Force from air pressure
A pneumatic cylinder turns compressed air into straight-line motion. The force it produces is simply the air pressure times the area the air pushes on. Because shop air is limited to about 90 to 120 psi (6 to 8 bar), the bore diameter is what sets the force, and choosing the right bore is the first step in designing any air-powered fixture, press or actuator.
The formulas
- Extend (push) force: F = p × π × D² / 4, where D is the bore.
- Retract (pull) force: F = p × π × (D² − d²) / 4, where d is the rod diameter.
- Real force: multiply by an efficiency of 85 to 95% to cover seal friction.
In metric units, 1 bar on 1 cm² gives 10 N, about 1 kgf. In US units, psi times square inches gives pounds-force directly.
Worked example
A 2-inch bore cylinder with a ⅝-inch rod runs at 90 psi. The piston area is π × 2² / 4 = 3.14 in², so the theoretical push is 283 lbf, and with 90% efficiency about 254 lbf (1,130 N). The rod takes up 0.31 in², leaving 2.83 in² for the return stroke: about 230 lbf of pull.
Sizing margins
- Moving loads: the cylinder must also accelerate the load and overcome guide friction. Engineers keep the load at 50 to 70% of the theoretical force, or lower for fast cycles.
- Clamping and pressing: the full force is available at the end of the stroke, so 80 to 90% is usually acceptable.
- Vertical lifting: remember that pressure in the supply line drops when many valves open at once; size for the lowest pressure you will actually see.
Air consumption
Each double-acting cycle fills the cylinder on both strokes. The volume per cycle is (piston area + annular area) × stroke. To express it as free air at atmospheric pressure, multiply by (gauge pressure + 14.7 psi) ÷ 14.7 psi, or (bar + 1.013) ÷ 1.013. Add the volume of the hoses for long lines. In the example, a 6-inch stroke at 10 cycles a minute consumes about 1.5 cfm (42 L/min) of free air, which helps size the compressor.
Choosing standard sizes
Common ISO bores are 32, 40, 50, 63, 80 and 100 mm; common US bores are 1½, 2, 2½, 3¼ and 4 inches. Pick the next size up from your calculation, and check that the rod is stiff enough for long strokes against buckling.