The formula
Extension force equals pressure times the full bore area, where bore area is pi times bore diameter squared divided by four.
Retraction force equals pressure times the annulus area, which is the bore area minus the rod area. The rod occupies part of the piston face on that side, so there is less area for the fluid to act on.
In metric, force in newtons equals pressure in bar times area in square centimetres times 10. A 80mm bore at 160 bar gives 50.3 cm² times 160 times 10, which is about 80,400 N or 8.2 tonnes.
Cylinder force by bore and pressure
Extension force in pounds for common bores. Read down the bore column and across to your system pressure.
These are theoretical figures. Real output is lower by the friction of the seals and any back pressure on the return line, typically 5 to 10 percent on a well-maintained cylinder.
| Bore | Area (in²) | 1,000 psi | 2,000 psi | 3,000 psi |
|---|---|---|---|---|
| 1.5 in | 1.77 | 1,767 | 3,534 | 5,301 |
| 2 in | 3.14 | 3,142 | 6,283 | 9,425 |
| 2.5 in | 4.91 | 4,909 | 9,817 | 14,726 |
| 3 in | 7.07 | 7,069 | 14,137 | 21,206 |
| 3.5 in | 9.62 | 9,621 | 19,242 | 28,863 |
| 4 in | 12.57 | 12,566 | 25,133 | 37,699 |
| 5 in | 19.63 | 19,635 | 39,270 | 58,905 |
| 6 in | 28.27 | 28,274 | 56,549 | 84,823 |
| 8 in | 50.27 | 50,265 | 100,531 | 150,796 |
How to measure a cylinder
Four numbers identify a cylinder for replacement: bore, rod diameter, stroke and the pin-to-pin retracted length.
Bore is the internal diameter of the barrel, not the outside. Measure the rod with a caliper. Stroke is the difference between fully extended and fully retracted pin-to-pin length, and measuring both is more reliable than trusting a stamped figure.
Also note the port size and thread form, the mounting type at each end, and the pin diameters. A cylinder that matches on force but not on mounting is no use.
Pneumatic cylinders
The same formula applies, but air pressures are far lower so the forces are a fraction of hydraulic. A 2 inch bore at 90 psi gives 283 lb, against 6,283 lb at 2,000 psi hydraulic.
Air is compressible, so a pneumatic cylinder will not hold position accurately against a varying load and the practical output is further reduced by pressure drop through the valve and hose. Size on at least 25 percent more force than the load needs.
