The force a pneumatic cylinder delivers is the first thing to calculate when choosing a bore. The formula is simple, but forgetting the retract-side area or the «load factor» leaves a cylinder too weak or too slow. This guide follows SMC's technical data (Best Pneumatics «Air Cylinders Model Selection», «Technical Data 1 and 3»).
Theoretical output = pressure × area
F (N) = P (MPa) × A (mm²) Extend A1 = π × D² ÷ 4 Retract A2 = π × (D² − d²) ÷ 4 (D bore, d rod diameter) ø50 / rod 20, 0.5 MPa: extend 1963 mm² × 0.5 = 982 N (100 kgf) retract 1649 mm² × 0.5 = 825 N (84 kgf)
SMC calls the force from pressure times area, assuming no resistance inside the cylinder, the «theoretical output». With MPa and mm² the result is directly in newtons (1 MPa = 1 N/mm²). Divide by 9.806 65 for kgf.
| Pressure | Extend N (kgf) | Retract N (kgf) |
|---|---|---|
| 0.3 MPa | 589 (60.1) | 495 (50.5) |
| 0.4 MPa | 785 (80.1) | 660 (67.3) |
| 0.5 MPa | 982 (100.1) | 825 (84.1) |
| 0.6 MPa | 1178 (120.1) | 990 (100.9) |
The table is for ø50 with a 20 mm rod. Force is proportional to pressure: if the supply drops from 0.5 to 0.4 MPa, force drops by 20 %.
Load factor — why you do not use the full output
A real cylinder has seal and bearing friction, and while moving, pressure left on the exhaust side pushes back. SMC notes these forces vary with size, pressure and speed, recommends always selecting a cylinder with margin, and expresses that margin as a «load factor η».
Required force F = η × A × P → area needed A = F ÷ (η × P)
| Use (SMC) | Load factor η |
|---|---|
| Static — clamping, low-speed press fitting | 0.7 or less |
| Dynamic — moving the load vertically or horizontally | 0.5 or less |
| Dynamic — horizontal movement on a guide | 1 or less |
For particularly fast motion, reduce the load factor further (SMC's graphs go down to 0.4, 0.3, 0.2); the spare force makes speed easier to reach. SMC also says the regulator is generally set to 85 % of the supply pressure.
Choosing a bore — SMC's three examples
SMC's procedure is ① choose the load factor for the use, ② choose the operating pressure, ③ read the bore off a graph from the force needed (a pressing force or a mass to move). Solved with the formula instead of the graph, all three examples land on SMC's bore.
| Example | Conditions | Area needed | Bore |
|---|---|---|---|
| 1 | Press 1000 N statically, η 0.7, 0.5 MPa, extend | 1000 ÷ (0.7 × 0.5) = 2857 mm² (ø60.3 or more) | ø63 |
| 2 | Move 30 kg horizontally on a guide, η 1, 0.4 MPa, retract | 294 N ÷ 0.4 = 735 mm² | ø40 (rod 14, retract 1103 mm²) |
| 3 | Pull 100 kg vertically upward, η 0.5, 0.5 MPa, retract | 981 N ÷ 0.25 = 3923 mm² | ø80 (rod 25, retract 4536 mm²) |
Examples 2 and 3 use the retract side: when the load moves both ways the smaller retract area governs, and example 3 lifts by pulling. If the pressure in example 3 dropped to 0.4 MPa, the area needed would be 4903 mm², too much for ø80 (4536 mm² retract), and you would need ø100 — so enter the lower pressure.
Reading SMC's theoretical output table
SMC's «Theoretical Output Table» (Data 3) gives area and output at 0.2–1.0 MPa for each bore and rod. Areas are rounded to three significant figures before multiplying by pressure, and outputs are rounded to three figures again, so the last digit can differ from the calculator. Rod diameter varies by series even for the same bore (ø40 has rows for 14 and 16 mm rods), so use your cylinder's catalogue value.
| Bore / rod | Extend mm² | Retract mm² | 0.5 MPa extend N | 0.5 MPa retract N |
|---|---|---|---|---|
| ø32 / 12 | 804 | 691 | 402 | 346 |
| ø40 / 14 | 1,260 | 1,100 | 630 | 550 |
| ø50 / 20 | 1,960 | 1,650 | 980 | 825 |
| ø63 / 20 | 3,120 | 2,800 | 1,560 | 1,400 |
| ø80 / 25 | 5,030 | 4,540 | 2,520 | 2,270 |
| ø100 / 30 | 7,850 | 7,150 | 3,930 | 3,580 |
What the calculation leaves out
- Speed and impact: theoretical output is a static force. Stopping the load at the end of stroke is a kinetic energy question for the cushion (the catalogue's allowable kinetic energy).
- Side load: let a guide, not the cylinder, take forces across the rod. SMC's example 2 uses load factor 1 precisely because the load runs on a guide.
- Air consumption and piping: fast motion needs valves, tubing and supply flow to match.
In PortDock
- «Pneumatic Cylinder Force Calculator» web tool: bore, rod and pressure (MPa, bar, kgf/cm², psi) → extend and retract theoretical output and force × load factor; pick a bore from SMC's table for a force or mass.
- «Pressure Unit Converter» web tool: convert regulator and gauge readings (bar, kgf/cm², psi) to MPa.
- Serial Plotter and Modbus Master: log a pressure sensor (4–20 mA → analog input → Modbus) to see how far the supply pressure drops while cylinders move.
Published 2026-10-24