |
| ø25 / 10 | 491 | 412 | 246 | 206 | 344 |
| ø32 / 12 | 804 | 691 | 402 | 346 | 563 |
| ø40 / 14 | 1,260 | 1,100 | 630 | 550 | 882 |
| ø50 / 20 | 1,960 | 1,650 | 980 | 825 | 1,370 |
| ø63 / 20 | 3,120 | 2,800 | 1,560 | 1,400 | 2,180 |
| ø80 / 25 | 5,030 | 4,540 | 2,520 | 2,270 | 3,520 |
| ø100 / 30 | 7,850 | 7,150 | 3,930 | 3,580 | 5,500 |
Like SMC's table, areas are rounded to three significant figures before multiplying by pressure, and outputs are rounded to three figures. The calculator above uses unrounded areas, so the last digit may differ slightly.
SMC selection examples (checked by tests to give the same result)
- Example 1 — press with 1000 N statically, load factor 0.7, 0.5 MPa, extend: area needed 2857 mm² → ø63.
- Example 2 — move 30 kg horizontally on a guide, load factor 1, 0.4 MPa, using the weaker retract side → ø40.
- Example 3 — pull 100 kg vertically upward, load factor 0.5, 0.5 MPa, retract → ø80.
How to read it
- The retract side has less area by the rod's cross-section, so it pushes less. If the load moves both ways, size for the weaker retract side.
- Use the pressure actually at the cylinder. Allow for drops in supply pressure (several cylinders moving at once) and enter the lower value.
- Theoretical output is a static force. Speed, cushioning and impact energy are not in this calculation; check the catalogue's allowable kinetic energy separately.
FAQ
What is the cylinder force formula?
Theoretical output F (N) = pressure P (MPa) × piston area A (mm²). A ø50 cylinder at 0.5 MPa: 1963 mm² × 0.5 ≈ 982 N (about 100 kgf). For the retract side, subtract the rod area.
How many kg does a ø40 cylinder push at 0.5 MPa?
1257 mm² × 0.5 MPa ≈ 628 N, about 64 kgf on the extend side. For dynamic use, apply load factor 0.5: about 32 kgf.
Why multiply by a load factor?
Friction inside the cylinder and exhaust back pressure make the real force smaller than the theoretical output. SMC's guideline is 0.7 or less for static, 0.5 or less for dynamic, and 1 or less for horizontal movement on a guide.
What if my pressure is in bar, psi or kgf/cm²?
Change the «Operating pressure» unit above. 0.5 MPa = 5 bar ≈ 72.5 psi ≈ 5.1 kgf/cm².
To convert pressure units, use the Pressure Unit Converter. For how to pick a bore and load factor, see the guide Pneumatic cylinder force and load factor. For the compressed air it uses, see the Pneumatic Cylinder Air Consumption Calculator; for gripping with vacuum pads, the Vacuum Pad Lifting Force Calculator.
Basis
Formulas, load factors and selection examples are from SMC's «Best Pneumatics» technical data «Air Cylinders Model Selection» and «Technical Data 1: Bore Size Selection»; the table is «Technical Data 3: Theoretical Output Table» (PDF on SMC's official site). Tests check that this calculator reproduces those values and SMC's CLQ catalogue output table. 1 kgf = 9.806 65 N uses standard gravity from NIST SP 811. Rod diameters and maximum pressure differ by series — check your cylinder's catalogue.