Push force (extend)
-Pull force (retract)
-Free air per cycle
-Free air flow, with allowance
-All results
| Bore (cap side) area | - |
| Rod area | - |
| Annulus (rod side) area | - |
| Push force, theoretical | - |
| Push force, usable (with efficiency) | - |
| Pull force, theoretical | - |
| Pull force, usable (with efficiency) | - |
| Compression ratio (p + atmospheric) / atmospheric | - |
| Free air, extend stroke | - |
| Free air, retract stroke | - |
| Free air per cycle | - |
| Free air flow at the cycle rate (net) | - |
| Free air flow with allowance | - |
Method and formulas
Static force balance and an ideal gas volume ratio, so every figure can be checked by hand. Force is set by gauge pressure and piston area; air consumption is the swept volume converted to free air.
| Quantity | Formula |
|---|---|
| Bore area | Ac = π D² / 4 |
| Annulus area | Aa = π (D² − d²) / 4 |
| Push force | Fpush = η p Ac |
| Pull force | Fpull = η p Aa |
| Compression ratio | r = (p + patm) / patm, with patm = 1.01325 bar = 14.696 psi |
| Free air per stroke | Vext = Ac L r, Vret = Aa L r |
| Free air per cycle | Vcycle = Vext + Vret |
| Free air flow | Q = Vcycle n, with allowance Qs = k Q |
| Metric unit shortcut | F (N) = p (bar) × A (mm²) / 10 |
Pressure is gauge pressure. Temperature is assumed constant, tubing and valve volume is not included, and the cylinder is assumed to exhaust fully each stroke. 1 ft³ = 28.3168 L.
Worked example: 50 mm bore, 20 mm rod, 6 bar, 100 mm stroke, 30 cycles/min
Bore area = π × 50² / 4 = 1963.5 mm². Annulus area = π (50² − 20²) / 4 = 1649.3 mm². Theoretical push force = 0.6 N/mm² × 1963.5 = 1178 N, and with 85 % efficiency 1001 N. Pull force = 0.6 × 1649.3 = 990 N theoretical, 841 N usable. Compression ratio = (6 + 1.01325) / 1.01325 = 6.922. Free air per cycle = (1963.5 + 1649.3) mm² × 100 mm × 6.922 = 2.501 L. At 30 cycles/min the net flow is 75.0 L/min, and with a 1.25 allowance 93.8 L/min free air.
Questions
How do you calculate pneumatic cylinder force?
Force equals gauge pressure times piston area: F = p x A. On the extend stroke the air acts on the full bore area A = pi D^2 / 4. On the retract stroke it acts on the annulus, bore area minus rod area. With p in bar and A in mm^2, F (N) = p x A / 10. In US units F (lbf) = p (psi) x A (in^2). Multiply by an efficiency of roughly 0.8 to 0.9 for seal friction to get the usable force at the rod.
How much compressed air does a pneumatic cylinder use?
Each stroke fills the cylinder volume with air at working pressure. Expressed as free air (air at atmospheric pressure) the volume is the swept volume times the absolute pressure divided by atmospheric pressure: V_free = A x L x (p_gauge + p_atm) / p_atm. The extend stroke uses the bore area and the retract stroke uses the annulus area. One full cycle uses the sum of both. Multiply by cycles per minute for the free air flow in L/min or scfm.
What is the difference between free air and compressed air volume?
Free air is the volume the same mass of air would occupy at atmospheric pressure. Compressor ratings (L/min, m3/min, scfm, cfm) are normally given as free air delivered, so the cylinder consumption must be converted to free air before it is compared to a compressor. At 6 bar gauge the compression ratio is about 7, so each litre of cylinder volume consumes about 7 litres of free air.
Why add an allowance to the air consumption?
Real systems lose air in tubing volume, valves, fittings, exhaust, leaks and pressure drop, and they rarely run exactly at the calculated rate. Allowances of 20 to 50 percent over the cylinder swept volume are common when sizing a compressor. This calculator applies the allowance factor you enter to the calculated free air flow and shows both the net and the allowance values. The tubing and valve volume is not added automatically.
Why is the retract force lower than the extend force?
The rod occupies part of the piston area on the rod side. The annulus the air acts on is smaller by the rod area, so for the same pressure the pull force is lower in the ratio of the annulus area to the full bore area.
How fast will the cylinder move?
Pneumatic speed is not fixed by flow alone. Air is compressible, so the speed is set by the supply pressure, the load, the valve and tubing flow capacity, the exhaust restriction and any flow controls. Typical piston speeds are in the range of 0.1 to 1 m/s (4 to 40 in/s) for standard cylinders. This calculator does not predict speed; use manufacturer flow data and the valve flow coefficient for that.
What does this calculator not cover?
It covers static force and mean air consumption. It does not cover rod buckling, side loads, cushioning, acceleration, dynamic pressure loss, valve and tubing sizing, tank sizing, temperature effects or humidity. For a long stroke with a slender rod, check buckling (see the column buckling calculator). Verify critical designs.
Engineering aid for guidance. It covers static force and mean air consumption and does not cover rod buckling, side loads, cushioning, acceleration, dynamic pressure loss, valve and tubing sizing, temperature or humidity. Verify critical designs.